In this variation on the Prisoners’ Dilemma, a suspect is convicted and receives a sentence of four…

In this variation on the Prisoners’ Dilemma, a suspect is convicted and receives a sentence of four years if he is finked on and goes free if not. The district attorney does not reward finking. Table 8.5 presents the normal form for the game before and after applying the procedure for underlining best responses. Payoffs are again restated in terms of years of freedom. Ties for best responses are rife. For example, given player 2 finks, player 1’s payoff is 0 whether he finks or is silent. So there is a tie for 1’s best response to 2’s finking. This is an example of the set of best responses containing more than one element: BR1ðfinkÞ = {ffink, silent}.

 

The underlining procedure shows that there is a Nash equilibrium in each of the fourboxes. Given that suspects receive no personal reward or penalty for finking, they are bothindifferent between finking and being silent; thus any outcome can be a Nash equilibrium.