The Ultimatum Game

[tomcollins]

That's pretty much exactly the question.  It is his to divide.  That's directly stated in the OP.

He gets to propose a split, and you get the final say.  That doesn't make the money his.  Until the game is concluded, the money remains the Faucet's property, and neither of you have any a priori claim on it.

There's a rational answer if you can calculate utility.

That's a tautology.  Do you mean that only money needs be taken into account in order to calculate utility?

There is a strong hardwired social expectation for a fair (and I won't even use quotes here) split, and there is an emotional cost in overriding that.  You can decide it's worth it, but if you just ignore this cost, you are, by definition, not being rational.  And once you start factoring any non-monetary factors, the $0.01 vs $4,999.99 Nash equilibrium breaks down.

If you go to the wikipedia page for the Ultimatum Game you'll see that across cultures, almost everyone will reject any offer below some 20%-30%.  So, you see, the vast majority of humanity is very "weak" of character.

This and other experiments suggests that we are hardwired to tend towards collaboration and towards punishing defectors, because it has proven evolutionarily stable.

In a real world where almost nobody will take less than 20%, is asking for $4,999 rational?

In the extreme case you were presented before, after the Splitter has killed your family, would you still accept his $10 vs $4,990?  What do you mean he "deserves" revenge?  That's not any more Nash-rational.  What does the killing of your family have to do with the deal, at all?  Is there something wrong with your character?

You are right that the majority of humans are weak.  That's why we have the problems we do.  It's the few strong that carry the weak.  

Taking someone who has actually wronged me is much different of a case.  What morally wrong act has the splitter committed in the original case?

The optimal play and the "rational" play are two different things.  I've already stated that I would be very unlikely to offer a low offer to my opponent, mainly because I figure he'll be an idiot and overvalue spite.

The interesting thing is, the natural reaction of people is fairly consistent with how one would act in real life, where you don't interact with people just once, there are repetitions to the game, and your reputation travels with you.  Our minds have evolved to play the game of life fairly well without actually thinking about it, which is why most people make a lot of fundamental mistakes for toy problems.

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[The Script]

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.

What about denying them something they have no claim to?  Why is their claim anymore legitimate than the second person?  The Game Owner gives the $5000 to both the people, but gives one of them the decision of distribution and the other a veto over the whole decision.  Neither has any "claim" on it or they both do.

[tomcollins]

Another interesting thing to think about is I am almost positive you could game the results by playing the same game but worded differently.

You go to a study.  They pick one person at random who has won a $5000 jackpot.  Let them get excited about it.  But then they draw a second person and say "this person is allowed to take as much of your jackpot as they want.  You can choose to accept what is left (and let the "stealer" keep what he took), or you can give all the money back.  You also can try to convince them to not take much."  I'd bet that the person choosing to accept or decline the amount would even reject a 50-50 split fairly often.  Even in the cases where he accepts the offer, he'd probably hold more animosity to the "stealer" than the first one.  He'd probably be mad at him when he takes half, but in the negotiating version, he'd be very happy to get half (or at least be neutral).

In a second version, you play the same game, except the second person "wins" the lottery.  He is allowed to give you some of the money.  If you choose to not accept what he gives you, he loses his prize.  In this game, I would expect small offers to be accepted much more easily and happily.  It wasn't your money to begin with, and he's just giving you some out of kindness and to ensure you don't screw him.  You won't be as mad at him for giving you a low amount since you weren't expecting any.

But in all 3 cases, it's the exact same game, all the rules are the same, it's just how the situation is presented is different.  You'd get widely differing results.  This is because people are absolutely terrible about logically thinking about situations.  They are very much emotion driven.  I find that to be a huge weakness.  It happens to be right in a lot of cases, and a lot of people are just not capable of logical thought processes, so it's better to have a compass that happens to point in the right direction even if you can't find north on your own.  It's a small minority of people who are capable of dissecting situations, actually stepping away from the problem, breaking it down, and figuring out their best course of action.  Another reason why democracy is awful.

[tomcollins]

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.

What about denying them something they have no claim to?  Why is their claim anymore legitimate than the second person?  The Game Owner gives the $5000 to both the people, but gives one of them the decision of distribution and the other a veto over the whole decision.  Neither has any "claim" on it or they both do.

That's the deal.  There's no such thing as "giving $5000 to both people".  It doesn't exist.  It can't exist in that situation.  If he gave me the money, it's mine and I walk away with it.  But I can't.  But he set up a game, where I *could* get $5000.  As the second person, the money does not even become remotely mine until the offer is made.  It is only at that instant that the money becomes mine.  I can take it, or leave it.  Before that was just an illusion that it was mine.  No different than the money that a Nigerian Prince promises me.

[BitterTea]

Another interesting thing to think about is I am almost positive you could game the results by playing the same game but worded differently.

Are you saying that you would react exactly the same in the two different scenarios?

That you feel there would be a difference in the reactions of others makes me believe that you would react differently as well, but you consider yourself to be more rational (for some - your - definition of rational) than others.

[NghtRppr]

As the second person, the money does not even become remotely mine until the offer is made.

As the first person, the money isn't even remotely yours until the second person accepts the offer, of which there is no guarantee. You've clearly already made up your mind and are now grasping at straws to justify your conclusion. Rational thinking is more effective when the conclusion comes at the end of debate, rather than at the beginning.

[tomcollins]

Another interesting thing to think about is I am almost positive you could game the results by playing the same game but worded differently.

Are you saying that you would react exactly the same in the two different scenarios?

That you feel there would be a difference in the reactions of others makes me believe that you would react differently as well, but you consider yourself to be more rational (for some - your - definition of rational) than others.

Gut instinct would of course kick in.  I might be more likely to view something as unfair.  But when rubber meets the road, I'm not turning down free money to screw someone over.

There's a difference between having emotions and being ruled by emotions.  I absolutely am better at removing my emotions from the equation than most people (50%+ of people are women).  Even a vast majority of people.

[tomcollins]

As the second person, the money does not even become remotely mine until the offer is made.

As the first person, the money isn't even remotely yours until the second person accepts the offer, of which there is no guarantee. You've clearly already made up your mind and are now grasping at straws to justify your conclusion. Rational thinking is more effective when the conclusion comes at the end of debate, rather than at the beginning.

You are correct.  It's not yours until then.  There are no straws to be grasped at.  We are only talking about my actions as the second person.  As the first person, you need to play psychologically, not logically.

[The Script]

Another interesting thing to think about is I am almost positive you could game the results by playing the same game but worded differently.

Are you saying that you would react exactly the same in the two different scenarios?

That you feel there would be a difference in the reactions of others makes me believe that you would react differently as well, but you consider yourself to be more rational (for some - your - definition of rational) than others.

Gut instinct would of course kick in.  I might be more likely to view something as unfair.  But when rubber meets the road, I'm not turning down free money to screw someone over.

There's a difference between having emotions and being ruled by emotions.  I absolutely am better at removing my emotions from the equation than most people (50%+ of people are women).  Even a vast majority of people.

I can see the logic in accepting the deal (even if you thought you "deserved" more), because free money is free money.  But out of curiosity, how far would you personally extend that?  If you were offered only $0.01, would you still take the deal?  One cent is not really going to benefit you at all. What about $0?  You would not gain anything, but would you still let them have all the money? 

[estevo]

The optimal play and the "rational" play are two different things.  I've already stated that I would be very unlikely to offer a low offer to my opponent, mainly because I figure he'll be an idiot and overvalue spite.

[Emphasis mine]
Your terminology suggests you're seeing this as a game that you play to maximize your score.  The very title of the thread supports that framing.  If that was in the "social contract" of the interaction (as it is in a game of poker) then going cutthroat would be protected from social stigmas by the "magic circle" of the game (just like in poker you can deceive and bluff, in Diplomacy you can stab, or in boxing you can punch, with ideally no hard feelings).  I was intending this more as a metaphor for social interactions in the wild.

What morally wrong act has the splitter committed in the original case?

Both players have equal claim (or lack thereof) on the money.  There's no moral basis for anything but an even split, which is just a sane and socially ingrained default.  As he deviates from an even split, the splitter not only gets utility at the boolean's expense, but he causes more harm than value he gets (because of the added grief of abuse).  By increasing the risk of a veto, this disequilibrium further reduces the global expected value.

You may contest that there are "irrational" forces at play here, like the expectation of an equal return as the basis of what is "fair" in absence of other claims, and the drive to punish exploitive behavior.  The conviction with which you call these irrational and idiotic suggests that you hold a reductionistic belief that game theory is straightforwardly applicable to (even stylized) real life interactions, despite assumptions like unbounded "rationality" on all parts, perfect information, perfect selfishness of actors, constrained time domain, isolated strategy space.

Don't you acknowledge the possibility that these "irrational" assumptions and biases may be evolutionarily stable, advantageous features for individuals and societies?

You do acknowledge that if you were the splitter, you'd be more generous than you think you "should", in anticipation for "idiocy".  Of course, it's the prevalence of such actual "idiocy" that makes it a credible threat.  And that, in turn, gets "idiots" a better payoff in this game.  So isn't this "smart", in a way?

[tomcollins]

Another interesting thing to think about is I am almost positive you could game the results by playing the same game but worded differently.

Are you saying that you would react exactly the same in the two different scenarios?

That you feel there would be a difference in the reactions of others makes me believe that you would react differently as well, but you consider yourself to be more rational (for some - your - definition of rational) than others.

Gut instinct would of course kick in.  I might be more likely to view something as unfair.  But when rubber meets the road, I'm not turning down free money to screw someone over.

There's a difference between having emotions and being ruled by emotions.  I absolutely am better at removing my emotions from the equation than most people (50%+ of people are women).  Even a vast majority of people.

I can see the logic in accepting the deal (even if you thought you "deserved" more), because free money is free money.  But out of curiosity, how far would you personally extend that?  If you were offered only $0.01, would you still take the deal?  One cent is not really going to benefit you at all. What about $0?  You would not gain anything, but would you still let them have all the money? 

It partially comes down to how the money is generated.  If it's cash,  it's not created out of thin air (unless Ben Bernake is in charge of the experiment).  If it was created out of thin air, it's stealing from everyone who has cash, including myself, so I reject it.  If it's actual wealth that's created out of thin air, I accept it, since it's better that someone has it than no one.  There are a ton of other variables, if I didn't like the guy for whatever reason, maybe I reject it (I'll spite someone for a penny, who hasn't thrown a penny at someone to screw with them?).  If the money would have been donated to charity, maybe I reject a quite high offer, even $500, since I'd pay $500 to have $5000 donated to charity.

A penny is pretty close to nothing.  I don't value pennies much.  I won't pick them up, I'll just throw them at things for target practice while I'm bored.  But any offer that would be an amount I'd pick up off the ground would be an instant accept.  Exceptions would be if the other person is someone I *really* wouldn't want to have the money.  For example, if someone was going to go out and get drunk then drive home because of getting the money.  There might be a price I'd pay to prevent that.  But it's surprisingly a low one.  If it were someone truly despicable, such as a murderer, a child rapist, etc..., I might sacrifice something myself to punish them.  But I certainly wouldn't sacrifice just because someone is a good game player.  So a dollar, I take in all but the most extreme cases.

[tomcollins]

The optimal play and the "rational" play are two different things.  I've already stated that I would be very unlikely to offer a low offer to my opponent, mainly because I figure he'll be an idiot and overvalue spite.

[Emphasis mine]
Your terminology suggests you're seeing this as a game that you play to maximize your score.  The very title of the thread supports that framing.  If that was in the "social contract" of the interaction (as it is in a game of poker).  I was intending this more as a metaphor for social interactions in the wild.

I use the word "play" in many contexts.  Do not read into it as just a game.

What morally wrong act has the splitter committed in the original case?

Both players have equal claim (or lack thereof) on the money.  There's no moral basis for anything but an even split, which is just a sane and socially ingrained default.  As he deviates from an even split, the splitter not only gets utility at the boolean's expense, but he causes more harm than value he gets (because of the added grief of abuse).  By increasing the risk of a veto, this disequilibrium further reduces the global expected value.

You may contest that there are "irrational" forces at play here, like the expectation of an equal return as the basis of what is "fair" in absence of other claims, and the drive to punish exploitive behavior.  The conviction with which you call these irrational and idiotic suggests that you hold a reductionistic belief that game theory is straightforwardly applicable to (even stylized) real life interactions, despite assumptions like unbounded "rationality" on all parts, perfect information, perfect selfishness of actors, constrained time domain, isolated strategy space.

Don't you acknowledge the possibility that these "irrational" assumptions and biases may be evolutionarily stable, advantageous features for individuals and societies?

You do acknowledge that if you were the splitter, you'd be more generous than you think you "should", in anticipation for "idiocy".  Of course, it's the prevalence of such actual "idiocy" that makes it a credible threat.  And that, in turn, gets "idiots" a better payoff in this game.  So isn't this "smart", in a way?

There's no moral basis for an even split either.  It just appears that way since the question is worded as an equal claim.  But there is not an equal claim, as both players have different rules they must follow.  If they were just told to take the money from a pile, and if they both could reject back and forth until they both agreed, and there was parity, it could be said they have equal claim.  But the rules specifically make it so they are unequal participants.

I pretty much already stated your last point, that this game is a very special case and not something likely to happen in normal life.  In normal life, especially during most of human evolution, people interacted with small groups on a repeated basis.  Reputation was (and still is), a HUGE part of life.  If someone is seen as generous, he will get more generosity from his neighbors.  Those who follow through with generosity will get even more in return.  By having that as the "default" interaction people have, it allowed people to trust each other, become more successful, and grow society.  If you played this game in multiple rounds, you would see a much more fair outcome go forward.  Punishing someone is not just spiteful, but a teaching lesson where you actually have the chance to benefit.  If I punish someone by giving me a small reward, next time, they may give me a bigger amount.  The game shifts more toward the person who stops things, who will play hardball more initially.  Early rounds he may even reject fair offers to try to show he means business, and then the first person will give up and start offering very large amounts.  Depending on how many rounds there are, the first person may choose to play hardball back, and refuse to offer anything too much.  Eventually it will swing to 50-50, which is what you'd expect in normal human interactions.

The key here is the situation deviates from typical human interactions and situations.  The trouble is, normal everyday life now is considerably different than it was 20,000 years ago.  But we haven't really evolved,  We're still the same hairless apes of 100,000 years ago.  To get beyond that, we need to use our brains instead of our emotions.  It was the few people who actually are capable and actually chose to use their brain that are the reason we are arguing on the internet instead of sitting in caves picking bugs out of each others heads.  It certainly wasn't the emotional reactions that got us past that point.

[estevo]

The positions of the splitter and boolean are asymmetric.  That doesn't imply that their moral claims on the money need be different.  It's "free money" for both, zero versus zero claim.  Zero equals zero.

On what basis do you assume that you can derive moral claims from expected outcome in an idealized, partial, and demonstrably unrealistic model of the conflict?

You lament that our wetware is obsolete and that we don't do our best to conform to an abstract, reductionist, disembodied model of rationality.  Well, we are what we are!  And the very concepts of utility and value, that are at the center of mathematical models of rationality, ultimately derive from the obsolete craves and ambitions you despise.  

What's the point of sex, 99% of the time?  What's the point of art?  Of anything, really?  You can tell yourself any story about what you want in life, you can build an intricate symbolic structure representing a rationalization about why you even bother waking up in the morning.  No matter how high and imposing the towers, that castle will ultimately rest on your mostly obsolete emotions.

Rationality helped a fair bit bring us away from the caves, but what ultimately took us from there, and what made that an improvement, were the same ultimately pointless craves and ambitions that got us in there in the first place.

So I repeat: overriding our emotions is often a requisite of rationality.  But ignoring our emotions is not automatically rational.  There must be some worthy reward, current or expected, to warrant the sacrifice.

Even if it's just "practicing restraint for when I need it."

In your case (and sorry for gratuitous speculation, but even if I'm wrong this illustrates my reasoning), accepting the $0.01 allows you to conform to a respected model of rationality and thus tell yourself, and signal to others, that you are above most of the hairless monkeys.  Bet that feels good, doesn't it?  This could be traced back to various sorts of primitive psychosocial mechanisms (self-image, self-esteem, dominance, status, ...).

In my case, $0.01 or $10 are not nearly worth the outrage of being abused.  The delta between that suffering and the satisfaction of giving greedy pig Splitter the finger is worth more than that.  Other people pay comparable amounts to get a movie or book and experience a weak version of similar emotions by proxy.  Who are you to tell me that my action is irrational?

And immoral?  My choice passes most sniff tests: Golden Rule, check.  "Think global, act local", sure.  I wouldn't mind if everyone did as me.

[Littleshop]

For me it is 10%.  I would need at least 10% of the money to take the offer.  I would offer a 50/50 split myself if I had done absolutely nothing and the money was free and clear. 

[tomcollins]

The positions of the splitter and boolean are asymmetric.  That doesn't imply that their moral claims on the money need be different.  It's "free money" for both, zero versus zero claim.  Zero equals zero.

On what basis do you assume that you can derive moral claims from expected outcome in an idealized, partial, and demonstrably unrealistic model of the conflict?

You lament that our wetware is obsolete and that we don't do our best to conform to an abstract, reductionist, disembodied model of rationality.  Well, we are what we are!  And the very concepts of utility and value, that are at the center of mathematical models of rationality, ultimately derive from the obsolete craves and ambitions you despise.  

What's the point of sex, 99% of the time?  What's the point of art?  Of anything, really?  You can tell yourself any story about what you want in life, you can build an intricate symbolic structure representing a rationalization about why you even bother waking up in the morning.  No matter how high and imposing the towers, that castle will ultimately rest on your mostly obsolete emotions.

Rationality helped a fair bit bring us away from the caves, but what ultimately took us from there, and what made that an improvement, were the same ultimately pointless craves and ambitions that got us in there in the first place.

So I repeat: overriding our emotions is often a requisite of rationality.  But ignoring our emotions is not automatically rational.  There must be some worthy reward, current or expected, to warrant the sacrifice.

Even if it's just "practicing restraint for when I need it."

In your case (and sorry for gratuitous speculation, but even if I'm wrong this illustrates my reasoning), accepting the $0.01 allows you to conform to a respected model of rationality and thus tell yourself, and signal to others, that you are above most of the hairless monkeys.  Bet that feels good, doesn't it?  This could be traced back to various sorts of primitive psychosocial mechanisms (self-image, self-esteem, dominance, status, ...).

In my case, $0.01 or $10 are not nearly worth the outrage of being abused.  The delta between that suffering and the satisfaction of giving greedy pig Splitter the finger is worth more than that.  Other people pay comparable amounts to get a movie or book and experience a weak version of similar emotions by proxy.  Who are you to tell me that my action is irrational?

And immoral?  My choice passes most sniff tests: Golden Rule, check.  "Think global, act local", sure.  I wouldn't mind if everyone did as me.

You don't understand the difference between enjoying something and making an incorrectly being able to analyze what you would enjoy more?

Accepting $.01 in a situation with a stranger I'll never see again, who cares what he thinks?  I'm not trying to impress him or anyone else.

Who is being abused again?  You are only letting yourself think you are being abused.  You were tricked into thinking that you are getting a raw deal.  The same reason why my other two situations, you might think you are being abused even more, or not abused at all, just because someone worded it slightly different.

[tomcollins]

For me it is 10%.  I would need at least 10% of the money to take the offer.  I would offer a 50/50 split myself if I had done absolutely nothing and the money was free and clear. 

If I offered you 1% of $100 million, you'd decline?

[Terpie]

The positions of the splitter and boolean are asymmetric.  That doesn't imply that their moral claims on the money need be different.  It's "free money" for both, zero versus zero claim.  Zero equals zero.

On what basis do you assume that you can derive moral claims from expected outcome in an idealized, partial, and demonstrably unrealistic model of the conflict?

You lament that our wetware is obsolete and that we don't do our best to conform to an abstract, reductionist, disembodied model of rationality.  Well, we are what we are!  And the very concepts of utility and value, that are at the center of mathematical models of rationality, ultimately derive from the obsolete craves and ambitions you despise.  

What's the point of sex, 99% of the time?  What's the point of art?  Of anything, really?  You can tell yourself any story about what you want in life, you can build an intricate symbolic structure representing a rationalization about why you even bother waking up in the morning.  No matter how high and imposing the towers, that castle will ultimately rest on your mostly obsolete emotions.

Rationality helped a fair bit bring us away from the caves, but what ultimately took us from there, and what made that an improvement, were the same ultimately pointless craves and ambitions that got us in there in the first place.

So I repeat: overriding our emotions is often a requisite of rationality.  But ignoring our emotions is not automatically rational.  There must be some worthy reward, current or expected, to warrant the sacrifice.

Even if it's just "practicing restraint for when I need it."

In your case (and sorry for gratuitous speculation, but even if I'm wrong this illustrates my reasoning), accepting the $0.01 allows you to conform to a respected model of rationality and thus tell yourself, and signal to others, that you are above most of the hairless monkeys.  Bet that feels good, doesn't it?  This could be traced back to various sorts of primitive psychosocial mechanisms (self-image, self-esteem, dominance, status, ...).

In my case, $0.01 or $10 are not nearly worth the outrage of being abused.  The delta between that suffering and the satisfaction of giving greedy pig Splitter the finger is worth more than that.  Other people pay comparable amounts to get a movie or book and experience a weak version of similar emotions by proxy.  Who are you to tell me that my action is irrational?

And immoral?  My choice passes most sniff tests: Golden Rule, check.  "Think global, act local", sure.  I wouldn't mind if everyone did as me.

slow clap....

[Littleshop]

For me it is 10%.  I would need at least 10% of the money to take the offer.  I would offer a 50/50 split myself if I had done absolutely nothing and the money was free and clear. 

If I offered you 1% of $100 million, you'd decline?

No, for $5000 I would decline 1%.  It is irrational but I would do it. 

For $100 million I would take 1%. 

[estevo]

You don't understand the difference between enjoying something and making an incorrectly being able to analyze what you would enjoy more?

I don't understand.  Guess something got lost in editing here.  Could you please complete or rephrase this?

You were tricked into thinking that you are getting a raw deal.  The same reason why my other two situations, you might think you are being abused even more, or not abused at all, just because someone worded it slightly different.

I claim that those other two situations are actually different, and the fact that they reduce to the same mathematical model only attests to the insufficiency of the model for these applications.  The anchor you establish with the initial claims makes it a morally different situation.

You may go to further extremes: imagine that I sue you for bogus claims but you can't afford a proper defense.  I offer to settle for all your stuff minus one dollar.  You can refuse, but let's imagine that the legal system in your country is broken enough that in that case you lose *all* of your money to legal expenses.  If we stick to money, the Nash equilibrium is the same.  Is this the same situation, only camouflaged to trick you into feeling more ripped off?  Would you still give me all the money but one dollar?

[Alex Beckenham]

Tom, I gotta say a big thank you.

I've read the entire thread now and you've pretty much typed out and submitted my views accurately.

The only other thing I can see influencing my decision is what effort would be involved in actually getting the money (eg. If I were offered $0.10, would I have to take that as a little metal coin and go deposit it into my bank?).

If it was purely electronic with no inconvenience caused to me, I'd take any offer.