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Author Topic: The Ultimatum Game  (Read 16210 times)
tomcollins
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April 21, 2011, 08:27:38 PM
 #61

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.

You are trying to burn $4990 in someone else's wallet for $10.  Who is making the bad deal again?
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estevo
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April 21, 2011, 08:41:04 PM
 #62

I don't agree that rejecting the $10 deal can be characterized as an act of jealousy or envy.  Let me illustrate with a few examples less loaded than the grandma heritage one.

Variant 1:

Imagine that the mysterious stranger came with the following proposal instead:  "I have $5000 to give you two guys, and I will split it randomly.  You don't get to further negotiate your shares, only take it or leave it.  If both accept, you get your share.  If either rejects, neither gets money."  Seeing that your expected outcome is $2500 and you have nothing to lose, you both immediately accept.  You get to confirm that the randomization method (die rolls, roulette, computer PRN generator, whatever) is fair.

So, you both cross your fingers and hope for the best.  Unfortunately for you, the dice give $10 to you and $4990 to the other guy.  Uncomfortably concealing his mix of joy and worry, the other guy accepts his $4990.  What do you do?

Variant 2:

The mysterious stranger proposes: "I'm feeling generous and I'd like to give away $5,000.  But honestly, I like you [smiles and taps the other guy in the shoulder] better, so have $4,990$.  I hope you [looks at you as if counting the nanoseconds to take his eyes elsewhere] don't mind you get $10.  You don't get to negotiate, just say yes or no, now.  If either of you rejects the offer nobody gets a dollar."

What would you do?

Note that I'm not saying that the above reformulations are equivalent to the original one.  They're equivalent in the game theoretical sense, but very different psychologically.  Actually, I'm using tomcollings's technique here to argue the opposite point.  I would have a different response to these reformulations (and to the ones advanced by tomcollings) than I would have to the original one.  But I argue that's not because I'm inconsistent or hypocritical, but because there are legitimate reasons why the differences in framing matter.
estevo
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April 21, 2011, 08:53:01 PM
 #63

@deadlizard: the original "game" is simple in its terms, and for every one person answering, the reply is simple and even obvious.  But the psychological and social implications are varied and complex, as the variety of responses, and reactions to responses, attests.  The little variations on the game help analyze our motivations and explore that psychological space.

For example, my latest reformulations try to prove that what drives most of us who would reject the original deal is not envy of jealousy, on the basis that most of us would respond differently to the modified games.
NghtRppr
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April 21, 2011, 08:54:59 PM
 #64

I find spite to be irrational.

All human emotions are nonrational, not irrational. If I tried to spite you by burning my house down and leaving yours completely unharmed, that would be irrational. Anyways, the difference between outright charity and taking advantage of a position of power has been explained to you. I'm sorry if you can't/won't see it.
tomcollins
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April 21, 2011, 08:55:43 PM
 #65

I don't agree that rejecting the $10 deal can be characterized as an act of jealousy or envy.  Let me illustrate with a few examples less loaded than the grandma heritage one.

Variant 1:

Imagine that the mysterious stranger came with the following proposal instead:  "I have $5000 to give you two guys, and I will split it randomly.  You don't get to further negotiate your shares, only take it or leave it.  If both accept, you get your share.  If either rejects, neither gets money."  Seeing that your expected outcome is $2500 and you have nothing to lose, you both immediately accept.  You get to confirm that the randomization method (die rolls, roulette, computer PRN generator, whatever) is fair.

So, you both cross your fingers and hope for the best.  Unfortunately for you, the dice give $10 to you and $4990 to the other guy.  Uncomfortably concealing his mix of joy and worry, the other guy accepts his $4990.  What do you do?

Variant 2:

The mysterious stranger proposes: "I'm feeling generous and I'd like to give away $5,000.  But honestly, I like you [smiles and taps the other guy in the shoulder] better, so have $4,990$.  I hope you [looks at you as if counting the nanoseconds to take his eyes elsewhere] don't mind you get $10.  You don't get to negotiate, just say yes or no, now.  If either of you rejects the offer nobody gets a dollar."

What would you do?

V1- I take any offer.

V2 - I take any offer.

I'd guess some people reject the offer even though it hurts an innocent guy and benefits the guy who is "unfair".
tomcollins
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April 21, 2011, 08:56:47 PM
 #66

I find spite to be irrational.

All human emotions are nonrational, not irrational. If I tried to spite you by burning my house down and leaving yours completely unharmed, that would be irrational. Anyways, the difference between outright charity and taking advantage of a position of power has been explained to you. I'm sorry if you can't/won't see it.

What's wrong with taking advantage of a position of power so long as you are not harming someone?  If you are playing poker and get AA, do you fold because you might be taking advantage of your position of power?
barbarousrelic
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April 21, 2011, 09:00:25 PM
 #67

This game is similar to the Cold War nuclear standoff between the USA and the USSR. Let's say that country A detects that Country B has launched 500 nuclear missiles. Should Country A fire back? What's the point? Country A will still be completely destroyed. Launching a counterattack won't help the situation.

However, it is in each country's interest to make the other country think they will fire back in this situation, to deter the first strike. It is in each country's interest to appear irrational.

Do not waste your time debating whether Bitcoin can work. It does work.

"Early adopters will profit" is not a sufficient condition to classify something as a pyramid or Ponzi scheme. If it was, Apple and Microsoft stock are Ponzi schemes.

There is no such thing as "market manipulation." There is only buying and selling.
tomcollins
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April 21, 2011, 09:03:24 PM
 #68

This game is similar to the Cold War nuclear standoff between the USA and the USSR. Let's say that country A detects that Country B has launched 500 nuclear missiles. Should Country A fire back? What's the point? Country A will still be completely destroyed. Launching a counterattack won't help the situation.

However, it is in each country's interest to make the other country think they will fire back in this situation, to deter the first strike. It is in each country's interest to appear irrational.

Firing back is neutral if anything, but it's a good example.  Obviously real world examples are a bit flawed since even a nuclear attack would not destroy everything, some people would live, etc...

Even so, firing back and killing a lot of innocent people just because they have asshole leaders is pretty disgusting.
NghtRppr
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April 21, 2011, 09:06:24 PM
 #69

What's wrong with taking advantage of a position of power so long as you are not harming someone?  If you are playing poker and get AA, do you fold because you might be taking advantage of your position of power?

Who said anything about it being wrong? I said there's a difference between that and charity. You do understand the difference, right?
tomcollins
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April 21, 2011, 09:08:12 PM
 #70

What's wrong with taking advantage of a position of power so long as you are not harming someone?  If you are playing poker and get AA, do you fold because you might be taking advantage of your position of power?

Who said anything about it being wrong? I said there's a difference between that and charity. You do understand the difference, right?

Why is him giving you anything beyond the first penny (or whatever significant amount of money to move you from neutral to taking action) any more than charity?  It's not your money, is it?

Put it another way.  If I end up with a package of $100 on my door, I am happy.  But some people, if they find out their neighbors got $1000, are no longer happy about it.
estevo
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April 21, 2011, 09:08:25 PM
 #71

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V1- I take any offer.

V2 - I take any offer.
I, who would reject the offer in the original formulation, would take these offers.

Quote
I'd guess some people reject the offer even though it hurts an innocent guy and benefits the guy who is "unfair".
Perhaps.  Then you can call them envious and jealous, respectively.  It's less plausible, though, that the people who, like me, reject the original offer but accept these reformulations, are acting out of envy or jealousy, since if I was envious I would not accept either V1 or V2, and if I was jealous I wouldn't accept V2.
NghtRppr
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April 21, 2011, 09:11:23 PM
 #72

It's not your money, is it?

It's our money, if and only if we can settle on how to distribute it.
estevo
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April 21, 2011, 10:17:58 PM
 #73

@tomcollins: It's not his money either.  The person who originally had it (let's call him the Faucet, for agility, and similarly call the other guy the Splitter and you the Boolean, since you only get to say yes or no) asked you to "split" it somehow.

Somehow you seem to imply that by putting the Splitter in the favorable side of a Nash Equilibrium, the Faucet has effectively given him the whole $5,000, so all that is left for you is to try and extort all you can from him, from a position of no legitimacy and hardly any force.  That is the game theoretical, abstractly "rational" framing, the one that ignores all human emotion and common sense conventions about fairness.  Very few people in the world would have seen it this way in pre-Nash times.

As we know, there are emotions and instincts at play.  Issues of self-image.  Empathy.  Perhaps genetically or culturally inherited notions and heuristics regarding property and fairness.  I can fight those notions, try to abstract away my own human nature, in pursuit of a rational ideal.  That, even to the extent we assume it's possible, doesn't come without a cost.  Those factors modify the real payoff matrix.  It's not purely about money.  Not even for those who act like it was (more on this later).

And what is my motivation to fight my own instincts?  The payoff I get for that effort is warping the game so I'm at the extreme sucker end.  Is that rational?

Repressing or overcoming emotion is often a requisite of rationality.  But that doesn't mean it is, in itself, automatically a rational thing to do.  For that, a benefit needs to be derived.

I argue that people who opt for --let's call it-- the Nash strategy do that self-restraint work in order to defend a self-image as "rational" beings, for a culturally established notion of rationality.  Nothing wrong with that, but it's a tradeoff, not inherently *the* rational thing to do.

Because it gets recursive and messy.  Once you convince yourself that going against primal emotions is the "good" thing to do, and if you manage to hide the costs under the carpet, then you won't feel as much of a sucker, so it will really "cost" less to you.  For example, by convincing yourself that the Splitter is not being a selfish greedy pig, you may actually dampen the primal outrage of being abused, and by doing that you may be justifying a greedy Splitter position.

This recursiveness means that beliefs on the game may be self-realising.

tl;dr:  Emotions alter not only what seems rational, but what is rational.  Beliefs about rationality, in turn, alter emotions, and thus, recursively, what is rational.  Any attempt at rationalizing the game transforms it, in some sort of Heisenberg uncertainty principle.  So a static game theoretical analysis that conflates money with utility doesn't settle the debate of what is rational.  

tl;dr's tl;dr: For all practical purposes, there is no rational answer.  What's right for you depends on your personality and cultural baggage.
tomcollins
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April 21, 2011, 10:29:50 PM
 #74

It's not your money, is it?

It's our money, if and only if we can settle on how to distribute it.

But it's not your money.  The only money that's yours is what is offered to you, if you so accept.
tomcollins
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April 21, 2011, 10:34:34 PM
 #75

@tomcollins: It's not his money either.  The person who originally had it (let's call him the Faucet, for agility, and similarly call the other guy the Splitter and you the Boolean, since you only get to say yes or no) asked you to "split" it somehow.

Somehow you seem to imply that by putting the Splitter in the favorable side of a Nash Equilibrium, the Faucet has effectively given him the whole $5,000, so all that is left for you is to try and extort all you can from him, from a position of no legitimacy and hardly any force.  That is the game theoretical, abstractly "rational" framing, the one that ignores all human emotion and common sense conventions about fairness.  Very few people in the world would have seen it this way in pre-Nash times.

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

As we know, there are emotions and instincts at play.  Issues of self-image.  Empathy.  Perhaps genetically or culturally inherited notions and heuristics regarding property and fairness.  I can fight those notions, try to abstract away my own human nature, in pursuit of a rational ideal.  That, even to the extent we assume it's possible, doesn't come without a cost.  Those factors modify the real payoff matrix.  It's not purely about money.  Not even for those who act like it was (more on this later).

And what is my motivation to fight my own instincts?  The payoff I get for that effort is warping the game so I'm at the extreme sucker end.  Is that rational?

Repressing or overcoming emotion is often a requisite of rationality.  But that doesn't mean it is, in itself, automatically a rational thing to do.  For that, a benefit needs to be derived.

I argue that people who opt for --let's call it-- the Nash strategy do that self-restraint work in order to defend a self-image as "rational" beings, for a culturally established notion of rationality.  Nothing wrong with that, but it's a tradeoff, not inherently *the* rational thing to do.

Because it gets recursive and messy.  Once you convince yourself that going against primal emotions is the "good" thing to do, and if you manage to hide the costs under the carpet, then you won't feel as much of a sucker, so it will really "cost" less to you.  For example, by convincing yourself that the Splitter is not being a selfish greedy pig, you may actually dampen the primal outrage of being abused, and by doing that you may be justifying a greedy Splitter position.

This recursiveness means that beliefs on the game may be self-realising.

tl;dr:  Emotions alter not only what seems rational, but what is rational.  Beliefs about rationality, in turn, alter emotions, and thus, recursively, what is rational.  Any attempt at rationalizing the game transforms it, in some sort of Heisenberg uncertainty principle.  So a static game theoretical analysis that conflates money with utility doesn't settle the debate of what is rational.  

tl;dr's tl;dr: For all practical purposes, there is no rational answer.  What's right for you depends on your personality and cultural baggage.

There's a rational answer if you can calculate utility.  But either way, getting upset at someone over this is silly.  Actually causing yourself harm to get back at them, for something so silly is quite telling about one's character.  It shows extreme weakness in your character.
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April 21, 2011, 10:44:39 PM
 #76

But it's not your money.

Of course it's not my money. It's our money, if and only if we can settle on how to distribute it. I think I just said that. Of course, it's not your money either. You're mistakenly considering that the money is already yours but if it were then you wouldn't need me to approve of the distribution. You could keep it no matter what. That's not the case. Therefore, it's not charity on your part anymore than it's charity on my part.

Read the first post again.

Quote
She will give us 5,000$ if we can agree on how to split it

Emphasis mine. Until we agree on how to split it up, the money still belongs to her. You're wrong. Just admit it so we can get on with our lives.
tomcollins
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April 21, 2011, 11:10:18 PM
 #77

But it's not your money.

Of course it's not my money. It's our money, if and only if we can settle on how to distribute it. I think I just said that. Of course, it's not your money either. You're mistakenly considering that the money is already yours but if it were then you wouldn't need me to approve of the distribution. You could keep it no matter what. That's not the case. Therefore, it's not charity on your part anymore than it's charity on my part.

Read the first post again.

Quote
She will give us 5,000$ if we can agree on how to split it

Emphasis mine. Until we agree on how to split it up, the money still belongs to her. You're wrong. Just admit it so we can get on with our lives.

Your being plural.  Our = your for the sake of discussion.  It's not anyone's money until it gets agreed upon.

I think that's why you are looking at this incorrectly.  If he gets to decide how much you get, clearly it's not even a share of your money.  You cannot possess something you don't possess.
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April 21, 2011, 11:16:13 PM
 #78

If he gets to decide how much you get, clearly it's not even a share of your money.

Wrong again. I get to decide how much the other person gets, nothing or whatever they suggested. They are merely narrowing down the options. I'm the one that makes the actual decision.
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April 21, 2011, 11:18:10 PM
 #79

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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.

Quote
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?
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April 21, 2011, 11:21:03 PM
 #80

Is there something wrong with your character?

I think we should all quit making this personal. It's a sign of weak character. (irony)
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