Musings on the ultimatum game [Archive] - Giant in the Playground Forums

RS14

2010-03-10, 12:16 AM

The ultimatum game is a game often played in economic experiments in which two players interact to decide how to divide a sum of money that is given to them. The first player proposes how to divide the sum between the two players, and the second player can either accept or reject this proposal. If the second player rejects, neither player receives anything. If the second player accepts, the money is split according to the proposal. The game is played only once so that reciprocation is not an issue.
Read More. (http://en.wikipedia.org/wiki/Ultimatum_game)

It seems that more-than-fair (e.g. first player offers greater than 50% of stake) offers are never given. I don't quite get why not. Why don't 2nd players reject fair offers? Why don't 1st players expect the second to reject fair offers, and offer more?

Icewalker

2010-03-10, 01:09 AM

Good show of human greed. If the second player ever rejects an offer they are making the wrong choice.

The Extinguisher

2010-03-10, 01:13 AM

The "correct" choice is to offer them the minimum possible amount, because to reject it would be to choose nothing over something.

However, experimental results show that anything more then 20& is usually rejected, which could show that humans don't act entirely in self-interest.

SensFan

2010-03-10, 01:15 AM

Good show of human greed. If the second player ever rejects an offer they are making the wrong choice.
Exactly this.

The best offer that the first person can make is (assuming increments of 1%) a division of 99:1.
The best move for the second player is then to accept the offer.

RS14

2010-03-10, 01:21 AM

And the offering player recognizes that trivial values are rejected, and tends to offer non-trivial amounts.

What I don't get is why this effect stops at fair values. Why doesn't the accepting player require more than 50%? Why doesn't the offering player offer more than 50%, anticipating a very demanding opponent?

Is it just that we're aware, in some sense, of fairness, and are reluctant to perpetuate unfair behavior? Thus, the offering player, with the advantage, in some sense, will be unfair, while the accepting player, feeling disadvantaged, has that in an addition to some inherent resistance to unfairness?

Edit: Also, I'm really interested to see so many people advocating the purely rational strategy.

skywalker

2010-03-10, 01:27 AM

What I don't get is why this effect stops at fair values. Why doesn't the accepting player require more than 50%? Why doesn't the offering player offer more than 50%, anticipating a very demanding opponent?

Because the game is only played once. The accepting player can't afford to reject so as to "teach" the giver. They must take, or they receive nothing.

The giver, knowing this, is in position to gain almost everything.

Now, if one or both sides lacks all the information, it becomes much more interesting.

RS14

2010-03-10, 01:32 AM

Because the game is only played once. The accepting player can't afford to reject so as to "teach" the giver. They must take, or they receive nothing.

The same could be said even of blatantly unfair offers. The accepting player can't afford to reject so as to "teach" the giver, even if offered only a small fraction of the pot. But this isn't what happens in practice.

The Extinguisher

2010-03-10, 02:40 AM

The same could be said even of blatantly unfair offers. The accepting player can't afford to reject so as to "teach" the giver, even if offered only a small fraction of the pot. But this isn't what happens in practice.

This is exactly what's interesting about it (like the Dictator "game")
It kind of undermines what we know about human economics and all that fun stuff. Acting purely in self-interest, the second player would accept all non-zero offers. Not accepting all non-zero offers means the second player isn't acting purely in self-interest (or alternatively, that there is some self interest in rejecting an offer and getting nothing)

However, iterated ultimatum game seems like it would be an interesting experiment to try as wall.

Totally Guy

2010-03-10, 05:15 AM

KuReshtin

2010-03-10, 06:04 AM

I saw an awful game show exploiting a dumbed down Prisoner's Dilemma game.

"Golden Balls" - every week on this show there is a sum of money to win and two finalists with the opportunity to win it.

They each pick Share or Steal.

Share & Share = The money is divided equally.
Share & Steal = Stealer wins the money.
Steal & Steal = Neither win the money.

Essentially the game trivial as the solution is to Steal every time because what you do has no bearing on whether you win or not. And every week the stupid show has logical people screw themselves out of the prize.
I hate it.

If I was in the position of playing that game I'd point out how wrong the show is and tell the opponent I was going to steal. Then I'd explain that the only effect the other player would have was whether the show got to keep the money or not. Then maybe the other player would see that their futile choice may as well let someone win for a change.

Then I'd reveal my choice. Share. At least that way I know the show would lose.:smalltongue: The perfect manipulation.

Oh, yes, the show that has people trying to lie about what amounts their Golden Balls contain, so that they get to stay for another round.
Game starts with three killer balls, that knock down the winnings by 90% each in the final game. So if there's been a prize ball with an amount of £50.000 and they get a killer ball, the prize amount gets knocked down to £5.000, and if they get another killer ball, the prize is again reduced by 90% to £500. With this in mind, the plan would always be to eliminate as many killer balls as possible, right? not for these people that go on this show. They don't care about the killer balls, and only look for the amounts shown by the other competitors and what amounts they claim to have hidden.
For each round, another Killer ball is added as well, so there have been times when the contestants have had to make the decision about Stealing or Splitting £1.35 or something stupid like that, because they've brought a shedload of killer balls to the final table.

Like Glug said, it's a really stupid gameshow, but I find it strangely enchanting, and if I happen to run across it, I can't help but to watch it.

Arti3

2010-03-10, 07:03 AM

Meh. It's all just Game Theory.

Zeb The Troll

2010-03-10, 07:08 AM

Totally Guy

2010-03-10, 07:15 AM

Meh. It's all just Game Theory.

The key to winning is to know which game you are playing. Once you're familiar with a few games you can try to spot instances of them where they naturally occur.

potatocubed

2010-03-10, 07:20 AM

It kind of undermines what we know about human economics and all that fun stuff. Acting purely in self-interest, the second player would accept all non-zero offers. Not accepting all non-zero offers means the second player isn't acting purely in self-interest (or alternatively, that there is some self interest in rejecting an offer and getting nothing)

There's plenty of that. Pride, for example, or the satisfaction of seeing an ass walk away with nothing - and if you make the purely rational offer of 99/1 then you've firmly established yourself as an ass.

It is, as previously pointed out, all game theory.

Winterwind

2010-03-10, 07:21 AM

As others already explained, there is a fault in the claim that the optimal choice for the second player is to always accept a non-zero offer, because it is only concerned with monetary maximization. In fact, it's a balance of monetary gain and emotional gain - if the offering player makes a proposal so blatantly unfair that the money the second player would still get drops below the amount of money the second player would be willing to pay in order to give the offering player his or her comeuppance, declining the offer becomes the optimal choice for the second player.

Of course, where this limit lies depends on the vindictiveness of the second player. Which is essentially what this game is designed to measure.

skywalker

2010-03-10, 12:05 PM

If I were the Accepting player, I might be of a mind to punish an Offering player for being too greedy. Having said this, as an Offering player, I would be hesitant to be greedy in my offer, expecting the Accepting player to refuse anything horrendously unfair.

I seem to be missing something here. I see people saying that the Accepting player "can't afford" to reject an offer. Why? Because he'd get nothing? So what. I am not a jobless bum living in a box next to the liquor store. If you offer me $1 out of $100, why should I let you have $99? $1 doesn't even buy me coffee when I leave. I can absolutely afford not to have an extra $1 in my pocket just to get back at the Offering player for not being more reasonable.

You can afford it, but it's sub-optimal. That's the point. You get less. And the general consensus in the economics discipline (you're talking about an economic experiment and, in my case personally, to an econ major) is that "more is better." So $1 is a much better outcome than $0.

As others already explained, there is a fault in the claim that the optimal choice for the second player is to always accept a non-zero offer, because it is only concerned with monetary maximization. In fact, it's a balance of monetary gain and emotional gain - if the offering player makes a proposal so blatantly unfair that the money the second player would still get drops below the amount of money the second player would be willing to pay in order to give the offering player his or her comeuppance, declining the offer becomes the optimal choice for the second player.

The point is that emotional gain, in this case especially, is pretty meaningless. You can sit there saying "He screwed me" and take your $0, or you can accept that "he made the most optimal decision within the rules provided" and take your much, much better $1. I suppose you gain something emotionally from "screwing someone who's screwed you," but if emotional gain kills actual gain, then what have you? It's not a very interesting game because it gives no incentive (other than foolish pride) to act in different ways. The most interesting part of the game is that it has caused a sort of debate over whether monetary optimization is optimization, I guess.

SensFan

2010-03-10, 12:24 PM

As others have said, if you are acting logically, then you will always offer no more than 1$, and you will always accept any offer of at least 1$.

In my mind, the people who are saying that its a 'jerk' or 'ass' move to offer only 1$ are the same type of people who go on shows like Survivor and whine about how people who lie don't deserve to win the game.

Eurus

2010-03-10, 12:42 PM

It's only logical to offer a 99:1 split if you're certain that your opponent is going to act totally logically. If you don't think they will, you're better off offering more. Therefore, isn't it actually most beneficial for the recipient to act illogically, so the offerer doesn't have his best course of action cut and dried? If a horribly unfair offer is made, isn't rejecting it so that future offers (probably made by other people to other people, but based on general trends and past experiences) will be "fairer" actually altruistic, and not vindictive?

SensFan

2010-03-10, 12:50 PM

If I make a 99:1 offer, I'm telling the other person "You can take 1$ or you can take 0$."

I wouldn't ever expect a rational person to pass on 1$.

Tirian

2010-03-10, 12:56 PM

You can afford it, but it's sub-optimal. That's the point. You get less. And the general consensus in the economics discipline (you're talking about an economic experiment and, in my case personally, to an econ major) is that "more is better." So $1 is a much better outcome than $0.

As an econ major, I'm surprised at such a naive analysis. It's well known even in pure math and game theoretical circles that the utility function of money is non-linear; in layman's terms that $1 is essentially valueless. In exchange for not feeling like a complete tool, I lose so much money that I have to have one fewer topping on my next pizza? There's no question what my decision is, and if your economic model doesn't see the rationality in it then you need a more robust model.

Also, the rules say that reciprocation is not an issue, but that isn't precisely true. The experiment is over, but the offerer goes out into the world just as poor as I am but knowing that behaving with a shred of sympathy for the common human plight would have put some money in her pocket. With the other decision, she leaves weighed down by $99 and the ego of dominating someone else. Which of these people would I rather have in my neighborhood? Would you pay a dollar to make your neighbor less of a jerk?

2xMachina

2010-03-10, 01:04 PM

Basically, they're paying $1 to spite the other out of $99.

It not non-viable, but... not the best way to spend $1.

SensFan

2010-03-10, 01:06 PM

As an econ major, I'm surprised at such a naive analysis. It's well known even in pure math and game theoretical circles that the utility function of money is non-linear; in layman's terms that $1 is essentially valueless. In exchange for not feeling like a complete tool, I lose so much money that I have to have one fewer topping on my next pizza? There's no question what my decision is, and if your economic model doesn't see the rationality in it then you need a more robust model.

Also, the rules say that reciprocation is not an issue, but that isn't precisely true. The experiment is over, but the offerer goes out into the world just as poor as I am but knowing that behaving with a shred of sympathy for the common human plight would have put some money in her pocket. With the other decision, she leaves weighed down by $99 and the ego of dominating someone else. Which of these people would I rather have in my neighborhood? Would you pay a dollar to make your neighbor less of a jerk?
If I make an offer of 99:1 and you turn it down, then logically, you wouldn't have even accepted an offer of 0:100, since you appear to not want free money or you'd have taken the free dollar I offered.

Eurus

2010-03-10, 01:12 PM

If I make a 99:1 offer, I'm telling the other person "You can take 1$ or you can take 0$."

I wouldn't ever expect a rational person to pass on 1$.

I'm no logician, but I might expect it. I feel like it's a mistake to look at these things in a vacuum; there are so many other costs and benefits besides just the money. Like Tirian said, you could look at it as one person paying 1$ to punish another person for violating social norms (the norm in this case being to keep up at least some facade of "fairness"); a perfectly rational thing to do.

If you use that rationale, offering a 50:50 or 0:100 split, or even something like 60:40 or 75:25 (exact proportions depending on the person) would still be accepted even though 99:1 wouldn't. Or, in other words: you can't really say that it's perfectly rational to completely ignore the amount that the other person is getting, because that only looks at one dimension of value and cost.

Pyrian

2010-03-10, 01:12 PM

As others have said, if you are acting logically, then you will always offer no more than 1$, and you will always accept any offer of at least 1$.Those choices are only rational in an absolute void - if both actors never make any other decisions, nor suffer/enjoy any other consequences, whatsoever. This means that in the real world and involving actual people, it is not logical at all, and indeed deeply fallacious.

Abstractions have value. Fairness has value, and can (and indeed must) be assigned dollar amounts, sometimes. The value of $1 is IMO negligible compared to the value of fairness. Even at $49, I would probably balk; I care about fairness, even 2% of it, but I don't care about $49. $490,000, though - I'd take the cash. :smalltongue: Obviously, my valuation of fairness lies somewhere in between, and I'd be hard put to state exactly where.

Eurus

2010-03-10, 01:14 PM

Those choices are only rational in an absolute void - if both actors never make any other decisions, nor suffer/enjoy any other consequences, whatsoever. This means that in the real world and involving actual people, it is not logical at all, and indeed deeply fallacious.

Abstractions have value. Fairness has value, and can (and indeed must) be assigned dollar amounts, sometimes. The value of $1 is IMO negligible compared to the value of fairness. Even at $49, I would probably balk; I care about fairness, even 2% of it, but I don't care about $49. $490,000, though - I'd take the cash. :smalltongue: Obviously, my valuation of fairness lies somewhere in between, and I'd be hard put to state exactly where.

Good point. If it's a 99:1 split of 100$, I'd throw away the 1$. If, on the other hand, it's a split of one million dollars... Well, I'm probably willing to compromise my principles for a "measly" ten thousand dollars. :smallamused:

SensFan

2010-03-10, 01:15 PM

Those choices are only rational in an absolute void - if both actors never make any other decisions, nor suffer/enjoy any other consequences, whatsoever. This means that in the real world and involving actual people, it is not logical at all, and indeed deeply fallacious.

Abstractions have value. Fairness has value, and can (and indeed must) be assigned dollar amounts, sometimes. The value of $1 is IMO negligible compared to the value of fairness. Even at $49, I would probably balk; I care about fairness, even 2% of it, but I don't care about $49. $490,000, though - I'd take the cash. :smalltongue: Obviously, my valuation of fairness lies somewhere in between, and I'd be hard put to state exactly where.
There is literally no sane/logical/rational reason to decline a 99:1 offer and accept a 0:100 offer.

Either you accept free money or you don't. The amount of free money has no bearing on the fact you are throwing away free money.

Winterwind

2010-03-10, 01:16 PM

The point is that emotional gain, in this case especially, is pretty meaningless. You can sit there saying "He screwed me" and take your $0, or you can accept that "he made the most optimal decision within the rules provided" and take your much, much better $1. I suppose you gain something emotionally from "screwing someone who's screwed you," but if emotional gain kills actual gain, then what have you? It's not a very interesting game because it gives no incentive (other than foolish pride) to act in different ways. The most interesting part of the game is that it has caused a sort of debate over whether monetary optimization is optimization, I guess.How is emotional gain meaningless?

Look, let's have an example. You go to the cinema and watch a movie for $10. After that, you have $10 less, and that's not an investment that you might hope will come back with interest - you have genuinely lost $10. Was that illogical? No - you got something you deemed was worth (at least) these $10 in return (seeing the movie). That's how trade works - you give A, you get B. If A is money, and B is not, you always end up with less money than before, but if you think the trade is worth it, it's merely logical to accept it nonetheless.

I feel you are making a mistake by attributing an objective value to money. Money is only valuable because we can turn it in for other things that are subjectively worthwhile for us, and hence its own worth is merely subjective. If there was nothing the money could be spent for, gathering as much of it as possible would be perfectly futile. If the second player would be willing to pay more money than he might receive for the satisfaction of teaching that other person a lesson, they make a good trade by declining the trade. They get what they want. You postulate monetary gain is somehow more "real", so to speak; I ask, how? Money is intrinsically worthless; it's using it to get what we want that defines its worth in the first place, so optimizing to get more money while at the same time screwing oneself out of getting what one wants is directly contrary to one's interests.

There is no difference between emotional gain and actual gain. It's all just a matter of what you want to have.

As others have said, if you are acting logically, then you will always offer no more than 1$, and you will always accept any offer of at least 1$.I contest this. Logic and prioritization are two completely different things that have nothing to do with each other. Logic doesn't tell you what is the most important to you, it only tells you how to act depending on what is the most important to you. If you will always offer no more than $1, and you will always accept any offer of at least $1, you are actually acting illogically if other aspects - like educating the other person for altruistic reasons or satisfaction for your pride - outweigh the monetary gain in your mind. Only if the monetary gain, no matter how small, outweighs these others aspects for you, would acting as you propose be the logical choice. Which is a matter of taste.

In my mind, the people who are saying that its a 'jerk' or 'ass' move to offer only 1$ are the same type of people who go on shows like Survivor and whine about how people who lie don't deserve to win the game.
I wouldn't ever expect a rational person to pass on 1$.
There is literally no sane/logical/rational reason to decline a 99:1 offer and accept a 0:100 offer.Yeah, good job insulting the people you are discussing with. :smallannoyed:

Eurus

2010-03-10, 01:19 PM

There is literally no sane/logical/rational reason to decline a 99:1 offer and accept a 0:100 offer.

Either you accept free money or you don't. The amount of free money has no bearing on the fact you are throwing away free money.

Well, I disagree, and have explained my reasons for disagreeing (as have others). And, as cheesy as it sounds, I suppose that just means that we have different ideas about what has value. :smalltongue:

Strawberries

2010-03-10, 01:20 PM

(Disclaimer: I speak without much knowledge of economic theories, but out of personal observation /disclaimer)

From a purely rational point of view, disregarding all other issues? Yes, 1$ is better than 0$.
From a human point of view, would I accept an offer of 99:1? Hell, no. No way. And I consider myself a rational person. I'd consider it 1$ well spent to teach another person the concept of solidarity between human beings.
And the mere knowledge that I would never accept such an offer would lead me not to make unfair offers. I'd venture a guess that this is the reason why unfair offers are rare.

Edit, wow, ninjaed so much. That's what I get for looking up translations in the dictionary :smalltongue:.

SensFan

2010-03-10, 01:22 PM

Yeah, good job insulting the people you are discussing with. :smallannoyed:
First of all, those posts came after someone (or perhaps multiple people) said that anyone who offers a 99:1 split is 'an ass' and not someone they would want to know in real life.
Secondly, I did not insult anyone. There is nothing inherently wrong with irrational arguments or illogical thinking. But if someone is acting irrationally or illogically, then it is impossible to predict what they will do. It comes down to this:
*If the person I am dealing with is acting logically/raitionally, then they will accept free money, so I should offer 99:1
*If the person I am dealing with is not acting logically/rationally, then there is no way to predict if they will accept or refuse, so any offer is just as likely to be accepted as any other, so I should offer 99:1

Eurus

2010-03-10, 01:24 PM

*If the person I am dealing with is not acting logically/rationally, then there is no way to predict if they will accept or refuse, so any offer is just as likely to be accepted as any other, so I should offer 99:1

Now that's silly. It may not be as iron-clad as game theory or physics, but basic psychology and sociology do have some predictive ability, particularly for understanding irrational people like myself.

Pyrian

2010-03-10, 01:25 PM

There is literally no sane/logical/rational reason to decline a 99:1 offer and accept a 0:100 offer.You have been given several. You have failed to refute any of them. Your arguement by tautology does not interest me. You are not going to convince anybody of anything by mere repeated assertions of arguments that have already been shown to be false.

Either you accept free money or you don't.Every single part of this is wrong, which is interesting given how short it is. The money isn't free, on any grounds (money doesn't tend to be, even if you literally print more of it you just devalue it as a whole). The decision tree is not tied to such a simplistic view of it - others are affected, and by affecting others, we ultimately affect both society as a whole and ourselves.

The amount of free money has no bearing on the fact you are throwing away free money.The money is not free, and is not thrown away. Those concepts don't work, economically; money is a placeholder, and any action with it affects either its supply as a whole (and therefore value) or somebody else's supply of it.

EDIT:
But if someone is acting irrationally or illogically, then it is impossible to predict what they will do.That is, of course, nonsense, but it brings up an interesting side-issue: Most people think they're acting logically, but aren't, most of the time. (Indeed, right now you think your argument is rational when it is merely narrow and short-sighted.)

SensFan

2010-03-10, 01:26 PM

Now that's silly. It may not be as iron-clad as game theory or physics, but basic psychology and sociology do have some predictive ability, particularly for understanding irrational people like myself.
With an offer of 99:1, I am offering you free money. If you are willing to throw away a free 1$, how should I know that you aren't willing to throw away a free 99$?

Eurus

2010-03-10, 01:29 PM

With an offer of 99:1, I am offering you free money. If you are willing to throw away a free 1$, how should I know that you aren't willing to throw away a free 99$?

By looking at general trends? "Irrational" is not the same as "random." Most people are irrational -- but most people are irrational in similar ways. It's not very difficult to get a feel for the mindset of most people, and figure out what offer will, most likely, satisfy whoever you're offering it to enough for them to not throw it away.

Strawberries

2010-03-10, 01:30 PM

With an offer of 99:1, I am offering you free money. If you are willing to throw away a free 1$, how should I know that you aren't willing to throw away a free 99$?

SesFan, people (including me) have explained that they wouldn't consider it a "thrown away" 1$. Money is used to purchase goods and services, is it not? As explained, I'd use the 1$ to "purchase" the teaching of basic solidarity to a fellow human being. A 1$ well spent, and that's all there is to it.

Pyrian

2010-03-10, 01:31 PM

He seems to take it as an absolute given that "rational" decisions are based entirely on what affects solely yourself in the immediate term.

Eurus

2010-03-10, 01:33 PM

SesFan, people (including me) have explained that they wouldn't consider it a "thrown away" 1$. Money is used to purchase goods and services, is it not? As explained, I'd use the 1$ to "purchase" the teaching of basic solidarity to a fellow human being. A 1$ well spent, and that's all there is to it.

Or if you're less charitable, you could say that it's used to "purchase" a temporary sense of superiority and self-satisfaction by punishing someone else. Depending on how high or low your faith in humanity is. :smallbiggrin:

Winterwind

2010-03-10, 01:35 PM

First of all, those posts came after someone (or perhaps multiple people) said that anyone who offers a 99:1 split is 'an ass' and not someone they would want to know in real life.
Secondly, I did not insult anyone. There is nothing inherently wrong with irrational arguments or illogical thinking. But if someone is acting irrationally or illogically, then it is impossible to predict what they will do. It comes down to this:Yeah, because stating people who do not follow your line of thought are whiners or are acting insanely is not offensive in the least. Sure.

*If the person I am dealing with is acting logically/raitionally, then they will accept free money, so I should offer 99:1Which I think is completely false, for reasons I outlined in my previous post (as well as many, many other people, in many, many other posts), reasons you have not addressed yet.

To summarize them again (at least, the arguments I presented myself): You are postulating that free money is somehow more valuable than the things one might get in return for declining the offer, which may be less tangible, but no less real. You'd better back that postulate up, because to me, it sounds rather absurd. If you don't do that, your entire argument falls apart, as it is decidedly more logical to decline the money if that nets you what you actually want, than accepting the money and ending up without the thing you want.

Oh, and another thing: Even if, for some unfathomable reason, we assume you are right, and maximizing monetary gain with no other considerations would be the logical thing to do, as the statements of many people in this thread prove, your strategy of offering the minimum possible amount would actually result in you losing out on money, as people would decline that offer. As, if getting as much money as possible is your one and only goal, that's clearly a sub-par strategy, wouldn't it be more logical to work out the exact threshold where the other person's greed outweighs their wish to get back on you, and offer that instead (impossible to do exactly, of course, but you could, for instance, question a large number of people to get a reasonable average value. And refine that, if you have additional information on the other player in question).

Strawberries

2010-03-10, 01:36 PM

Or if you're less charitable, you could say that it's used to "purchase" a temporary sense of superiority and self-satisfaction by punishing someone else. Depending on how high or low your faith in humanity is. :smallbiggrin:

That too. :smallbiggrin: I like to think I'm a good person, though, so I'll go with my first rationale :smallwink:.

Tirian

2010-03-10, 01:39 PM

If I make an offer of 99:1 and you turn it down, then logically, you wouldn't have even accepted an offer of 0:100, since you appear to not want free money or you'd have taken the free dollar I offered.

We might be talking about two different games here.

Scenario 1:
Overseer (privately to SensFan): Here is $100 for you to keep as long as you get Tirian to agree to take some of it.
SensFan: Here's a dollar for you, Tirian.
Tirian: Yippee! Free dollar!!!1!

Scenario 2:
Overseer (publicly to both SensFan and Tirian): Here is $100 for the two of you to keep as long as SensFan and Tirian can agree on the distribution, but SensFan has to make the deal and has only gets to make one offer.
SensFan: You're powerless, Tirian. Take $1 or nothing.
Tirian: From my perspective, you just took $49 away from me. It turns out I have the power to do that to you too. I make decisions that waste a dollar every waking hour of my life, and passing on this deal is just one more of them.

Scenario 2b:
SensFan: I am so deliriously fair that I insist that we share the money equally.
Tirian: Oh rainbows and puppy dogs and sunshine, I accept!

Scenario 2c:
SensFan: I offer you $20 and keep $80 for myself. It isn't fair, but you can have dinner at a cheap restaurant with a friend with that money, or not.
Tirian: I accept. Grrr.

Now, from the tone of that article, the fact is that scenario 2 is the accurate assessment of the experiment, and that specifically scenario 2c is close to the break-even point where the 99-1 split is not. So, if it surprises you, then you should try to figure out why it shouldn't.

SensFan

2010-03-10, 01:41 PM

Wow. I never thought I'd be in the minority for accepting free money when its offered to me, for absolutely nothing in return.

There is absolutely nothing to be gained from turning down the offer. You aren't snobbing the other person at all. As I've said, if I made an offer of 99:1 and it was refused, I wouldn't feel slighted at all, other than annoyed that luck paired me with someone who has no interest in economic gain in an economic game. By declining the offer, you're not teaching anyone anything. You're saying "I don't want to get free money unless I get more free money than you", which is a concept I don;t understand.

Edit:
I'm aware that it is scenario 2, and that both people are aware of the premise of the game.

Telonius

2010-03-10, 01:41 PM

Seems pretty simple to me. A person who offers much less than 50% is a jerk. At least some people would get more satisfaction out of punishing a jerk than they would get by doing anything with the money. This is not irrational; treating money as anything other than a means to an end is irrational.

As to why they don't offer more than 50%: people assume that most often the other guy will be a "dove" or a "retaliator," not a "hawk." Basically, absent any other information to the contrary, the offering person assumes the other person will have a baseline belief of fair play. The chance that somebody will turn down a fair split is a lot lower than somebody getting pleasure by punishing somebody who's proved themselves to be a jerk. Yeah, offering them more than 50% would almost automatically result in acceptance, but then you wouldn't have gotten as much for yourself. So 50% would be the floor offer.

Eurus

2010-03-10, 01:45 PM

SensFan

2010-03-10, 01:45 PM

Tirian

2010-03-10, 01:50 PM

SensFan

2010-03-10, 01:53 PM

Heh.

Heh heh heh.

So after being thoroughly disagreed with from every corner, you'd rather start reporting people for insulting you when they're referring to a performer in a hypothetical experiment.

Let me ask you this, would YOU accept a dollar from me in this experiment? Would you really?
First of all, I didn't report anything or anyone.
Secondly, he didn't talk about a hypothetical, he said that any "person who offers much less than 50% is a jerk." I would offer much less than 50%, and so he is saying I'm a jerk. Besides, I didn't bring up the personal attacks thing, I can accused of insulting people for calling an argument irrational.
Thirdly, of course I would. I will always take free money.

Eurus

2010-03-10, 01:53 PM

As I've said, if I made an offer of 99:1 and it was refused, I wouldn't feel slighted at all, other than annoyed that luck paired me with someone who has no interest in economic gain in an economic game.

Also, this may be the reason for the disagreements here. You're looking at it as a purely economic game, but I'm looking at it as more of a psychological one, as it sounds like many other people are doing. The problem is, the actual results of the games that have been performed seem to support the latter more than the former; you don't see all that many 99:1 splits in practice.

Douglas

2010-03-10, 01:55 PM

You're saying "I don't want to get free money unless I get more free money than you", which is a concept I don;t understand.
No, the person refusing is saying either "I value punishing a jackass, which is what I perceive you as because you made such a blatantly unfair division proposal, more than the paltry amount you offered me" or "I value supporting fairness, which would in this case be a 50-50 split, more than the paltry amount you offered me." These values are very widespread in humanity due to a combination of cultural upbringing (cultures with such values are usually better off as a whole) and an expectation of reciprocity.

The game as stated eliminates any possibility of future reciprocity, but it is obviously an artificial elimination, the cultural influence is still there, and humans have a strong tendency to adhere to their values even if all logical reasons for those values are not currently in play. It's much simpler for a person to value fairness than for the same person to value fairness if factors X, Y, and Z are present, and the sheer number of values, reasons for them, situational factors, and so forth is prohibitively high for a typical human being to always keep them all in mind rather than simplifying it down to "I have these values, the reasons don't matter too much" in short term decision making.

Winterwind

2010-03-10, 01:59 PM

See? Now that's a personal insult. Calling me a jerk for absolutely no good reason, just because I am looking to maximise my chances of economic profit in an economic game. Just like people who claim its a 'jerk' move to lie in a game that's based on the premise of betrayal.Replace "jerk" with "unfair" in Telonius' post, and the point still stands. People are willing to spend money in order to punish unfair behaviour, so your point that:

Wow. I never thought I'd be in the minority for accepting free money when its offered to me, for absolutely nothing in return.is evidently wrong, because they do get something in return: The satisfaction to have punished the other player for an unfair proposal. You are in a minority, but it's not the minority of not accepting free money; it's the minority of putting more preference on an amount of money, however small, than moral satisfaction. Which is perfectly fine, but it has about as much to do with logic and reason as whether one is willing to spend money for tickets to a football game - it's a matter of personal taste, nothing more.

Also, you speak of "maximizing your chances of economic profit", but as this thread shows, you are actually very effectively minimizing them.

You're saying "I don't want to get free money unless I get more free money than you", which is a concept I don;t understand.Nobody in this thread has proposed anything even remotely similar to that, except for you. Most people are talking about wanting fair proposals, which is a 50:50 split, and would probably accept a 40:60 or 30:70 split in their disfavour, too. It's outrageously unfair splits like 1:99 which people are no longer willing to accept, as these splits have dropped below the threshold where the possible gain is lower than the amount of money people are willing to pay to get their moral satisfaction.

Zen Monkey

2010-03-10, 02:17 PM

Terminology gets to be a problem here. When money is at stake, for most people, the impact becomes more significant. We think of 'games' as something trivial, a fairly meaningless contest or set of rules with which to play. If my playing of this game involves bettering myself at the expense of another, improving my well-being by taking away from theirs, then my actions now have a moral weight greater than those held by a match of checkers.

By hoarding the money for yourself (again, assuming neither participant is wealthy), you are putting more value on your needs than the needs of others. The 50/50 offer is the only real moral choice, the only one that respects the other human being as being of equal value to yourself. Shorting the other person when neither of you have really earned any portion of the wealth, is essentially that player saying "I am more valuable than this other person" which is a statement that will be supported by very few schools of ethics.

If the two contestants are millionaires trying to split a dollar, then it largely is just a game. Then again, if you beat a child enough times at cards/checkers/etc it's still an ethically sound move to lose a game once in a while. The loss means nothing to you, and the win means a lot to them. Even when the game is utterly meaningless, 'win at all costs by as much as possible' is only really excuseable against a computer or the deck of cards in solitaire.

SensFan

2010-03-10, 02:21 PM

Then again, if you beat a child enough times at cards/checkers/etc it's still an ethically sound move to lose a game once in a while. The loss means nothing to you, and the win means a lot to them. Even when the game is utterly meaningless, 'win at all costs by as much as possible' is only really excuseable against a computer or the deck of cards in solitaire.
This may be part of the problem here. I would consider it wrong if I purposefully lost a game of checkers or something against a child.

Fifty-Eyed Fred

2010-03-10, 02:28 PM

I would join the discussion, but since you have seemed to reach an impasse in morality versus monetary gain between you, I will just say that I agree with the majority in that I would want to uphold my own values of fairness in refusing a highly unfair offer in order to teach the offerer a lesson, and that I think SensFan may in fact be a robot, as emotion and humanity do not appear to be factors in his wholly logical assessment. :smallsmile:

Douglas

2010-03-10, 02:35 PM

This may be part of the problem here. I would consider it wrong if I purposefully lost a game of checkers or something against a child.
That is a completely separate issue, and I think you'd get a lot more understanding and agreement with your position on that than with the ultimatum "game".

Supporting fairness and punishing unfairness are highly desirable traits for a society to have, even purely from the perspective of economic welfare for the society as a whole. Thus, the cultures that reinforced these traits in their members grew dominant, and the vast majority of the world teaches children to value fairness and punish unfairness from a very young age. By the generally accepted definition of "fair", a 99-1 split is extremely unfair and a great many people value the fairness aspect of the split much more than they value a single dollar.

Irbis

2010-03-10, 02:39 PM

Read More. (http://en.wikipedia.org/wiki/Ultimatum_game)

It seems that more-than-fair (e.g. first player offers greater than 50% of stake) offers are never given. I don't quite get why not. Why don't 2nd players reject fair offers? Why don't 1st players expect the second to reject fair offers, and offer more?

Because it works both ways. Discussion above from "logical" (actually, completely fallacious) viewpoint completely misses this. Humans are social animals. Ever heard of Evolution? We evolved in such a way because cooperation is ultimately the optimal choice in the environment we evolved. It might not be today, but we still carry it, by inertia. Someone is a jerk who doesn't share with society? He gets punished, chances of reproduction fall. You share too much? Similarly, chances fall. Thus both sides tend to be about average.

Fortunately, it is impossible to hardcode equal sharing into us, so every population, a few jerks and altruists will be born, "testing" if the balance should change. We still carry with +/- equality for all, but jerks seem to be better off in this age, possibilities of screwing society and getting away with it being bigger than in "small world" barely centuries ago :smallannoyed:

Still, I guess such a jerk could throw away a fair split, so you might be on to something, but we don't generally encourage such behavior. It would need to be some weird altruist/jerk combo to even consider working.

If I make an offer of 99:1 and you turn it down, then logically, you wouldn't have even accepted an offer of 0:100, since you appear to not want free money or you'd have taken the free dollar I offered.

This is absurd on so many levels I don't know where to start :smallsigh:

Only a (hypothetical) complete sociopath can make such an argument. Normal person will care about future, so even if this is the only game, the negligible loss is reason enough to tech the other to not cheat. It is hard-wired into us. It might not agree with void sociopathic "logic" because real people don't live in the void - if everyone made such "logical" decisions society would fall apart and every hardship would eliminate every human who would be unable to "borrow" (in any form) resources/strength from others leading to elimination of such self-serving groups. They want to maximize their chances of survival.

What a pile of gold is worth if you're the only survivor? Nothing.

Even from purely game perspective, trying to gain 99$ with 99.9% chance of being rejected is fail strategy that doesn't result in profit maximization at all. Quite the contrary. You're seeing one curve, where you need to see two.

Thirdly, of course I would. I will always take free money.

It is like saying people will happily accept 10% of their current wage because it is "free" money. No it isn't.

KuReshtin

2010-03-10, 02:59 PM

I was going to quote a few people here to get my response across, but I decided that I'll just make it a blanket statement.
Everyone will have the option to figure out what posts I'm referring to.

First premis of this as far as I see it is that it's not about the money. It's about the principle of the offers.
In the scenarios described above by Tirian, we have been clearly informed that it's a matter of scenario 2, where both participants are aware of the rules.
In this case, I would personally assume that when given these circumstances, person A will have to start thinking about how to maximise his gain, while person B will have to start thinking about minimising his loss.

The fair offer would be a 50/50 split. Offering any more than 50% to person B would be stupid, as that would be instantly accepted as it would be well above the baseline set by person B.
Offering more than 50% would be stupid on the part of Person A.
Since Person B is on the defensive from the start, Person A needs to find what he would most certainly accept for himself, and then decide if it's worth matching that offer, offering a bit more, or even offering less than what he himself would accept.

Here comes the fun part, though. Every person is different.
SensFan has already stated that any offer would be accepted as that means he gets free money. Therefore, he would only offer $1 to the other party.
Personally, I think that if anyone making that offer 100 times, would get maybe 1 or 2 acceptances. Tops.

The amounts of offer acceptances would rise along with the amount offered to person B where only maybe 1 or 2 would not accept an offer of just less than £50.

The notion of "I don't want to get free money unless I get more free money than you" offered by SensFan is flawed, as I would venture to say that very few people would wait for an offer where they get more than Person A as they are aware from the get-go that they will not be getting an offer better than 50/50.

Here.. I made a graph of what I think would happen as the offered amount would get higher. I know that it's a very unscientific graph, and it's incomplete, so any maths majors or statisticians or whatever out there that want to complain about it, please don't bother, cause I'm already aware of the flaw. It's there for illustrative purposes only.

http://myweb.tiscali.co.uk/kureshtin/images/Graph.jpg

However, I will also say that when talking about money, the total amount of money is very much an issue to consider as well.

As has been mentioned before, if you're going by percentages, a 99:1 ratio on an amount of $100 isn't a whole lot, and that's the basis of the graph.
However, if the base amount of money is $1.000.000, a split of 99:1 might very well get a lot more acceptances, as Person B would get $10.000, which is still a pretty decent amount of money. It'd be a hell of a lot harder to decline $10.000 than it is to decline $1.

Of course, if the base amount of money was $1.000.000, I'd venture to say that the offer made by SensFan would still only be $1, and he'd still wonder why Person B would reject his offer.

I'm sure there have been several new posts since I started this one, but these are my thoughts on the matter, and I hope they at least make a bit of sense.

SensFan

2010-03-10, 03:12 PM

Of course, if the base amount of money was $1.000.000, I'd venture to say that the offer made by SensFan would still only be $1, and he'd still wonder why Person B would reject his offer.
Absolutely. And I say that with complete sincerity.

Sneak

2010-03-10, 03:26 PM

Absolutely. And I say that with complete sincerity.

If you're keeping $999,999 and giving me $1, you're just obnoxious and don't deserve that $999,999. Me? I don't need that $1. I'm not going to starve without it.

Why would I ever accept that deal?

You see, human beings are not automatons of pure greed. We have emotions.

Douglas

2010-03-10, 03:39 PM

Absolutely. And I say that with complete sincerity.
Person B would most likely reject your offer because $1 doesn't really matter to him, he thinks you're being a ridiculously huge jerk, and punishing you for being that much of a jerk is worth a lot more to him than $1. What part of this do you not understand?

Telonius

2010-03-10, 03:40 PM

RS14

2010-03-10, 03:57 PM

It can also be considered as solidarity with others in your position. Certainly the only thing that matters is the offering player's perception of what will be rejected and what will not be. But, having convinced the offering player to offer something, there is no longer any reason not to accept--no reason not to below-average in your demands.

Consider a soldier at war, though. He can fight valiantly (and probably die) or cower and probably survive. But if everyone cowered, his army would lose. Thus there is a strong societal pressure towards solidarity. Accepting a poorer deal than everyone else is akin to treason.

SensFan

2010-03-10, 04:10 PM

Person B would most likely reject your offer because $1 doesn't really matter to him, he thinks you're being a ridiculously huge jerk, and punishing you for being that much of a jerk is worth a lot more to him than $1. What part of this do you not understand?
So he's willing to throw away free money for the sole purpose of insuring I don't get more free money than he gets, and I'm the jerk?
Yeah, I don't follow.

Strawberries

2010-03-10, 04:15 PM

Absolutely. And I say that with complete sincerity.

Well, as the comments of the thread prove, making such an offer would be a suboptimal move, because it's very likely (shall we say, 99%? 99.9%?) that it will be refused.
So, I could turn the tables on you, saying I can't understand why you would choose such a strategy, which is obviously losing. I could argue that if you are choosing to maximize your economical gain, the best strategy would be an offer of 50:50, which gives you an ironclad certainty that you are going to get your money. Any offer below that, and you are taking a risk (if we are talking of splitting 1000000$ it may not be a huge risk, because very few people are going to refuse 499999$, but if we are talking about,say, 10$...there are some people that may refuse 4$, depending on circumstances that are completely beyond your control).

Totally Guy

2010-03-10, 04:18 PM

I caught a taxi across town and the driver didn't ask me for money until I was already at my destination. The fool! I no longer had a reason to pay him anything. He'd already done exactly as I'd planned!

Bwahahaha!

:smalltongue:

Winterwind

2010-03-10, 04:18 PM

So he's willing to throw away free money for the sole purpose of insuring I don't get more free money than he gets, and I'm the jerk?
Yeah, I don't follow.You really don't see how setting up a split of 99:1 is blatantly unfair towards the other person? How it's absolutely devoid of any solidarity? You really wouldn't have a bad conscience for proposing such a deal (incidentally, yet another reason why one might want to disregard the choice you propose as 'logical')? How most people would propose a fair deal (50:50 split or close to it) for the sake of being able to look the other person in the eye alone without having to burn with shame?

Well, alright. I fear we have nothing in common, then, and lack any basis for any sort of communication. Therefore, my apologies, but I shall be withdrawing from this debate; I do not think we can reach a common ground. Too different mentalities.

thubby

2010-03-10, 04:28 PM

If I make a 99:1 offer, I'm telling the other person "You can take 1$ or you can take 0$."

I wouldn't ever expect a rational person to pass on 1$.

except a person in a society where there are vindictive receivers will have to weigh the likelihood of the receiver being vindictive, inclining them toward offering more.

KuReshtin

2010-03-10, 04:34 PM

So he's willing to throw away free money for the sole purpose of insuring I don't get more free money than he gets, and I'm the jerk?
Yeah, I don't follow.

No, he wouldn't reject the offer because he got less than you, he'd reject it because he got so significantly less than you that it's not worth accepting it.
Probably 99.99% of the world's population would consider it worth that $1 to deny you of the money.

Let's expand things a bit.
Base value on offer is $10.000. There are 5 participants. All are in the room at the same time. You have been given the $10.000 and the same premise is i effect.
One offer. One response. Only you have to make an offer to each of the other four participants.
If all offers are rejected, the money is lost.
All offers are made publicly in front of the other participants.
Would you still only offer each of the other participants $1 each?

Graymayre

2010-03-10, 04:41 PM

money is better than no money. The name of the game isn't appeasing the other person, it's seeing how much you can rip him off until he thinks it's more profitable to just say no.

In most cases you'll be able to get away with a 60-40 split, probably convince him to do 70-30, and have a possibility of going even higher depending on how much is at stake and what that person's personality is like.

If you really want to go for gold in the Beijing olympics, just tell the person that you'll take all the money and we can haggle after the game is done.

Bucky

2010-03-10, 04:44 PM

Let's expand things a bit.
Base value on offer is $10.000. There are 5 participants. All are in the room at the same time. You have been given the $10.000 and the same premise is i effect.
One offer. One response. Only you have to make an offer to each of the other four participants.
If all offers are rejected, the money is lost.
All offers are made publicly in front of the other participants.
Would you still only offer each of the other participants $1 each?

What's the payout if more than one offer is accepted? If it's the highest accepted offer, I offer the first one $5,000, the second $2,500, the third $1,250 or $3,750 (depending on whether the second accepted) and the fourth halfway between the lowest accepted offer and the highest unaccepted offer. My 7/8 offer suddenly seems fair given that I'm making a fair offer in a game of Ultimatum on the 1/4 of the money I don't already have.

If the payout is the first offer accepted, I do the above offers in reverse order, assuming that each offer will be accepted (i.e. starting with an offer of $625 and doubling my offer after each rejection).

Irbis

2010-03-10, 05:02 PM

So he's willing to throw away free money for the sole purpose of insuring I don't get more free money than he gets, and I'm the jerk?
Yeah, I don't follow.

Out of curiosity, are you by any chance a supporter of free market and flat tax rate?

KuReshtin

2010-03-10, 05:09 PM

What's the payout if more than one offer is accepted? If it's the highest accepted offer, I offer the first one $5,000, the second $2,500, the third $1,250 or $3,750 (depending on whether the second accepted) and the fourth halfway between the lowest accepted offer and the highest unaccepted offer. My 7/8 offer suddenly seems fair given that I'm making a fair offer in a game of Ultimatum on the 1/4 of the money I don't already have.

If the payout is the first offer accepted, I do the above offers in reverse order, assuming that each offer will be accepted (i.e. starting with an offer of $625 and doubling my offer after each rejection).

You have $10.000. If you're person A, you make an offer to Person B, wait for his response. Then make an offer of the remaining money you've got to Person C, wait for his response. And so on..

Strawberries

2010-03-10, 05:17 PM

You have $10.000. If you're person A, you make an offer to Person B, wait for his response. Then make an offer of the remaining money you've got to Person C, wait for his response. And so on..

I'd personally start with an offer of 3500$. Any less than that, and I wouldn't be able to look myself in the mirror.
However, with these kind of sums (and my current economical situation), I'd accept an offer of 1000$. I can live without 900$ to teach the other person a lesson. It would be a matter of principle more than anything.

Whoops, disregard. I managed to misunderstand the explanation of the rules. In that case I'd offer 2000 each (a fair split). It's the best way to be sure that all the offers are accepted (minimizing the risk is a worth strategy in my book).

Telonius

2010-03-10, 05:20 PM

For a bit colder of an analysis: Money is power. There exists a person who is willing to accept (and in fact bring about) a situation where he gets 99% of a division of goods, while I get 1%. There also exist other people who would give me better deals than 99:1. Would it not be in my best interests to injure, thwart, and otherwise prevent the person who wants 99:1, from getting any more power? Even in a "game" situation, the consequences are never totally confined to the game.

Douglas

2010-03-10, 05:25 PM

So he's willing to throw away free money for the sole purpose of insuring I don't get more free money than he gets, and I'm the jerk?
Yeah, I don't follow.
The reasoning goes something like this: you start with $1,000,000, to be divided between the two of you. Fairness would indicate a split of $500,000 to each of you. Like it or not, that is the basis of comparison person B is probably going to be thinking about. You took the first jerk move by arbitrarily reducing B's profit from the fair split by $499,999. Yes, B refusing is also being a jerk, but it's in response to you being a jerk first. It is, in B's view, you getting your just desserts. That $1 B could still get? That's effectively meaningless. It is so small that B almost doesn't care at all about it. The $499,999 that you screwed him out of (which is how he will perceive it)? That's big money and a major jerk move, and B wants to punish you for it.

He's willing to throw away a negligible amount of free money in order to punish the guy who "stole" his fair share. It's not that you're getting more than him, it's that he's getting less than he thinks he should, and "should" for the vast majority of the population in a case like this is defined by the "fair" even split. In a more realistic scenario, B's refusal would effectively be an announcement that he will punish any person who does not treat him fairly, which would increase the chance of any future deals offered being fair towards B, likely resulting in B getting a lot more in the future than the $1 he's giving up now. This reasoning, strictly speaking, does not apply in this game as stated, but human behavior often ignores the reasons for such things after the behavior has been established in the first place, so the conclusion of rejecting the unfair offer still gets used most of the time.

The Extinguisher

2010-03-11, 01:12 AM

Strawberries

2010-03-11, 01:41 AM

Except that future deals are not applicable. The game is played once and only once. You aren't able to teach the other player anything.

Anything about the game, I'll grant you that. But I don't think it is a big stretch to say that a person's behaviour in the context of the game would reflect behaviour in other similar social situations. So it would "teach" the other player something about human interaction.

SensFan

2010-03-11, 01:45 AM

Anything about the game, I'll grant you that. But I don't think it is a big stretch to say that a person's behaviour in the context of the game would reflect behaviour in other similar social situations. So it would "teach" the other player something about human interaction.
You turning down an offer doesn't teach anyone anything, no more than it would teach me anything if we were playing a game of chess, we flipped a coin to see who would be White, and when you lost that coin flip you flipped the board and left because I had an advantage in the game.

RS14

2010-03-11, 02:04 AM

Aiani

2010-03-11, 02:17 AM

This discussion is all kinds of interesting to me just seeing how other people think. Anyway my take on it is that I would turn down a 99:1 offer because $1 isn't worth much to me. To me $1 is a snack from a vending machine at work and honestly I don't need that snack because it's just going to go right to my thighs. So I would probably turn it down but not to teach a lesson, more because I am just that vindictive. I realize that makes me a bit of a jerk but I guess I can accept that about myself.
On the other hand I think I would accept a 70:30 offer even though it isn't strictly fair because $30 is worth something to me. That's half the price of that new video game I want to buy or a dinner in a decent restaurant. If I was penniless and without a job I would probably accept the 99:1 split though because if you have nothing every little bit helps. I guess it all just depends on how vindictive someone is (or how much they want to teach a lesson) and how much they value the money that you offer them.

Now I'm going to go back to lurking like I usually do. :smallredface:

Zeb The Troll

2010-03-11, 02:18 AM

You turning down an offer doesn't teach anyone anything, no more than it would teach me anything if we were playing a game of chess, we flipped a coin to see who would be White, and when you lost that coin flip you flipped the board and left because I had an advantage in the game.That analogy doesn't work. In a game of chess there are dozens of moves before a winner is determined and the player who goes second can overcome the disadvantage quite easily. It's not as if the person who goes first always wins. Also, chess is solely about strategy. Emotion has no bearing on who is the better strategist in the long run.

You're stating that, in this Ultimatum Game, the person who offers invariably "wins" if they choose to do so. But they don't. If they make a craptastic offer that the recipient has no compulsion to accept, the Accepting player can, and I submit would, make sure that the Offering player "loses" too.

Again, a $1 offer means nothing to me. It is absolutely valueless in my day to day life. I can do nothing with it. It's not even a good nose wipe. For all intents and purposes, it is $0 for all that I can do with it. If you offer me $1 I would turn you down flat for being a twit, just so that you don't get to have your $99.

And that's where Pyrian's point about the undisclosed scale comes into play. What if we weren't playing for $100 split, but $1,000 or a $1,000,000? If you were the Accepting player in a million dollar game, would you still accept $1 and let the Offering player walk away with the rest? I submit that the VAST majority of people would not.

EDIT: As an example...

To me $1 is a snack from a vending machine at workIt doesn't even buy me a snack from the vending machine at work. That's how value-less it is to me in my situation.

SensFan

2010-03-11, 02:23 AM

A bad example: in the ultimatum game, the advantage or disadvantage is determined by one player.

I expect that nobody here would have any trouble accepting 99:1 (or even 100:0) offers if those were determined by a dice roll, and they were simply unlucky.

A better example would be a war-game. You and the other player pick out a large, flat, open map. He insists that you should play an infantry only force while he takes armor. Most players will walk away; such a game is biased against them.
What are you talking about? Of course the advantage is determined randomly in this game. Whoever is chosen as the first player has the advantage.

The war game analogy doesn't hold for that reason. Offering 99:1 is not trying to get an unfair advantage, its using the rules of the game to maximize your gain.

Zeb The Troll

2010-03-11, 02:35 AM

What are you talking about? Of course the advantage is determined randomly in this game. Whoever is chosen as the first player has the advantage.He's not talking about the advantage being random, but the split. If he were the Accepting player, and the Offering player simply said "I'm going to roll these percentile dice, and whatever they come up, that's the percentage I'm going to offer you. *roll* Wow, 01. That sucks for you. Do you accept?" In that scenario, he would accept because it's not the Offering player trying to maximize his take. It's just an unlucky roll.

SensFan

2010-03-11, 02:41 AM

He's not talking about the advantage being random, but the split. If he were the Accepting player, and the Offering player simply said "I'm going to roll these percentile dice, and whatever they come up, that's the percentage I'm going to offer you. *roll* Wow, 01. That sucks for you. Do you accept?" In that scenario, he would accept because it's not the Offering player trying to maximize his take. It's just an unlucky roll.
I know. My argument is that the advantage in the game is determined randomly; namely by who gets to be the Offering player. Just like the advantage in chess is often determined randomly.

Zeb The Troll

2010-03-11, 02:44 AM

I know. My argument is that the advantage in the game is determined randomly; namely by who gets to be the Offering player. Just like the advantage in chess is often determined randomly.I got your point, but you're arguing two different things. He's not disputing the advantage being random at all. He's not even talking about advantage. He just said he'd be more likely to accept a randomly bad split.

RS14

2010-03-11, 02:54 AM

What are you talking about? Of course the advantage is determined randomly in this game. Whoever is chosen as the first player has the advantage.

The war game analogy doesn't hold for that reason. Offering 99:1 is not trying to get an unfair advantage, its using the rules of the game to maximize your gain.

Ah, I misunderstood. I thought you were comparing the receiving player's decision to reject a bad offer to throwing the table if randomly assigned black.

Bouregard

2010-03-11, 02:57 AM

*edit*
Read it again and yes it's played only once. So yes the right decision is to accept anything. Where is the point in teaching one person out of 6.000.000.000?

And why thinks anyone 50:50 is fair? For me, clearly person two is in control. Yes person one can choose how much anyone get's, but person two is the one who chooses if ANYONE INCLUDING PERSON ONE gets anything. If I'm the guy to choose the ratio, I would say that my "opponent" will receive 51% and I 49%.

Some other things:

People here mention 100$ as an example. I guess the money-to-be-shared plays a significant role. Say the prize is 100.000.000$ and your opponent wants to give you a puny 1.000.000$ would you still turn it down?
And if you still say "Yes!", then for which amount you will accept?

Next problem resulting from the above mentioned is that money is not always worth the same for different persons. So the players themselves are also significant to the process. A rich guy will most certainly be more likely to turn down a small offer, as he a) don't need it and b) may want to teach the other player a lesson.

thubby

2010-03-11, 03:11 AM

Power distribution:
The "Splitter" can choose how much anyone gets

The "Accepter" can choose if both players receive their share

The problem is that the second persons powerbase is not always the same. As we don't know if this game occurs more then once. If it just happens irregular/seldom or only once, then there's no point in teaching the Splitter a lesson. The most logical step would be to accept any split. As long as you get anything it's more then nothing...

the "lesson" is already taught by society. we already know that more than a few of the people here would shoot down a 1$ offer. someone could do the numbers, but it comes to X/(total number of people) chance of a 99/1 offer getting shot down.
if some percentage of people refuse the low amount, a fair split becomes a more viable option for the splitter.

it's essentially a threat, and threats are only workable when they will be acted on.

RS14

2010-03-11, 03:17 AM

it's essentially a threat, and threats are only workable when they will be acted on.

Except you can totally back down with no repercussions.

It's all a sense of solidarity. We want society to enforce some notion of fairness, so that we get a decent share. We want society to reject poor offers, and a sense of duty compels us to do so ourselves.

thubby

2010-03-11, 03:33 AM

Except you can totally back down with no repercussions.

not in the short term no. but you screw up the odds, making it worse for everyone else, and yourself in future instances with similar circumstances.

KuReshtin

2010-03-11, 04:42 AM

For me, clearly person two is in control.

I agree. That's why person A can't just make a 99:1 offer in his own favour, as Person B has the power to ensure that person A goes away with nothing.

Winterwind

2010-03-11, 06:49 AM

Except that future deals are not applicable. The game is played once and only once. You aren't able to teach the other player anything.

Person A makes the offer, and person B must choose either something or nothing. The logical choice is for person B to always accept any non-zero sum, and for person A to always over the smallest possible amount. That makes the most sense, looking from a perspective of "something is better then nothing" which is generally true.

However, the fact that this doesn't hold true is kinda the point in studying the game. If everyone actually did everything they would do logically, the game wouldn't be worth analyzing.As has been stated several times throughout this thread, this is because walking away with zero money does not equate 'nothing' for most people, if they got something worth more than the money they might have gotten otherwise in return: The satisfaction of denying a blatantly unfair person the victory.

Tirian

2010-03-11, 07:28 AM

People here mention 100$ as an example. I guess the money-to-be-shared plays a significant role. Say the prize is 100.000.000$ and your opponent wants to give you a puny 1.000.000$ would you still turn it down?
And if you still say "Yes!", then for which amount you will accept?

There are two competing forces influencing the balance point on the second player. The first is the sense of justice, which in my mind is what's behind the people who would be troubled by 51-49 splits. The second is the utility value of the offer made to the second player.

One common refrain in this thread is that a dollar is more than nothing, but really? It isn't. Here (http://www.embracingchaos.com/pix/utility-curve.GIF) is a good estimate of how it appears to the average person in developed society. Think about lottery tickets or slot machines for a minute. You buy a ticket (or pull the lever) for a dollar for a chance to win a couple million when you know that only half of the money collected goes into the jackpots. But it works anyway, because to people a dollar is worthless and a million dollars is economic freedom for life.

Everybody's curve is a little bit different. Twenty dollars means more to a ten year-old child than it does to a lawyer. If you're saving money for the down payment on a new car, your curve is going to have a bulge that someone else's wouldn't. But for nearly everyone, a dollar is something that can be (and is) spent on impulse, like the impulse to stand up to an economic bully in this experiment.

Now, there probably isn't so much hard data on a hundred million dollar case that you suggest, since very few people would underwrite that experiment. As you suggest, I'd probably go ahead and take the million dollars you offer, because it is worth much more than nothing. (I'll tell you that I'm going to kick you hard in the shins just before accepting.) What interests me, though, is why YOU would think to gamble on my lack of outrage just so you can make $99M instead of $50M. Either would put you in virtually the same economic fairyland for the rest of your life and half of your next one, but having a sense of fairness would ensure that I would agree to your luxury and allow you to sleep at night (from both a clear conscience and a lack of fear that I'm coming after you).

Player_Zero

2010-03-11, 07:40 AM

If Liar Game has taught me anything it's that people are horrible and life itself is a zero sum game. Also musical chairs is an intense life-or-death gamble.

Even when games have trivial solutions which are beneficial for all players people still may not play the rational strategies.

If you're surprised by people acting stupidly then you should probably take your fingers out of your ears, open your eyes and climb out of the hermit cave you've been hiding in, because it's quite apparent most people are idiots.

Winterwind

2010-03-11, 07:43 AM

If you're surprised by people acting stupidly then you should probably take your fingers out of your ears, open your eyes and climb out of the hermit cave you've been hiding in, because it's quite apparent most people are idiots....did you just call nigh everyone in this thread idiots? For having a sense of justice and conscience, no less? :smallconfused:

SensFan

2010-03-11, 07:53 AM

As has been stated several times throughout this thread, this is because walking away with zero money does not equate 'nothing' for most people, if they got something worth more than the money they might have gotten otherwise in return: The satisfaction of denying a blatantly unfair person the victory.
I still find it amusing that person B is voluntarily passing on free money just to get some sense of satisfaction in keeping free money from someone else, and yet you all call person A 'a jerk' and 'blatantly unfair'.

Winterwind

2010-03-11, 08:02 AM

I still find it amusing that person B is voluntarily passing on free money just to get some sense of satisfaction in keeping free money from someone else, and yet you all call person A 'a jerk' and 'blatantly unfair'.Not a sense of satisfaction for keeping free money from someone else. For preventing someone who made a blatantly unfair offer from winning. Two completely different things.

Look at Zeb the Troll's example - if the amount the first player offered was randomized, he would accept a 1:99 split - the same split he would decline if the first player had actively chosen that split. Because in one case, it's a matter of getting back on the first player for lacking any solidarity, in the other, it's in no way the first player's fault.

KuReshtin

2010-03-11, 08:12 AM

Now, there probably isn't so much hard data on a hundred million dollar case that you suggest, since very few people would underwrite that experiment. As you suggest, I'd probably go ahead and take the million dollars you offer, because it is worth much more than nothing.

SensFan has stated that if the initial sum of money was $100 million, he'd not give you $1Million. He'd still only give you $1.
And he's also stated that he'd be honestly surprised when you reject the offer if that single dollar so that he can have $99.999.999.

...did you just call nigh everyone in this thread idiots? For having a sense of justice and conscience, no less?

No, Zero just called most people, no matter where they are, idiots. Something I have to actually grant is pretty close to being correct.

Winterwind

2010-03-11, 08:18 AM

No, Zero just called most people, no matter where they are, idiots. Something I have to actually grant is pretty close to being correct.Ah. Well, I'd contest that, too (most people are fairly smart, actually; it's just that idiots tend to stand out more, so our perception is occasionally skewed), but that's a different topic entirely. :smallwink:

I do have to disagree with him for deeming putting one's sense for justice above negligible monetary gains stupid (if my interpretation that his post stated that is correct), though; material profits, while maybe more tangible than others, are nonetheless not the only relevant ones.

Totally Guy

2010-03-11, 08:20 AM

What if the first player offered no money? None at all.

What would player 2 do then?

Brother Oni

2010-03-11, 08:24 AM

There's a lot of discussion about rational and 'irrational' decisions, but let's look at it from an expectation probability point of view.

Suppose you play the game with 100 different people, with 100 dollars/euros/pounds, with the amount known to both players. None of the results from other games affect the current game. Assume the chance of accepting the offer is sigmoidal (like the earlier diagram), with the 50% probability of accepting set at the break even point (assume it's 80:20).

At a 99:1 distribution, suppose 5 people accept. This will net you 495 units of currency.

At the breakeven point, 50 people accept. This will net you (80 X 50) = 4000 units.

At 50:50, suppose 95 people accept. This will net you (50 X 95) = 4750 units.

For the goal of maximising economic return with the above assumptions, 50:50 is best. The breakeven point will obviously vary depending on the scale of the initial amount, but while higher amounts will lower the breakeven point, it will make extremely biased distributions against the accepting players even more unlikely to be accepted if they know what the initial amount is.

2xMachina

2010-03-11, 08:42 AM

How if we adjust the exp a little.

I give you $1. If you accept, I will give someone else $99. Do you accept?

And the base exp... I'd say rejecting the offer is a jerk move.

Tirian

2010-03-11, 08:52 AM

SensFan has stated that if the initial sum of money was $100 million, he'd not give you $1Million. He'd still only give you $1.
And he's also stated that he'd be honestly surprised when you reject the offer if that single dollar so that he can have $99.999.999.

I suspect that life will offer SensFan very many honest surprises.

No, Zero just called most people, no matter where they are, idiots. Something I have to actually grant is pretty close to being correct.

"Idiot" is a loaded term, one that it is as mean as it is inaccurate. If you believe that the vast majority of the population is irrational, then chances are that you are the one that needs to look harder for the true reason.

The evidence is insurmountable that people don't make every decision in their life to maximize their financial worth. Indeed, they don't even try to do that but come short because they're being outplayed by superior thinkers and an unexpected degree of bad luck. People give away money on entertainment and charity with no practical hope of financial gain. Why? Because they're "idiots", or because the theory that we should want to do anything for a dollar is flawed?

I think it would be more accurate (but still naive) to claim that people live to maximize their comfort and pleasure. Money is an important factor in that, of course, as it can be used to buy comfort and pleasure, but the poets are right that there are some pleasures that money can't buy. Many people in this thread seem to be suggesting that the joy of receiving a dollar is not compensated by the shame and anger that they were swindled out of $50, and the candy bar that you could buy for that dollar isn't going to fill that hole.

Douglas

2010-03-11, 08:56 AM

I still find it amusing that person B is voluntarily passing on free money just to get some sense of satisfaction in keeping free money from someone else, and yet you all call person A 'a jerk' and 'blatantly unfair'.
From the point of view where the even split is the expected default, person A is being a blatantly unfair jerk by arbitrarily reducing B's reward by a huge amount solely for A's own personal gain. That kind of act is very nearly a defining trait of jerks. A combination of genetics (maybe) and overwhelmingly prevalent cultural standards have firmly established the even split as the collectively expected default for most of humanity, so this is the point of view person B will most likely be using. B then rejects your offer in order to, whether he really understands this reason or not, reinforce that cultural standard.

Regardless, you don't have to understand and agree with B's decision and his reasons for it in order to act appropriately, only recognize that this is the reality of how B will likely act. Given advance knowledge of that, you should not be surprised at all at B's rejection if you offer a mere $1, and if you truly want a high payout you should propose a deal that the quite clearly dominant view would accept.

KuReshtin

2010-03-11, 09:57 AM

I suspect that life will offer SensFan very many honest surprises.

I would agree with that.

"Idiot" is a loaded term, one that it is as mean as it is inaccurate. If you believe that the vast majority of the population is irrational, then chances are that you are the one that needs to look harder for the true reason.

This is true. I admit to being very biased and jaded when it comes to people, as I work in a customer facing job where I interact with a lot of people that I would happily slap in the face given half a chance.

Winterwind

2010-03-11, 10:28 AM

This is true. I admit to being very biased and jaded when it comes to people, as I work in a customer facing job where I interact with a lot of people that I would happily slap in the face given half a chance.Which reminds me - I find this thread really quite reassuring. Seeing that the vast majority of people seems to have the decency to still care about the other and have the compassion to offer a fair deal goes a long way towards keeping my faith in mankind up. And I'd like to thank you all for that. :smallsmile:

KuReshtin

2010-03-11, 10:49 AM

Which reminds me - I find this thread really quite reassuring. Seeing that the vast majority of people seems to have the decency to still care about the other and have the compassion to offer a fair deal goes a long way towards keeping my faith in mankind up. And I'd like to thank you all for that. :smallsmile:

I don't think I've mentioned my personal preferences on the actual offers, but I believe that if we're talking about $100 being split I am pretty sure that I'd use the following numbers for determining my decisions.

- If I'm the person making the offer, I'd probably offer something like a 60/40 split in my favour, as I'd be pretty confident that the other person would agree to it. Even if offering 50/50 would be the most decent thing to do, I'm sure I'd still try to get a bit extra for myself.

- If I'm person B, having to accept of decline the offer, I'd probably accept an offer as low as $20, but any lower than that, it'd be quite likely that I'd reject the offer. I don't mind that I get less money than the other person, as long as his offer isn't an obvious insult, which I would find anything under $10 to be.

Winterwind

2010-03-11, 10:58 AM

I don't think I've mentioned my personal preferences on the actual offers, but I believe that if we're talking about $100 being split I am pretty sure that I'd use the following numbers for determining my decisions. You know, now that I think about it, I don't think I have either.

Essentially, the same as you - when offering, I'd probably go with 55/45 or 60/40 in my favour, too (any lower than 60/40, and I couldn't look myself in the eye anymore, but I'd be fine with teasing the other by skewing the split a bit - it is a game after all). When accepting, I think I'd go down to about 25/75; I'm not very vindictive, but I have a too strong sense for justice to let a person too blatantly disinterested in the well-being of other people get away with it. Unless that person could, somehow, convince me s/he simply needed the money that badly, in which case I'd be willing to accept an even far more unfavourable split.

Brother Oni

2010-03-11, 11:40 AM

Interesting enough, I remember a report regarding 'fairness' and social groups' natural tendancy towards it.

From what I remember, they got a group of chimpanzees and set them a group task. Once they figured it out and completed it successfully, they all got rewarded. This carried on for a while, until the researchers changed it and only rewarded specific chimps (and the same chimps every time) on completion.

After a while the chimps that weren't being rewarded downed tools and refused to participate in the task.

This would suggest that while the social group is willing to work together for the betterment of all, there is a limit to their working in a cohesive group when there is reward disparity (quite possibly the 'selfish' gene manifesting).

With humans, we have an extended social group called society and we appear to have found a good example of when it breaks down with reward disparity.

Edit:

With regard to me, if I were player A, I'd offer a straight 50/50 split.
If I were player B, it becomes a lot more complicated. While I'd probably accept anything down to a 20/80 to 25/75 split (I generally accept that life is unfair for reasons that can't be discussed on this board), anything lower and I'd start looking very carefully at player A.
If they can convince me they need the money and seem genuinely honest about it, then I'd accept lower.
If they were being arrogant and/or pushy about it, I'd refuse it on principle to spite them (I'm not THAT accepting :smalltongue:).

Bouregard

2010-03-11, 11:50 AM

Now, there probably isn't so much hard data on a hundred million dollar case that you suggest, since very few people would underwrite that experiment. As you suggest, I'd probably go ahead and take the million dollars you offer, because it is worth much more than nothing. (I'll tell you that I'm going to kick you hard in the shins just before accepting.) What interests me, though, is why YOU would think to gamble on my lack of outrage just so you can make $99M instead of $50M. Either would put you in virtually the same economic fairyland for the rest of your life and half of your next one, but having a sense of fairness would ensure that I would agree to your luxury and allow you to sleep at night (from both a clear conscience and a lack of fear that I'm coming after you).

I would offer my "opponent" 51% of the money, and myself accept anything. Of course I wouldn't say so before. The game will be played once.

And yes, I would be pissed too if someone chooses to offer me 1%.

Daimbert

2010-03-11, 12:51 PM

I think the real problem here is that there's a lot of confusion over what it means to be "rational". And so you have people on one side -- and the economists -- saying that taking anything is what is rational, and other people saying that $1 isn't worth it to them and so they are rationally denying the unfair person the monetary advantage.

So, let's start with a rough-and-ready definition of "rational". The one I use is "The person acts according to their beliefs in such a way as to achieve their desires".

This seems to start out nicely because we all do have a desire for money and so we should want money, and so getting $1 seems to satisfy that desire, and we believe that that is what we'll get -- and that we'll get nothing otherwise -- so it seems rational to take the 99-1 offer. However, what this leaves out are OTHER desires, which I have to fulfill as well to be rational. So, sure, someone who only cared about money would be rational to take that, but not all people only care about money in this sort of case.

For me, I also have desires to be treated fairly, to feel that I've been treated fairly, and to treat people fairly. And there are a number of other desires that could come into play. Taking the 99-1 offer violates the first two, and as people have pointed out the desire for $1 probably isn't going to be strong enough to overcome that; $1 just isn't that good at fulfilling my desire for money to make up for the unsatisfied desires to feel like I'm treated fairly. However, at some point it is; you "swallow your pride" and take the cash. And there may be an average for this, but this will vary from person to person, depending on how much they desire money. For example, I might hold out to an even split (or close to it) because I really don't care about money, and care more about being treated fairly and feeling like I've been treated fairly. Some will take the $1.

For the offering, I might always offer the 50-50 split. After all, that gives me a good deal of money AND satisfies my desire to treat people fairly. That makes it best at satisfying my desires and so is the MOST RATIONAL decision. For me. That might not be the case for someone else.

Considering that desires are personal and subjective, we can look at the rational decision again (and even things like the Prisoner's Dilemma). The problem with the initial assessment is that it doesn't consider desires that aren't just "money" or "time in prison", and so it makes conclusions about rational behaviour building that in. But now that we take that into account, we can look at it from the perspective of the offerer who knows this, and see a different story: the rational decision if they want money might be to offer an even split, even if they don't want to treat the other person fairly. Why? Because that person on the other end might be me, whose desire to be treated fairly is stronger than any unfair amount, and if it is me then they get nothing, whereas with a fair offer they'll get something. In short, almost no one will reject a fair offer, but a large number of people may reject unfair ones. Offer an even split and you'll almost always get at least something, which might not be the case otherwise. You could make offers in their favour and get more certainty, but this gets into diminishing returns since there are very few people that won't accept 50-50.

Note that neither side are really being jerks where; they are all trying to maximize the satisfaction of their desires. These games fail to describe rationality when they don't consider all of the desires of the people that they are evaluating.

Dallas-Dakota

2010-03-11, 01:13 PM

Actually, economically speaking, taking 1$ of the 100$ would be bad. Since the amount of money in the game changes the value of money.
So if the other one gets 99$, your 1$ would actually have less value.(And thus any other money you may have will have less value too)

Though we're living in such a big society that that actually doesn't matter in the scale of deciding, since one other person getting that 99$ for free doesn't matter.

But purely economically speaking, it'd make that 1$ less worth it and the rest of your previously owned money less worth it.

But as I said, so not on your thoughts when deciding.

I agree with most of the posters going for the 50/50 deal. Seems fair and the most likely to be accepted without giving away money yourself.(I'd give it away if I were rich, but alas I am a poor student)

And as many people have said, there's this social group/society that you're a part of. 1$ can be worth teaching a jerk(who's basically not sharing with you but being greedy) that sometimes it's good to be fair.

Delta

2010-03-11, 01:18 PM

Actually, economically speaking, taking 1$ of the 100$ would be bad. Since the amount of money in the game changes the value of money.

Wouldn't that only be the case if the 100$ we're talking about would be printed fresh only for the specific purpose of this game, and would be destroyed if the second player rejects the deal? Otherwise, we're talking about money that has been part of the system before and will be a part of it after the game, regardless of the game's outcome, so it wouldn't change a thing.

SensFan

2010-03-11, 01:22 PM

Alright, I'm done with this thread. I've had enough of being called a jerk and not having compassion just because I'm willing to maximize my advantage in a game.

Douglas

2010-03-11, 01:26 PM

Alright, I'm done with this thread. I've had enough of being called a jerk and not having compassion just because I'm willing to maximize my advantage in a game.
Considering that this thread overwhelmingly demonstrates that actually following your strategy would almost certainly result in you getting nothing, you are actually not maximizing your advantage at all. You are, in fact, shooting yourself in the foot quite thoroughly.

All mentions of you being a jerk have been in the context of explaining your hypothetical "opponent's" point of view and why he would refuse.

Murska

2010-03-11, 01:32 PM

I'd offer from 65/35 to 55/45 depending on whether I get to talk with the other person and evaluate his personality, but when it comes to accepting or not, it's more complicated.

See, above, I'm making a decision which means it's very likely for it to be accepted, which means I'm getting as much money as possible with the least risk possible. If I go and offer the other player too little, it's more and more likely that he will not take it and thus I won't be gaining money. Getting 55 is better than getting 0, according to most people's logic, so it's a sound decision in my opinion.

Meanwhile, if I were to work with that person again in any other circumstance, I'd offer 50/50. The value of trust is much more important and useful than 50$.

If I'm on the receiving end, I'd accept anything above 30. The thing is, if it's less than that, me 'winning' is not as important as the other guy 'losing'. I'm a bit of a jerk, maybe, but I would be highly amused and satisfied at the other guy losing more money than I did for expecting me to agree to such a split.

Maybe that means I'm the kind of person who would mark his shed with red lights for enemy bombers just so his neighbour's grand villa would be demolished aswell, at least if the neighbour bought that grand villa with money I believe to be rightfully mine, but there's nothing wrong with that.

Delta

2010-03-11, 02:04 PM

Alright, I'm done with this thread. I've had enough of being called a jerk and not having compassion just because I'm willing to maximize my advantage in a game.

You try to maximize your gain by following a strategy that, judging by the experimental sample of this thread, most often lets you walk away with nothing at all. Maybe that isn't a very rational strategy, then?

Daimbert

2010-03-11, 03:07 PM

You try to maximize your gain by following a strategy that, judging by the experimental sample of this thread, most often lets you walk away with nothing at all. Maybe that isn't a very rational strategy, then?

I think the comment here is that if people were rational, it would pay off, but that it only doesn't because people insist on being irrational. I disagree with that, but that's a bit different than what you're claiming.

Brother Oni

2010-03-11, 03:09 PM

Alright, I'm done with this thread. I've had enough of being called a jerk and not having compassion just because I'm willing to maximize my advantage in a game.

Your strategy, while logical from one viewpoint in that it both maximises your gain and offers the other player something, fails in at least two key points:

1) You're viewing the other player as an opponent, something to be beaten, rather than co-operated with.

2)You're not accounting for human behaviour which will have an effect on whether they'll accept or not (this has been covered in quite some detail in the thread).

If you treat the game as zero sum, that is, there can only be one winner and one loser, then your strategy is logical. If you take the non zero sum view that you and the other player can walk away richer, thus beating the game rather than each other, then your strategy will not work.

Delta

2010-03-11, 03:22 PM

I think the comment here is that if people were rational, it would pay off, but that it only doesn't because people insist on being irrational. I disagree with that, but that's a bit different than what you're claiming.

The thing is: He's wrong. It's as simple as that. He claims that his strategy is the only viable one, while presented with overwhelming experimental proof that it is not only not optimal, but actually one of the worst potential strategies. Then he claims that if you were to reject his 99/1 offer, you'd be acting completely irrational and so any other offer could as well be completely random, because there'd be absolutely no way to make a prediction over an irrational decision. Again, he is presented with overwhelming proof that the decision is in fact pretty predictable, that for example a 50/50 deal would always be accepted.

The problem is, that if you view it as a purely theoretical problem, played by completely unaffected players in a vacuum, then of course his strategy is absolutely correct and the best way to play it. But in reality, humans don't work that way. No human decision is ever made in a complete vacuum, things like cultural and socially acceptable behaviour always affect our decisions, and those factors are really hard to measure and quantify. But to deny those factors when you know they exist and influence the world is just as irrational as throwing away free money, if not more so.

Lin Bayaseda

2010-03-11, 03:37 PM

There are two competing forces influencing the balance point on the second player. The first is the sense of justice ...

Close. It's not justice, it's self-esteem. If you take the 1% offer, you'll be a tiny bit richer, but your self-esteem will be lowered by accepting an unfair offer. On the other hand, rejecting the 1% will make you a bit poorer, but boost your self-esteem, as you didn't let the other party walk over you, and "showed them who's the boss". You called the shots.

What does one's self-esteem cost? Hard to say. For myself, I'm pretty sure that if the initial pot was $100, I'd reject a 1% offer, as my self-esteem is worth a lot more than $1. On the other hand, had we started with $100,000,000, I could take a small hit to my self-esteem to become a millionaire.

Zocelot

2010-03-11, 05:54 PM

I wouldn't offer $1 out of $100 million, because to the other player that is equivalent to nothing at all and so they would likely turn me down out of spite. Even something like $100 seems like nothing when compared to the amount that I'm getting. I might offer something more like $100000, the amount of money that wouldn't be turned down just to spite me, but still a negligible amount of my winnings. If I had $10, I'd think that anything less than $5 would be insubstantial, so I would offer 50%.

The solution to the problem is to offer the lowest amount possible that your opponent will still accept. That amount depends on the mindset of the opponent, so you've got to judge them, and err on the side of caution. If your opponent is perfectly logical, then the amount is the smallest possible amount, but since I am not aware of any perfectly logical humans, the problem cannot be answered from the viewpoint of logic, but has to become a psychological problem.

I much prefer an iterated version of the problem. When it's iterated, teaching is an option. If 1% is offered, the accepter can turn it down to try to make the offerer raise the amount. However, this works both ways and the offerer can refuse to raise the amount, making the accepter have to choose between trying to teach the offerer and possibly making a larger profit, or settling for a small profit.

Strawberries

2010-03-11, 06:14 PM

The solution to the problem is to offer the lowest amount possible that your opponent will still accept. That amount depends on the mindset of the opponent, so you've got to judge them, and err on the side of caution. If your opponent is perfectly logical, then the amount is the smallest possible amount, but since I am not aware of any perfectly logical humans, the problem cannot be answered from the viewpoint of logic, but has to become a psychological problem.

I agree up to a point. I dont't think the problem depends just on the mindset of the opponent. I think the mindset of the proposer is an issue as well. Personally, if thr sum was 10000000$, I won't be able to look myself in the mirror if I offered less than 3000000$, and that's knowing that almost surely offers of, say, 500000$ (or even 100000) would be accepted as well. It's the psychology of both players that define the issue. In a more standard situation (for instance, a sum of 100$) I'd go with 50-50 or 60-40 splits.

PirateMonk

2010-03-11, 10:20 PM

If your opponent is perfectly logical, then the amount is the smallest possible amount

That's only logical if they have no goals other than to amass as much money as possible. If they are perfectly logical but value feeling that they have been treated fairly more than the smallest possible amount of money, they will still reject it.

The Extinguisher

2010-03-12, 12:11 AM

I much prefer an iterated version of the problem. When it's iterated, teaching is an option. If 1% is offered, the accepter can turn it down to try to make the offerer raise the amount. However, this works both ways and the offerer can refuse to raise the amount, making the accepter have to choose between trying to teach the offerer and possibly making a larger profit, or settling for a small profit.

I disagree. I think an iterated version of this game would just be rejection until a 50/50 split and then that's it.

MethosH

2010-03-12, 12:15 AM

"It's not just about winning. Someone has to lose." :smallbiggrin:

Zocelot

2010-03-12, 09:36 AM

It's not really the sort of thing that has to be argued about. It's certainly within the realm of possibility to perform the experiment using some sort of point system instead of cash.

Player_Zero

2010-03-12, 12:06 PM

...did you just call nigh everyone in this thread idiots? For having a sense of justice and conscience, no less? :smallconfused:

No, Zero just called most people, no matter where they are, idiots. Something I have to actually grant is pretty close to being correct.

More like that. Bearing in mind I am rather a misanthrope.

Ah. Well, I'd contest that, too (most people are fairly smart, actually; it's just that idiots tend to stand out more, so our perception is occasionally skewed), but that's a different topic entirely. :smallwink:

I do have to disagree with him for deeming putting one's sense for justice above negligible monetary gains stupid (if my interpretation that his post stated that is correct), though; material profits, while maybe more tangible than others, are nonetheless not the only relevant ones.

I more stated that people are prone to irrationality. But I would disagree here in that justice in this sense would be incredibly subjective here. Maybe your opponent feels they need the money more, for instance. And personally I don't agree with the mindset of turning down any deal in order to 'punish' your opponent. It seems petty to me.

Tirian

2010-03-12, 01:16 PM

And personally I don't agree with the mindset of turning down any deal in order to 'punish' your opponent. It seems petty to me.

But the strategy of offering an unequal distribution (whether grossly or subtly) is also petty. The first player didn't earn that spot from what we know of the experiment. One might say that they have been granted the privilege to be unfair, but I'd suggest that they also have the responsibility to not abuse their authority.

2xMachina

2010-03-12, 02:07 PM

However, we do not need to stoop to their level (though I agree that it is a bit much to ask from people).

Tirian

2010-03-12, 02:23 PM

The game is about cooperation, even though it is framed as hierarchical. The second player is not wholly responsible for rejecting an imbalanced offer.

Here's another way of describing the problem. A philanthropist calls you and a stranger into a room and gives you both a thousand dollars in cash (let's say in small denominations just for lulz), but if either of you say to him before returning home that the other one isn't worth it, you both have to forfeit all of the money. On the way out of the estate on the way to two limousines that will take you in different directions, you note that you are much larger and stronger than the other person. Would you threaten him to give you some of the money with threats of physical violence, and if so how much of his money would you feel safe demanding knowing that he has the power to have the deal annulled if you take too much from him?

Pyrian

2010-03-12, 02:31 PM

Refusing to be part of unfair distribution is not stooping to their level, it is rising above it.

The Extinguisher

2010-03-12, 11:51 PM

thubby

2010-03-13, 12:18 AM

This is actually a different example. In this, you both start with a sum, and you are taking away the sum from the other person.

In the actual game, only you start with the sum, and you give the other person some of that sum. It's a very large difference.

the divider is no more entitled to the money than the receiver.

Erts

2010-03-13, 12:26 AM

I remember studying this in my game theory class... Was pretty interesting.

Not much more to say that hasn't been said.

The Extinguisher

2010-03-13, 12:29 AM

the divider is no more entitled to the money than the receiver.

Except that in the ultimatum game, person B has no money and then can receive some or get nothing.

In Tirian's game, Person B has some money, and then can lose some or get nothing.

It's an interesting game to analyze, but it's still different.

thubby

2010-03-13, 12:44 AM

Except that in the ultimatum game, person B has no money and then can receive some or get nothing.

In Tirian's game, Person B has some money, and then can lose some or get nothing.

It's an interesting game to analyze, but it's still different.

in the original game neither party has any money. neither party has any more right to the money than the other, either. so it can't be treated as if A has all the money and is doling it out.

Tirian

2010-03-13, 12:53 PM

Except that in the ultimatum game, person B has no money and then can receive some or get nothing.

In Tirian's game, Person B has some money, and then can lose some or get nothing.

The only difference is that Player A has to commit a clear act of asshattery to get an unfair distribution in my experiment, while in the original experiment evidently some Player A's can convince themselves that it's just "part of the game" to deny Player B an equal share.

In both cases, neither player has money until both players agree that the distribution is better than nothing, and in both cases Player A gets to choose that distribution and Player B only has the power to cancel the experiment. It's the same game; it's just that the first player has to face what she's doing and how it is perceived by the second player the way I describe it. If it seems different, then it's because you're not prepared to take ownership of your unjust actions.

PirateMonk

2010-03-13, 01:40 PM