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.