Assume that there are 2 firms playing an infinitely repeated game where firms choose prices for a homogeneous product. Let P = 5 - Q. Hence, a single-shot (one period) game is a homogenous product Bertrand game. The marginal costs of production are ci = i for i ∈ {1,2}. Let R ∈ (0,1) be the discount rate, p ∈ (0,1) be the probability that the game will continue to the next period, and ρ = pR. Assume that there is a smallest monetary unit ε> 0. Also, when calculating you can approximate ε≈ 0. Assume that the firms share the profit equally when cooperating.

a) What is the critical value of ρ so that the cooperation is sustained via a grim trigger strategy?

b) What is the critical value of ρ so that the cooperation is sustained via a grim trigger strategy, when the punishment delays 1 period?