Question

Exercise 2 - A variation ofthe Prisoner's Dilemma game. Consider the following Prisoner's Dilemma game. The game coincides with that we discussed in class, except for the fact that every player sees his payoff decrease by m>0 when he chooses to confess. For instance, prisoner 1's payoff decreases by m in the top row (where he confesses) but is unaffected when he is at the bottom row (where he does not confess). A similar argument applies to prisoner 2, who sees his payoff decrease in the left column (where he confesses) but not in the right-hand column (where he remains silent). Intuitively, m represents the punishment that the confessing prisoner suffers from other criminals, either in jail (when he serves some time) or on the streets (when he does not serve any time in jail) Prisoner 2 Prisoner 1 Confess Not confess O-m, -15 Confess Not confess -15, 0-m a) b) c) Find if either player has a strictly dominated strategy. Does your result depend on the value of the punishment, m? Using your results from part (a), which is the strategy profile (or profiles) surviving Iterative Deletion of Strictly Dominated Strategies (IDSDS)? Find if either player has a strictly dominant strategy? Does your result depend on the value of the punishment, m?

Answer 1

a)

If 0 < m < 1, Confess gives a higher payoff to both the players.

Hence each player has a strictly dominated strategy to not confess for 0 < m <1. This result is dependent on the value of punishment m. For very small amount of punishment, non confess is a strictly dominated strategy.

If however, 1 < m < 15, both (confess, confess) and (not confess, not confess) are nash equilibria and there is no strictly dominated strategy for either player.

For m > 15, both players prefer not to confess and thus confess is a strictly dominated strategy for m > 15.

b)

For 0 < m < 1, since non confess is a strictly dominated strategy, it is removed during IDSDS and the strategy profile (confess, confess) survives.

For 1 < m < 15, no strategy is removed during IDSDS since there is no strictly dominated strategy.

For m > 15, since to confess is a strictly dominated strategy, it is removed during IDSDS and the strategy profile (non confess, non confess) survives.

c)

For 0 < m < 1, since confess gives a strictly higher payoff to both the players, it is a strictly dominant strategy.

For 1 < m < 15, no strategy is strictly dominant.

For m > 15, since non confess gives a strictly higher payoff to both the players, it is a strictly dominant strategy.

Thus, the results depend on the value of punishment m.