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I'm trying to compile multiple scenarios of the breakdown of game theory. Specifically, I'm looking for scenarios where game theory predicts certain behaviours, but in real-world scenarios or experiments, people tend to behave quite differently.

Here's an example of the kind of thing I'm looking for, based on the ultimatum game:

  • Two players, A and B, are offered a certain amount of money, for example, 100€, to share between them.
  • Player A first decides the split (e.g. 50-50, 60-40, 90-10, or whatever player A decides).
  • Player B chooses to either to accept Player A's split, in which case each player receives the amount dictated by Player A; or Player B refuses Player A's split, in which case both players receive 0€.
  • The game is played only once; there is no repitition.

Classic game theory predicts that as long as Player A offers any split in which Player B receives more than 0€, Player B would accept the offer. For example, if Player A offers 99-1, then Player B would accept the offer since 1€ is better than nothing. However, from what I understand, experiments have shown that for many offers below 50-50, Player B refuses the offer. The explanation is that when Player B perceives that Player A is being unfair, Player B often prefers that both players receive nothing rather than undergoing what they perceive to be unfair treatment. Apparently, the refusal depends on how much Player B would eventually receive. (For example, Player B might refuse a 90-10 split if 100€ is at stake, but might grudgingly accept it if 1000€ is at stake.)

Could anyone please offer any examples where game theory predictions are known to differ from actual human behaviour?

Edit to add an important parenthical note:

Strictly speaking, this isn't a problem with the theory part of game theory; it's a problem with correctly specifying the utilities. The players' real utility is a function of both the money they would receive and their perception of fairness. Because the game classicly only specifies their utility in terms of money, the prediction fails because the perception of fairness is also important, yet neglected. It is neglected because it is much harder to quantify and to accurately specify on the same scale as money. In fact, I strongly suspect that all cases that I'm asking for would involve a similar element: the game theoretic prediction fails because players have some very important behavioural aspects of their utilities which are not specified in the game model because they are hard to quantify.

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    $\begingroup$ Actually, I'm not sure if this is the best SE site to post this question. Would it be appropriate to cross-post it in the Economics and Cognitive Sciences sites as well? $\endgroup$ – Ochado Jun 3 '17 at 19:09
  • $\begingroup$ I concur with @Ochado: this question bears little relevance to the mathematics of game theory. $\endgroup$ – mlc Jun 4 '17 at 11:38
  • $\begingroup$ Since no examples have been provided, I've cross-listed the question: cogsci.stackexchange.com/q/17521/16180 and economics.stackexchange.com/q/17190/13656 $\endgroup$ – Ochado Jun 16 '17 at 8:30
  • $\begingroup$ I eventually got good answers citing relevant articles in the cross-posting at economics.stackexchange.com/q/17190/13656. $\endgroup$ – Ochado May 14 '18 at 10:06
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You are therefore asking for a reference list of experiments where predictions are violated?.. That is not a question, is a request. Look, experimental game theory appeared on the late 50's, mainly on Caltech. And since then, two branches are identifiable. Those experiments that explicitly intend to validate the theoretical prediction, and does that don't. Hence, this means that we are speaking about many thousands of articles and experiments to cover.

Therefore is somewhat unwise to post such a question. You have the experiments of Roth et al in the 90's, you have some recent developments in the prisoner's dilemma with repetition. And the list could continue on and on...

Moreover, the claim that the only question is the specification of the utilities is simply incorrect. Focal points, salience effects. They don't have anything to do with the utility specification. Yet, they will allow, if known, to understand which outcome players want to choose.

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