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Author Topic: The Ultimatum Game  (Read 16211 times)
estevo
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April 21, 2011, 05:46:50 PM
 #41

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How is it different?  Because in one case there is a "rightful" owner, and the first case, the money appears to be "shared" at one point in time?
Very precisely.  You think that shouldn't matter?

That is also why db's framing ("they give you 5000$ and I get to say how much you pay me to keep the rest") makes the problem subtly different, even though the underlying reward matrix remains identical in monetary terms.

I have insisted you don't necessarily treat this as a game theoretical abstract problem where utility is perfectly encoded in the monetary payoff and your job is just to maximize that.  That is, not unless that's honestly how you would frame it in real life.

The purpose of the thought experiment is exactly to explore how real human emotions and perceptions, and how real social dynamics, transform a problem which otherwise (that is, in an abstract game theoretical formulation) would have a clear unambiguous solution, invariant from all the different framings that maintain the same monetary reward structure.  That is, to explore the difference between rationality as formally defined in game theory and what makes sense to you in real life.

Whether you choose to call the latter "rational" or not is a matter of definitional nuance and not the main point.
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tomcollins
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April 21, 2011, 05:54:19 PM
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How is it different?  Because in one case there is a "rightful" owner, and the first case, the money appears to be "shared" at one point in time?
Very precisely.  You think that shouldn't matter?

That is also why, in a subtle sense, db's framing makes the problem different.

I have insisted you don't necessarily treat this as a game theoretical abstract problem where utility is perfectly encoded in the monetary payoff and your job is just to maximize that.  That is, not unless that's how you honestly would frame it in real life.

The purpose of the thought experiment is exactly to explore how real human emotions and perceptions, and how real social dynamics, transform a problem which otherwise (that is, in an abstract game theoretical formulation) would have a clear unambiguous solution, invariant from all the different framings that maintain the same monetary reward structure.  That is, to explore the difference between rationality as formally defined in game theory and what makes sense to you in real life.

Whether you choose to call the latter "rational" or not is a matter of definitional nuance and not the main point.


Oh, I'm aware of human emotions being quite irrational (a lot of people would rather be the richest person in a very poor country than the poorest person in a very very very wealthy country, even if the poorest guy has a lot more stuff than the richest guy).  Envy is a huge human emotion.  I just find it to be a huge weakness and not a characteristic I admire at all.

It's all about how people want to punish the person offering the deal.  Why do they deserve punishment?  What are they doing unfairly?  What are you owed by them?  Who are they harming by offering you a low offer?

People hate when other people get something for free and they do not.  Therefore they'd actually pay a fine to make sure no one else got free stuff.  It's borderline sociopathic to me, but it's part of many peoples personality.

If I was playing this game as the person making the offer, I would do my best to try to determine what is the lowest payout my opponent would take.  Then I would try to figure out how certain I was at each level.  If I was 99% sure he would take an even split, and 80% sure he'd take 3000-2000, I'd go with the even split.  If I had to deal with this person again, I'd offer more than if I never saw him again.  If I was certain he was rational and not spiteful, I'd offer him a penny.  If I was receiving the bet, I would try to make sure the person negotiating thought I was as crazy as possible and that I was capable of spite.  Hell, I'd even try to convince him I wouldn't even take half.  I don't need the money that much, so it's not worth my trouble unless he gives me $4k.  Then I'd accept any offer he throws my way.  But I would definitely not let him know that while the game is being played.

But the idea that someone wants to take away a huge sum of money from someone else just because they didn't give you enough seems almost mentally ill to me.  Any amount over a trivial sum would be considered a gift and insurance that his opponent is not a fool.
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April 21, 2011, 05:54:43 PM
 #43

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How is it different?  Because in one case there is a "rightful" owner, and the first case, the money appears to be "shared" at one point in time?
Very precisely.  You think that shouldn't matter?

That is also why, in a subtle sense, db's framing makes the problem different, even though the underlying reward matrix remains identical in monetary terms.

I have insisted you don't necessarily treat this as a game theoretical abstract problem where utility is perfectly encoded in the monetary payoff and your job is just to maximize that.  That is, not unless that's how you honestly would frame it in real life.

The purpose of the thought experiment is exactly to explore how real human emotions and perceptions, and how real social dynamics, transform a problem which otherwise (that is, in an abstract game theoretical formulation) would have a clear unambiguous solution, invariant from all the different framings that maintain the same monetary reward structure.  That is, to explore the difference between rationality as formally defined in game theory and what makes sense to you in real life.

Whether you choose to call the latter "rational" or not is a matter of definitional nuance and not the main point.

Any definition of rationality that only takes into account monetary incentives is completely flawed. Money is a means to some further ends, something that will satisfy some other human desire. If you're poor and starving, I'd imagine you would take any amount because you value your next meal over any chance to exact vengeance. On the other hand, if you have everything in the world, what's $10 over the chance to share your views on cooperation/vengeance with someone that just seemingly slighted you? The psychological satisfaction that results would be worth more than another $10 in your pocket.
tomcollins
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April 21, 2011, 05:57:34 PM
 #44


Any definition of rationality that only takes into account monetary incentives is completely flawed. Money is a means to some further ends, something that will satisfy some other human desire. If you're poor and starving, I'd imagine you would take any amount because you value your next meal over any chance to exact vengeance. On the other hand, if you have everything in the world, what's $10 over the chance to share your views on cooperation/vengeance with someone that just seemingly slighted you? The psychological satisfaction that results would be worth more than another $10 in your pocket.

I find spite to be irrational.  And I certainly wouldn't spend $10 to teach a lesson to some random stranger.

Getting satisfaction out of harming others is for sociopaths.
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April 21, 2011, 05:59:06 PM
 #45

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How is it different?  Because in one case there is a "rightful" owner, and the first case, the money appears to be "shared" at one point in time?
Very precisely.  You think that shouldn't matter?

That is also why, in a subtle sense, db's framing makes the problem different.

I have insisted you don't necessarily treat this as a game theoretical abstract problem where utility is perfectly encoded in the monetary payoff and your job is just to maximize that.  That is, not unless that's how you honestly would frame it in real life.

The purpose of the thought experiment is exactly to explore how real human emotions and perceptions, and how real social dynamics, transform a problem which otherwise (that is, in an abstract game theoretical formulation) would have a clear unambiguous solution, invariant from all the different framings that maintain the same monetary reward structure.  That is, to explore the difference between rationality as formally defined in game theory and what makes sense to you in real life.

Whether you choose to call the latter "rational" or not is a matter of definitional nuance and not the main point.


Oh, I'm aware of human emotions being quite irrational (a lot of people would rather be the richest person in a very poor country than the poorest person in a very very very wealthy country, even if the poorest guy has a lot more stuff than the richest guy).  Envy is a huge human emotion.  I just find it to be a huge weakness and not a characteristic I admire at all.

It's all about how people want to punish the person offering the deal.  Why do they deserve punishment?  What are they doing unfairly?  What are you owed by them?  Who are they harming by offering you a low offer?

People hate when other people get something for free and they do not.  Therefore they'd actually pay a fine to make sure no one else got free stuff.  It's borderline sociopathic to me, but it's part of many peoples personality.

If I was playing this game as the person making the offer, I would do my best to try to determine what is the lowest payout my opponent would take.  Then I would try to figure out how certain I was at each level.  If I was 99% sure he would take an even split, and 80% sure he'd take 3000-2000, I'd go with the even split.  If I had to deal with this person again, I'd offer more than if I never saw him again.  If I was certain he was rational and not spiteful, I'd offer him a penny.  If I was receiving the bet, I would try to make sure the person negotiating thought I was as crazy as possible and that I was capable of spite.  Hell, I'd even try to convince him I wouldn't even take half.  I don't need the money that much, so it's not worth my trouble unless he gives me $4k.  Then I'd accept any offer he throws my way.  But I would definitely not let him know that while the game is being played.

But the idea that someone wants to take away a huge sum of money from someone else just because they didn't give you enough seems almost mentally ill to me.  Any amount over a trivial sum would be considered a gift and insurance that his opponent is not a fool.

Show me how it's irrational to reject an offer. Is it irrational to pay to go to Disney world? It causes a loss in financial standing to only satisfy some psychological need. What's the difference?
Terpie
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April 21, 2011, 06:01:18 PM
 #46


Any definition of rationality that only takes into account monetary incentives is completely flawed. Money is a means to some further ends, something that will satisfy some other human desire. If you're poor and starving, I'd imagine you would take any amount because you value your next meal over any chance to exact vengeance. On the other hand, if you have everything in the world, what's $10 over the chance to share your views on cooperation/vengeance with someone that just seemingly slighted you? The psychological satisfaction that results would be worth more than another $10 in your pocket.

I find spite to be irrational.  And I certainly wouldn't spend $10 to teach a lesson to some random stranger.

Getting satisfaction out of harming others is for sociopaths.

Without trying to be too morbid, if a psychopath murdered your entire family, then played this game with you, and offered you $1. You would accept it?
tomcollins
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April 21, 2011, 06:01:24 PM
 #47


Show me how it's irrational to reject an offer. Is it irrational to pay to go to Disney world? It causes a loss in financial standing to only satisfy some psychological need. What's the difference?

I'm saying getting enjoyment out of harming others is disgusting, not irrational.
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April 21, 2011, 06:02:10 PM
 #48


Any definition of rationality that only takes into account monetary incentives is completely flawed. Money is a means to some further ends, something that will satisfy some other human desire. If you're poor and starving, I'd imagine you would take any amount because you value your next meal over any chance to exact vengeance. On the other hand, if you have everything in the world, what's $10 over the chance to share your views on cooperation/vengeance with someone that just seemingly slighted you? The psychological satisfaction that results would be worth more than another $10 in your pocket.

I find spite to be irrational.  And I certainly wouldn't spend $10 to teach a lesson to some random stranger.

Getting satisfaction out of harming others is for sociopaths.

Without trying to be too morbid, if a psychopath murdered your entire family, then played this game with you, and offered you $1. You would accept it?

In that case, vengeance is at least deserved.  Someone not giving you something you have no claim to is not.
estevo
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April 21, 2011, 06:04:41 PM
 #49

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Also, there's actually a way to win as the receiver if there is communication.  If you can make a binding decision ahead of time, you could say "I will reject any offer less than $4990".
If you can make such a binding decision you are effectively reversing the roles.  You are now the one calling the quantity and the other guy is the one that only gets to accept or veto.  From your perspective, you are not playing, and therefore not winning, the original game.

In the problem as formulated, you cannot make such a binding decision.

Now, imagine you could make a non-binding declaration of how much you will accept, and that the other guy offers you $10 nevertheless.  Does that change your choice?
tomcollins
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April 21, 2011, 06:06:39 PM
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Also, there's actually a way to win as the receiver if there is communication.  If you can make a binding decision ahead of time, you could say "I will reject any offer less than $4990".
If you can make such a binding decision you are effectively reversing the roles.  You are now the one calling the quantity and the other guy is the one that only gets to accept or veto.  From your perspective, you are not playing, and therefore not winning, the original game.

In the problem as formulated, you cannot make such a binding decision.

Now, imagine you could make a non-binding declaration of how much you will accept, and that the other guy offers you $10 nevertheless.  Does that change your choice?

If I never see the guy again, never play the game again (basically the problem postulated), I take any offer.  But I absolutely don't let him know that ahead of time.  Even if he gives me $0, I'll let him have all $5000.  Unless that money came from a charity to feed orphans or something.
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April 21, 2011, 06:14:45 PM
 #51

If I never see the guy again, never play the game again (basically the problem postulated), I take any offer.  But I absolutely don't let him know that ahead of time.  Even if he gives me $0, I'll let him have all $5000.  Unless that money came from a charity to feed orphans or something.

Good point. This game is designed so that the people discussing it will have a tendancy to lie about how they would really act: Potential players discussing the game are incentivized to provide the appearance that they would deny small values of money, but are incentivized to accept all values of money when they are actually in the situation.

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April 21, 2011, 06:23:06 PM
 #52

If I never see the guy again, never play the game again (basically the problem postulated), I take any offer.  But I absolutely don't let him know that ahead of time.  Even if he gives me $0, I'll let him have all $5000.  Unless that money came from a charity to feed orphans or something.

Good point. This game is designed so that the people discussing it will have a tendancy to lie about how they would really act: Potential players discussing the game are incentivized to provide the appearance that they would deny small values of money, but are incentivized to accept all values of money when they are actually in the situation.

And you do whatever you can to convince him.  Perhaps if he seems like he has a high sense of fairness.  You could appeal saying "come on, we should split it half way, I'd do the same for you".  If he seems weak or desperate, tell him you don't care that much, and burn a $100 bill in front of him to show him how much you don't care.  It's all negotiating techniques and reading people at that point.

I think the most believable situation without pissing off the person making the deal is to start out at 50-50.  If you try to demand more, he may just spite you.  If he mentions A Beautiful Mind or Nash, I start making him think I'm irrational.  How the second guy reacts to the offer is the least interesting part to me.  Either you are rational or spiteful.  What the first guy offers, and what the second guy tries to get is much more interesting.
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April 21, 2011, 06:25:43 PM
 #53

You can play all sort of mind games to make her believe that you won't take an "unfair" offer, but the formulation states that she'll offer you $10 nevertheless.  Your option (or not) to communicate before she makes her call only matters as far as that would affect your decision.

I mean, would you accept more or less money if you had a chance to state your position first?  If you swore you wouldn't take anything but half and she offered $10, would you be any more or less likely to accept it, in relation to the case where you didn't get a chance to talk before her offer?

If not, then all this talk about mind games is irrelevant to the question, isn't it?
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April 21, 2011, 06:38:27 PM
 #54

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Any definition of rationality that only takes into account monetary incentives is completely flawed.
Depends on the purpose and scope of your definition.

You could say that any model of movement that ignores friction and gravitational forces is "completely flawed".  It is certainly not realistic, yet it can be useful to abstract away those things for the sake of isolating other things for study.

In game theory, utility is often given a number (call it money or abstract utility points), and rationality is described as optimization of that.  Game theory doesn't pretend that this definition of rationality is adequate for real life.  It's just useful for mathematical study.

I understand that some game theory uses this definition of rationality, but I find it to be a misnomer. It's really just financial optimization. If a psychological need is valued more than a fixed monetary amount, it's not illogical to prefer the psychological satisfaction. Otherwise, paying to ride a rollercoaster is irrational. Or paying to give medical treatment to a loved one is irrational. Or willing to pay a lawyer more in legal fees than will be recouped in a tort case, in order to satisfy a sense of fairness, is irrational.
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April 21, 2011, 06:41:31 PM
 #55

You can play all sort of mind games to make her believe that you won't take an "unfair" offer, but the formulation states that she'll offer you $10 nevertheless.  Your option (or not) to communicate before she makes her call only matters as far as that would affect your decision.

I mean, would you accept more or less money if you had a chance to state your position first?  If you swore you wouldn't take anything but half and she offered $10, would you be any more or less likely to accept it, in relation to the case where you didn't get a chance to talk before her offer?

If not, then all this talk about mind games is irrelevant to the question, isn't it?

It's irrelevant if you are dealing with robots or people who aren't spiteful.

But some people would actually kick themselves in the nuts just to watch you get hit by a truck.  People do it all the time.  Just pay attention to politics.  A huge segment of the population is motivated by spite, envy, and jealousy, and would make themselves suffer as long as people they consider undeserving suffer more.  It's quite sick.
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April 21, 2011, 07:01:10 PM
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I understand that some game theory uses this definition of rationality, but I find it to be a misnomer. It's really just financial optimization. If a psychological need is valued more than a fixed monetary amount, it's not illogical to prefer the psychological satisfaction.
What if you consider that the utility measure already accounts for all these psychological factors?  So the numbers in the matrix don't represent raw dollars,  but an accurate estimation1 of how happy would it make you, in relative terms, to pick that option, all things considered.  Then rationality is accurate enough a name for optimization of that, isn't it?

That is formally equivalent to calling the utility money and assuming (again, for the sake of mathematical simplification) that that is all you care about.

1: Don't ask me how would you go about attributing a scalar value to the hairy mess of actual human preferences and biases, though.  Game theory doesn't even try to do this.
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April 21, 2011, 07:13:36 PM
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accepting 5000/0 is not rational btw. why would you care more about the greedy unknown person taking all the money than the unknown person offering it?
Formally, this assumes that first you try to maximize your own payoff, and that being equal, you try to maximize global utility.

It can be argued that the "unknown person offering" the money has signaled a lower preference for keeping it than the "greedy unknown person" taking it.

This is a minor point, though, and somewhat besides the question.  Just got curious about whether the folks that would take one cent would go all the way to accepting nothing at all.
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April 21, 2011, 07:15:50 PM
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I understand that some game theory uses this definition of rationality, but I find it to be a misnomer. It's really just financial optimization. If a psychological need is valued more than a fixed monetary amount, it's not illogical to prefer the psychological satisfaction.
What if you consider that the utility measure already accounts for all these psychological factors?  So the numbers in the matrix don't represent raw dollars,  but an accurate estimation1 of how happy would it make you, in relative terms, to pick that option, all things considered.  Then rationality is accurate enough a name for optimization of that, isn't it?

That is formally equivalent to calling the utility money and assuming (again, for the sake of mathematical simplification) that that is all you care about.

1: Don't ask me how would you go about attributing a scalar value to the hairy mess of actual human preferences and biases, though.  Game theory doesn't even try to do this.


Most economists retreat away from basing measurements on cardinal utility, instead opting for ordinal utility. That being said, assuming (very big assumption) that you could accurately measure cardinal utility (assuming this existed) of all potential choices, and prove that an agent (person) chose an outcome that was suboptimal in utility, then you have to essentially explore the possibility that human action lacks an element of free will. Or redefine the idea of preferences.
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April 21, 2011, 07:31:42 PM
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accepting 5000/0 is not rational btw. why would you care more about the greedy unknown person taking all the money than the unknown person offering it?
Formally, this assumes that first you try to maximize your own payoff, and that being equal, you try to maximize global utility.

It can be argued that the "unknown person offering" the money has signaled a lower preference for keeping it than the "greedy unknown person" taking it.

This is a minor point, though, and somewhat besides the question.  Just got curious about whether the folks that would take one cent would go all the way to accepting nothing at all.

It really depends where the money is coming from.  If it's wealth that's just created (a $5000 car drops out of the sky) from thin air, it makes sense to create it (unless you sold used cars or something silly where you would personally be hurt).  If it was transfered from one random person to another, and the person transferring it was voluntarily giving it up, then it doesn't matter either way which way you act.
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April 21, 2011, 08:05:57 PM
 #60

I love how everyone is adding new rules and justifications.
if it's a full moon and the other guy is under 30 and I'm wearing pants and it's a weekday and I can negotiate the price and Muslims bomb the royal wedding and China goes on the gold standard and David letterman retires and the money wasn't stolen and it would be used to open a soup kitchen for stray cats,  I'll undoubtedly, probably, almost, conditionally take the money. Unless Bono clubs starving children in Africa for a benefit concert or Porsche builds a new car that isn't a 911 or I didn't have my 20 daily cups of coffee or the guy with the money falls under a bus and we have to have a knife fight to the death (which I never win on the first try anyway) or fukushima finally melts down properly, I mean shit or get off the pot already. how long will they keep propping those cores up like the US economy.

This isn't that complicated. The other guy is trying to buy $4990 for $10. that's just a bad deal.

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