Consider a contributions game with 2 players. Each player can either ‘Contribute’ or ‘Not.’ If either (or both) Contribute, a good is provided to both. The good is worth 2 jollies to each player. If a player Con tributes, she pays a cost of 1 jolly (deducted from the 2 jollies that the good is worth to her). If a player does Not contribute, she has no cost deducted from her jollies. If both players choose Not to contribute, both players receive 0 jollies.
(a) Suppose player 1 uses a mixed strategy. What is player 2’s expected payoff?
(b) Suppose player 2 uses a mixed strategy. What is player 1’s expected payoff?
(c) What is the mixed strategy Nash equilibrium in this game?
(d) Suppose the good is worth 3 jollies to both players instead of 2. What is the mixed strategy Nash equilibrium of this game?