Thursday, September 27, 2012

Game Theory

I've posted about Game Theory (the application of mathematics and reason to optimise decision making) before. It was a term coined by mathematician John von Neumann in 1944 and is now used in fields as diverse as economics, political science, psychology, logic, biology and military stretegy.

I came across a really nice example recently. It is a situation known as the 'prisoner's dilemma' - where two subjects have the choice to cooperate (which is in the best interests of both), or attempt a gamble to win everything for themselves. This is the classic version of the dilemma quoted by Wikipedia:
"Two men are arrested, but the police do not have enough information for a conviction. The police separate the two men, and offer both the same deal: if one testifies against his partner (defects/betrays), and the other remains silent (cooperates with/assists his partner), the betrayer goes free and the one that remains silent gets a one-year sentence. If both remain silent, both are sentenced to only one month in jail on a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept secret from his partner. What should they do? If it is assumed that each player is only concerned with lessening his own time in jail, the game becomes a non-zero sum game where the two players may either assist or betray the other. The sole concern of the prisoners seems to be increasing his own reward. The interesting symmetry of this problem is that the optimal decision for each is to betray the other, even though they would be better off if they both cooperated."
Here is a clip from the British TV game show 'Golden Balls'. The only twist on the classic version of the situation above is that both contestants are allowed to speak to each other prior to making their decisions. The guy on the right has obviously read about the Prisoner's Dilemma before and has a strategy sorted out in order to optimise his chances of winning the money (or at least not losing it). His partner seems to be left in a state of panic.


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