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Author Topic: The Ultimatum Game  (Read 16213 times)
eMansipater
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April 22, 2011, 03:28:31 AM
 #101

The problem with long threads is that it takes too long to read them, and I haven't done so.  However, this is an interesting topic.

Personally, I would offer 50/50 to someone whether they knew about game theory or not.

And, because of knowing game theory, I would refuse any offer of less than 50% under most circumstances.

The reason is simple:  taking a less-than-50% offer is only optimal with respect to the monetary variable in the question.  With respect to the social variable, there's nothing to be gained by making anti-social people wealthy.  And I have no reason to believe that me gaining 2499 bucks or less would outweigh the value, with respect to society at large, of sending a clear message to this person.

The reason for the "most circumstances" variable is that the social variable could be modified in other ways.  I just assumed for the sake of simplification that I am playing the game with a complete stranger whose identity I don't know.  And yes, the answer to this question does become very complicated if the amount to be split were more like 5 million.  I would then have to do a much more complex cost-benefit analysis over the social variable.

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April 22, 2011, 03:58:23 AM
 #102

The problem with long threads is that it takes too long to read them, and I haven't done so.  However, this is an interesting topic.
tl;dr version
Code:
10 subjective opinion
20 I'm right and you're wrong
30 'fraid not
40 'fraid so
50 GOTO 30

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April 22, 2011, 04:51:32 AM
 #103

When deciding whether to take the deal or not, i would weightt my gains in absolute terms (ignoring the total amount that got splitted) versus how much my decision would teach the other guy to be a better person; if what i would be paid was a big amount, even if it was just a small percentage of the even greater amount that got splitted, i would be more inclined to overlook the unfairness of the split, but if i would only get paid a more insignificant amount, i would be more inclined to not take the deal to teach the other guy to not be so selfish; but on the other hand if the amount the other guy gets even after giving me only a small fraction is already insignificant, rejecting the deal wouldn't teach much, and even a small amount of free money is already better than no money at all, so in such circunstances i would be more inclined to take the deal anyway.

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April 22, 2011, 05:07:04 AM
 #104

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.

And being an "idiot" this player will come out way, way better off than otherwise. Doesn't sound very idiotic to me.
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April 22, 2011, 07:13:49 AM
 #105

The problem with long threads is that it takes too long to read them, and I haven't done so.  However, this is an interesting topic.
tl;dr version
Code:
10 subjective opinion
20 I'm right and you're wrong
30 'fraid not
40 'fraid so
50 GOTO 30

Heh-heh-heh. You're funny...but don't worry, looks aren't everything.   Wink
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April 22, 2011, 07:21:40 AM
 #106


Invite everybody involved in the game to pray together and to let themselves be filled with the Holy Spirit for guidance on who should leave with the money or if it should all be donated to a worthy charity?

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April 22, 2011, 07:52:56 AM
 #107

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.

Damn, Estevo.  I wish you lived in my town.  I would buy you a beer at the pub and we would talk for hours.  Smiley
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April 22, 2011, 08:04:33 AM
 #108

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.

So you are saying that you would turn down free money to spite someone if the price was low enough or the situation was just right?  That doesn't make you any better than the rest of us, you just have a different set of preferences.  If I give up $50 to "spite" Splitter (or "teach him a lesson"), then you say I am irrational or an ape ruled by emotions, but you would do it if the situation warranted it (in your opinion) or the price was sufficiently low.  It's the same behavior simply shifted by your specific morals, ethics, utility values and preferences.
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April 22, 2011, 01:03:46 PM
 #109

It is impossible for a person to 'override emotion.' No decision can ever be made without emotion, you can only substitute one emotion for another. In this case, you can choose between the good feelings you get from receiving the most money for the good feelings you get for protecting your pride.

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April 22, 2011, 02:32:10 PM
 #110

The problem with long threads is that it takes too long to read them, and I haven't done so.  However, this is an interesting topic.

Personally, I would offer 50/50 to someone whether they knew about game theory or not.

And, because of knowing game theory, I would refuse any offer of less than 50% under most circumstances.

The reason is simple:  taking a less-than-50% offer is only optimal with respect to the monetary variable in the question.  With respect to the social variable, there's nothing to be gained by making anti-social people wealthy.  And I have no reason to believe that me gaining 2499 bucks or less would outweigh the value, with respect to society at large, of sending a clear message to this person.

The reason for the "most circumstances" variable is that the social variable could be modified in other ways.  I just assumed for the sake of simplification that I am playing the game with a complete stranger whose identity I don't know.  And yes, the answer to this question does become very complicated if the amount to be split were more like 5 million.  I would then have to do a much more complex cost-benefit analysis over the social variable.

Nothing to be gained... EXCEPT $2499.
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April 22, 2011, 02:33:28 PM
 #111

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.

And being an "idiot" this player will come out way, way better off than otherwise. Doesn't sound very idiotic to me.


Any idiot chooser would never come out ahead.  He'll reject some offers.  Only if the negotiator knows this is he in trouble.


Of course, having an idiot negotiator or coming across as someone who won't accept a low deal would have you come out ahead as well.
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April 22, 2011, 02:35:04 PM
 #112

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.

So you are saying that you would turn down free money to spite someone if the price was low enough or the situation was just right?  That doesn't make you any better than the rest of us, you just have a different set of preferences.  If I give up $50 to "spite" Splitter (or "teach him a lesson"), then you say I am irrational or an ape ruled by emotions, but you would do it if the situation warranted it (in your opinion) or the price was sufficiently low.  It's the same behavior simply shifted by your specific morals, ethics, utility values and preferences.

No, I'm saying if there is no cost borne and it was just a transfer from one person to another.  For example, if I like Person A more than Person B, I might let Person A keep their money if the money was insignificant to me.

If $50 means nothing to you (you would not care if I just shipped you $50 for fun), then sure, it's perfectly fine.  I highly doubt you would reject $50, but some people certainly would.  There are some rich people who would turn down a lot.
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April 22, 2011, 02:59:52 PM
 #113

Imagine that a stranger proposes you and me the following deal.  She will give us 5,000$ if we can agree on how to split it.  It works like this: I choose a split and you don't get to negotiate it, you can only accept the deal (in which case each of us gets what I chose) or reject it (in which case neither of us gets anything).

After giving it a short thought, I propose that I get 4,990$ and you get 10$.

Would you accept the deal?

(I'm not asking what you think is the rational thing to do from either a selfish or political standpoint, but what would you actually do.)

I would accept your offer for $10, estevo.

I find the phrasing of the problem interesting. "She will give us $5000" is very important. Before hearing the rest of the problem, I'm inclined to feel like I'm about to receive $2500. When it turns out that I stand to receive $10 at the most, my immediate reaction is to feel cheated and insulted. I think this is a very irrational, but understandably human reaction. However, this is only because of an artificial feeling of entitlement. I didn't do anything to deserve any of that money, so why should I be upset?

In the end I think I'd realize that $10 can buy a 6 pack of good beer and that that's better than nothing.

Lesser amounts might change my decision, however. My rejection wouldn't necessarily be out of spite (which has been discussed here already), but because smaller amounts of money can't buy me much. For instance, $1 doesn't even get me a gallon of gas -- it's a waste of time for me to stand around talking with strangers for so little.

In the end, I think it just comes down to answering, "How much is $10 worth to you?". As an American with Australian roots, I tend to value money in relation to gas (USA) and beer (Australia). $10 can get me a useful amount of either  Grin
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April 22, 2011, 03:00:59 PM
 #114

Ten dollars is such a negligible amount. I would get more value from watching the man suffer from his gamble.
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April 22, 2011, 03:10:07 PM
 #115

Ten dollars is such a negligible amount. I would get more value from watching the man suffer from his gamble.

What if you didn't get to watch him suffer?

Why does making him suffer bring you joy?

Do you enjoy watching teenagers beat homeless men as well to watch them suffer?
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April 22, 2011, 03:14:07 PM
 #116

Ten dollars is such a negligible amount. I would get more value from watching the man suffer from his gamble.

What if you didn't get to watch him suffer?

Why does making him suffer bring you joy?

Do you enjoy watching teenagers beat homeless men as well to watch them suffer?
Well, just knowing he didn't get $4,990 for being a moron is value enough. Somehow this may encourage similar incidents to have a different fate.

The fact is $10 means nothing to me and I don't like morons polluting the gene pool with negligent prosperity.
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April 22, 2011, 03:58:33 PM
 #117

Ten dollars is such a negligible amount. I would get more value from watching the man suffer from his gamble.

What if you didn't get to watch him suffer?

Why does making him suffer bring you joy?

Do you enjoy watching teenagers beat homeless men as well to watch them suffer?
Well, just knowing he didn't get $4,990 for being a moron is value enough. Somehow this may encourage similar incidents to have a different fate.

The fact is $10 means nothing to me and I don't like morons polluting the gene pool with negligent prosperity.


Why is he a moron?  What would make him not a moron?
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April 22, 2011, 05:25:18 PM
 #118

Ten dollars is such a negligible amount. I would get more value from watching the man suffer from his gamble.

What if you didn't get to watch him suffer?

Why does making him suffer bring you joy?

Do you enjoy watching teenagers beat homeless men as well to watch them suffer?
Well, just knowing he didn't get $4,990 for being a moron is value enough. Somehow this may encourage similar incidents to have a different fate.

The fact is $10 means nothing to me and I don't like morons polluting the gene pool with negligent prosperity.


Why is he a moron?  What would make him not a moron?
He's a moron in not acting in his own rational self-interest. He denied himself the prize money by making an irrational offer. The optimal solution would be giving me an actual incentive to say yes. You know, by me actually gaining $100 or so.
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April 22, 2011, 05:31:45 PM
 #119

He's a moron in not acting in his own rational self-interest. He denied himself the prize money by making an irrational offer. The optimal solution would be giving me an actual incentive to say yes. You know, by me actually gaining $100 or so.

You've just plucked out another arbitrary figure.

So by your standards if I offer $99.99 I'm a moron, but if I offer $100.01 I'm a nice guy.

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April 22, 2011, 05:39:16 PM
 #120

He's a moron in not acting in his own rational self-interest. He denied himself the prize money by making an irrational offer. The optimal solution would be giving me an actual incentive to say yes. You know, by me actually gaining $100 or so.

You've just plucked out another arbitrary figure.

So by your standards if I offer $99.99 I'm a moron, but if I offer $100.01 I'm a nice guy.

It's not arbitrary. It's very relevant if I am involved in the game. The number is what I would consider value. It's subjective by its very nature, a moot point.
 
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