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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?

Strictly speaking, in the example I gave, the problem isn't with the "theory" part of game theory; the problem is 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 classically 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.

I cross-posted this question with Cognitive Science StackExchange because I originally posted it on the Mathematics StackExchange but didn't receive much helpful answers there.

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    $\begingroup$ Btw: The paper "Testing Game Theory" by Jörgen Weibull discusses your question in great detail. $\endgroup$ – Michael Greinecker May 14 '18 at 15:20
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    $\begingroup$ @MichaelGreinecker. I looked it up (scholar.google.fr/scholar?cluster=15101774852584562659), and sure enough, it is the kind of thing I'm asking about. Could you please turn your comment into an answer so that I can vote on it? $\endgroup$ – Ochado May 14 '18 at 15:29
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Here is an article that reports about several laboratory experiments showing large inconsistencies between theoretical predictions and observed behavior for some payoff structures:

Goeree, J.K. and Holt, C.A., 2001. Ten little treasures of game theory and ten intuitive contradictions. American Economic Review, 91, 1402-1422. https://doi.org/10.1257/aer.91.5.1402

There are also papers studying variants of the ultimatum game in order to quantify players’ preferences for fairness. One approach to do so is to compare (i) games in which two human players interact with each other and (ii) games in which a human player interacts with a computer (so there is no scope for social preferences):

Hoppe, E.I. and Schmitz, P.W., 2013. Contracting under incomplete information and social preferences: An experimental study. Review of Economic Studies, 80, 1516-1544. https://doi.org/10.1093/restud/rdt010

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  • $\begingroup$ The "10 treasures" article is exactly the kind of thing I was looking for. Thanks! $\endgroup$ – Ochado May 14 '18 at 10:03
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This question is discussed in detail in the paper:

Weibull, Jörgen W. "Testing game theory." Advances in Understanding Strategic Behaviour. Palgrave Macmillan, London, 2004. 85-104.

Weibull discusses the issues with not knowing the actual payoff functions, the players not knowing the actual payoff functions (incomplete information), and situations where game theorists are less clear about what game theory is supposed to predict.

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The game you describe is known as the dictator's or ultimatum game, and indeed people typically refuse offers that are less than a 2/3-1/3 split. A lot of research has gone into this in the behavioural economics literature.

There are many other situations where the predictions from the theory do not match actual behaviour, among others: people contribute more to a public good than they should (especially if the game is not repeated), people invest more than they should, people don't defect in a prisoner's dilemma et cetera.

Colin Camerer has an old but very readible piece in the Journal of Economic Perspectives here and has written a full book on the subject: "behavioral game theory".

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

I can think of many outliers, however, outliers are not typical human being. e.g. Philosopher, economist, mathematicians, etc.

In behavioral science such as game theory, "punishment" play more important roles than rewards. When rationality lies on the punishment (of unfair practice), so you will not see people move towards rewards.

The said behavior is in fact, correctly describe typical human being behavior. If the stake is known, it will move towards 50/50 or nothing, equilibrium reach. When utilities are not equal, IMHO increasing the state still move towards 50/50 or nothing. However, nobody will fund such stakes.

However, there are ways to manipulate the punishment and shift the paradigm using a bait, a bait that called Investment return promises. E.g. In the ancient era, the promises are entering heaven after death; rewards from joining a war, etc.

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    $\begingroup$ This answer contains no references to back up its claims. The claims also seem vague and somewhat difficult to understand, and they are suspiciously general. $\endgroup$ – Giskard Jun 17 '17 at 7:02
  • $\begingroup$ @denesp : Perhaps you can help me to find any citation on repetitive experiment state by OP, with higher stake, e.g. 1 millions dollars. $\endgroup$ – mootmoot Jun 19 '17 at 7:39
  • $\begingroup$ I would not know how to do that. This is why I do not make such claims. $\endgroup$ – Giskard Jun 19 '17 at 10:59
  • $\begingroup$ @denesp : Would you claim theory is flawed if the scientist cannot simulate all possibilities? $\endgroup$ – mootmoot Jun 19 '17 at 11:04

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