Suppose that each of two prisoners has the independent choice of confessing to a crime or not confessing to a crime they were both alleged to commit. if neither confesses, they spend 2 years in jail; if both confess, they spend 3 years in jail. if one confesses and the other does not, the confessor gets off with 1 year in jail while the other gets 6 years in jail. according to game theory, the likely strategy of the prisoners is that:

this is an example of the prisoners' dilemma and the Nash equilibrium:

                                                         prisoner 1

                                       confess                       not confess

                                       3 /                                      6 /

                   confess          3                                         1

prisoner 2

                                        1 /                                      2 /

               not confess         6                                       2

The dominant strategy for both prisoners will be to confess, since the expected time in jail is lowest = 3 + 1 = 4 years.

If a prisoner does not confess, the expected time in jail would be 6 + 8 = 8 years.

So a Nash equilibrium exists when both prisoners confess.

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