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Author Topic: The Ultimatum Game  (Read 16212 times)
estevo
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April 21, 2011, 09:41:32 AM
 #1

I read this interesting experiment from The Origin of Wealth, a book by Eric B. Beinhocker (paraphrased):

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.)
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vuce
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April 21, 2011, 09:48:59 AM
 #2

Well obviously I would. However you made a mistake, since the only nash equilibrium is 4999.99 (taking in account that the minimum value for a trade is 1 cent), in which case I still should accept the deal.
Metal
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April 21, 2011, 09:51:55 AM
 #3

Spite the other guy for not being more "fair", or run with the 10 bucks and get 3 free tall no-whip mochas...

Does "Take the deal, but mug the guy as soon as he starts to walk away with his $4,990 gain" count as an option?
estevo
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April 21, 2011, 10:04:37 AM
 #4

@vuce:  Your analysis is flawless, and settles the game-theoretic interpretation of the problem.  Then again, this question isn't a riddle in game theory, nor necessarily about maximizing payoff, nor are you asked to take money as a representation of utility.  I think you understand that and mean what you say, but just to make sure: would you really take one cent if this actually happened tomorrow?

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Does "Take the deal, but mug the guy as soon as he starts to walk away with his $4,990 gain" count as an option?
No,  that is not an option. Smiley
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April 21, 2011, 10:10:02 AM
 #5

[J]ust to make sure: would you really take one cent if this actually happened tomorrow?

Even a cent is better than nothing, especially when it comes to a bitcent.  I would.

Cheers,

Klaus Alexander Seistrup
http://about.me/kseistrup
vuce
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April 21, 2011, 10:12:40 AM
 #6

@vuce:  Your analysis is flawless, and settles the game-theoretic interpretation of the problem.  Then again, this question isn't a riddle in game theory, nor necessarily about maximizing payoff, nor are you asked to take money as a representation of utility.  I think you understand that and mean what you say, but just to make sure: would you really take one cent if this actually happened tomorrow?
I most definitely would. Not for the 1 cent I would get, but because I'm not a selfish bastard Smiley (not that all those who wouldn't are selfish bastards, I meant no offense to anyone Smiley)
estevo
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April 21, 2011, 10:51:41 AM
 #7

Nice.  There is really no "right" or "wrong" response, so please keep 'em coming.

I figure many forum users know about this experiment or can easily see what it tries to test.  For those not versed in game theory and up for a spoiler, Wikipedia has an article1 that explains what this is about, and what results were obtained in different cultures.  But if you intend to reply please do so before reading that page.

I think it would be interesting to have a chat about some implications of this experiment, but I'd rather allow some time for replies first.

For whatever it's worth, and knowing full well it's not the "rational" thing to do, I know I'd tell the greedy bastard to go #%@! himself.

Two perhaps interesting questions:

If you were in the position of the one who made the offer, what would you offer:

 a) to someone who you expect to know about game theory and this game in particular,
 b) to someone who you expect not to know about game theory and this game in particular.

in either case, you know nothing else about this other person.  Not even sex, race, nationality, etc.  Imagine it happens in some anonymous chat room (not #bitcoin-otc Smiley ).

[1] http://en.wikipedia.org/wiki/Ultimatum_game
db
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April 21, 2011, 10:57:56 AM
 #8

Reject. I would reject anything under half.
db
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April 21, 2011, 11:04:00 AM
 #9

If you were in the position of the one who made the offer, what would you offer:

 a) to someone who you expect to know about game theory and this game in particular,

Half.

b) to someone who you expect not to know about game theory and this game in particular.

Half.
deadlizard
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April 21, 2011, 11:10:05 AM
 #10

If you were in the position of the one who made the offer, what would you offer:

 a) to someone who you expect to know about game theory and this game in particular,

Half.

b) to someone who you expect not to know about game theory and this game in particular.

Half.

+1

If I got the 4,990$ offer I'd say "That wasn't very bright" and walk away

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db
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April 21, 2011, 11:10:58 AM
 #11

The same game can also be phrased like this: I get given 5000 $. You then get the option of making me return it again. How much must I offer you to not do that?
estevo
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April 21, 2011, 11:21:41 AM
 #12

@vladimir: It's a one-off.

@vuce: So you would accept that the other guy keep $5000 and you $0?  Technically (and again, assuming we identify utility with monetary payoff, as you seem to have done), that is a Nash equilibrium too: rejecting the deal would hurt the other guy while netting you nothing.

@db: That would be the exact same deal, with a different framing.  My guess is that if you did a parallel study, dividing the subjects in two halves and asking either question, you'd get significantly different results.  Ironically, I think your framing favors the first guy.  Guess why?
deadlizard
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April 21, 2011, 11:22:01 AM
 #13

Do we get to repeat this game more than once with the same players? If so, than risk/reward model changes quite a bit i.e. both parties than can engage in tit for tat game to maximize profit.

no it's a one shot deal, which is why I think 50/50 is the only logical offer.

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estevo
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April 21, 2011, 12:01:55 PM
 #14

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no it's a one shot deal, which is why I think 50/50 is the only logical offer

This is besides the question, but in game theoretical terms, an iterated version of the game would promote more equality.  If we're going to play repeatedly, I (proposer) know that you have a rational reason to veto an "unfair" proposal --that is, so I'll learn to be fairer next time.  So I'll probably offer a more equal split to begin with.

In a one-shot game, there is never any purely financial incentive to reject whatever offer.  As I said, not even a 5000$/0$ one.
grondilu
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April 21, 2011, 12:02:24 PM
 #15

Interesting question.  You should turn this thread into a poll.
estevo
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April 21, 2011, 12:05:07 PM
 #16

I thought of a poll, but I'm more interested in the explanations than the breakdown.
grondilu
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April 21, 2011, 12:14:37 PM
 #17


Honnestly I could say no.  I don't give a crap about getting 10$ for free, and I would enjoy better punishing the other guy for being really too much greedy.
vuce
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April 21, 2011, 01:08:10 PM
 #18

@vladimir: It's a one-off.

@vuce: So you would accept that the other guy keep $5000 and you $0?  Technically (and again, assuming we identify utility with monetary payoff, as you seem to have done), that is a Nash equilibrium too: rejecting the deal would hurt the other guy while netting you nothing.

@db: That would be the exact same deal, with a different framing.  My guess is that if you did a parallel study, dividing the subjects in two halves and asking either question, you'd get significantly different results.  Ironically, I think your framing favors the first guy.  Guess why?
In this case im indiferent Smiley

To anyone saying 50:50: it's more important to you to "teach them a lesson" than 2499$?
Terpie
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April 21, 2011, 01:16:26 PM
 #19

If value of pride/satisfaction of rejecting subjectively "unfair" offer > amount offered, then I reject. If not, I accept. That's why there is no wrong answer and it's not irrational to reject any offer.
tomcollins
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April 21, 2011, 01:45:42 PM
 #20

It's hilarious how pretty much everyone on here would take $10 for free in an isolated situation.  But the second you find out someone else gets $4990, you get upset.  Jealous much?
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