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# The Prisoners' Dilemma

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Nash Equilibrium
The concept of a Nash Equilibrium was codified by mathematician and game theorist John Nash. Simply put, a Nash Equilibrium is a set of best-response strategies. For a two-player game, a Nash equilibrium is an outcome where player 2's strategy is the best response to player 1's strategy and player 1's strategy is a best response to player 2's strategy.

Finding the Nash equilibrium via this principle can be illustrated on the table of outcomes. In this example, player 2's best responses to player one are circled in green. If player 1 confesses, player 2's best response is to confess, since -6 is better than -10. If player 1 doesn't confess, player 2's best response is to confess, since 0 is better than -1. (Note that this reasoning is very similar to the reasoning used to identify dominant strategies.)

Player 1's best responses are circled in blue. If player 2 confesses, player 1's best response is to confess, since -6 is better than -10. If player 2 doesn't confess, player 1's best response is to confess, since 0 is better than -1.

The Nash equilibrium is the outcome where there is both a green circle and a blue circle, since this represents a set of best response strategies for both players. In general, it is possible to have multiple Nash equilibria or none at all (at least in pure strategies as described here).

Jodi Beggs
Economics Guide