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I have heard of an interesting game that produces a very counter-intuitive result. It is an auction of a $100 bill, but one in which both the first person in the auction and the second need to pay for the bill (while only the first one gets the bill). What is the most interesting, most often the bill is sold for over $100, sometimes going up to $500. The explanation is that the second-highest bidder doesn't want to lose a lot of money, so they opt to outbid the highest bidder by a bit to minimize their losses.

So my question is, what other game theory games are out there that produce very counter-intuitive results?

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Your question is probably better off at Math.SE. (Even then it might be too open-ended for StackExchange's Q&A format.) Game theory, despite the name, doesn't have a lot to do with game development. See also this question: Is there any relation between Game Theory and Game Development? –  Eric Mar 4 '13 at 12:33
    
@Eric Hmm, I am not sure of Math would be the best place to ask questions about how people act under certain conditions. At the same time, I understand that GameDev is more focused on computer games, and there isn't really another SE for more related questions. I think it is best suited for this SE, as it is dealing with game design / gameplay and psychology of players in the game. Math would probably be better suited for mathematical analysis of game theory problems (say, finding a Nash Equilibrium for game X). –  ThePiachu Mar 4 '13 at 12:47
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@ThePiachu Game theory is actually a branch on math. the auction game you described is a booktext example. en.wikipedia.org/wiki/Game_theory –  petervaz Mar 4 '13 at 12:57
    
"Generate a list" questions aren't a good fit for the Q/A format of the site. I recommend you check out the FAQ and try one of the more discussion oriented sites listed there. –  Byte56 Mar 4 '13 at 16:01
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closed as not constructive by Byte56, Sam Hocevar, bummzack, Maik Semder, Sean Middleditch Mar 4 '13 at 17:34

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up vote 2 down vote accepted

Go read about the Prisoner's Dilemma. It's kind of the mother of all of these. Goes like this:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch ... If both prisoners testify against each other, both will be sentenced to two years in jail.

Long story short, the optimal solution for each prisoner is to rat out the other, even though this is not as good a result as if each prisoner stayed quiet. The wikipedia page inked to above is pretty thorough and will provide you with a game-theory explanation as well as a great-many examples of the prisoners dilemma in the real world.

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