Tacit Collusion:

Two firms, which have zero marginal cost and no fixed cost, produce some good, each producing q_i ≥ 0, i ∈ {1, 2}. The demand for this good is given by p = 200 - Q, where Q = q₁ + q₂.

a. First consider the case of Cournot competition, in which each form chooses qi and this game is infinitely repeated with a discount factor δ

b. For which values of δ can you support the firms' equally splitting monopoly profits in each period as a subgame-perfect equilibrium that uses grim-trigger strategies (i.e., after one deviates from the proposed split, they resort to the static Cournot-Nash equilibrium thereafter)? (Note: Be careful in defining the strategies of the firms!)

c. Now assume that the firms compete a la Bertrand, each choosing a ' price p_i ≥ 0, where the lowest-price firm gets all the demand and in case of a tie they split the market. Solve for the static stage-game Bertrand-Nash equilibrium.

d. For which values of δ can you support the firms' equally splitting monopoly profits in each period as a subgame-perfect equilibrium that uses grim-trigger strategies (i.e., after one deviates from the proposed split, they resort to the static Bertrand-Nash equilibrium thereafter)? (Note: Be careful in defining the strategies of the firms!)

e. Now instead of using grim-trigger strategies, try to support the firms' equally splitting monopoly profits as a subgame-perfect equilibrium in which after a deviation firms would resort to the static Bertrand competition for only two periods. For which values of δ will this work? Why is this answer different than your answer in (d)?