Two firms compete on price every year. The inverse demand function each firm faces depends on which firm has chosen the lowest price that year. The one that did captures the entire market. If, on the other hand, both prices are the same then they split the market evenly. Consumers round up prices to the nearest integer. For the firm with the lowest price p, demand is given by: q = 24-2p: Marginal costs are constant and equal to $4 for both firms.
a. Define the Normal form of the stage game and determine the Nash Equilibria, the Cooperative Equilibrium and the Optimal Deviation from cooperation.
b. For the once repeated (2 stages) game, determine if a Nash Equilibrium exists that improves on simply playing the (better) Nash Equilibrium of the stage game twice
c. For the infinitely repeated game, determine what the interest rate would have to be to prevent the firms from cooperating.
d*. Determine the relation between the interest rate and the number of punishment periods in a forgiving trigger strategy that guarantees cooperation.