Consider a two-players game where each player can either contribute (C) to a public good or free ride (defect, D). If a player chooses to contribute, he pays a fixed private cost c. The public good benefits both players: the benefit is b if only one player contributes, while the benefit is k × b if both contribute, with k > 1.

1. Give the normal-form representation of this game. 2. Write down the payoff matrix.

(a) For which values of k is this a Prisoner’s Dilemma when b = 3 and c = 6?

(b) What equilibrium does the game have when b = 3 and c = 6 and k ∈ (2,3)?