Investment in the Future:

Consider two firms that play a Cournot competition game with demand p = 100 q and costs for each firm given by ci(qi) = 10qi. Imagine that before the two firms play the Cournot game firm 1 can invest in cost reduction. If it invests the costs of firm 1 will drop to c1(q1) = 5q1. The cost of investment is F > 0. Firm 2 does not have this investment opportunity.

a. Find the value F for which the unique subgame-perfect equilibrium involves firm 1 investing.

b. Assume that F>F. Find a Nash equilibrium of the game that is not subgame perfect.