For each one of the following four versions of the prisoner's dilemma, find the range of discount factors ₁ and 2 such that cooperation (the outcome (C, C)) can be sustained as a subgame perfect equilibrium if the game is repeated infinitely many times: C D C 5,7 6, -1 D -2,9 0,0 1 C D C 3,2 4, -2 D -1,5 0,0

parameter x = 5 List all pure strategies for either player that are weakly dominated.

Does this game have a prisoner’s dilemma flavor? That is, could the n firms do better by jointly choosing their individual output? If so, which individual farmer’s quantity would maximize their joint profits? Why would one need a binding contract to enforce this agreement?

Game theory: Consider a collective action game with thirty individuals (N = 30). When the number of participants in the joint project is n, each individual, including shirkers, receives a benefit of B(n) = 18n and each participant incurs a cost of C(n) = 32 − 2n. 1. Find all of the Nash equilibria, both stable and unstable ones. 2. Find the socially optimal outcome. 3. Check if any of the Nash equilibria is socially optimal. Explain your answer.