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 firm1 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.

8.6 Investment in the Future: Consider two rms that play a Cournot com- petition game with demand p = 100 q and costs for each rm given by clifi'i) = 1093-. Imagine that before the two rms play the Coumot game rm 3+5 Exercises I 171 1 can invest in cost reduction. If it invests the costs of rm I will drop to em\") = 5m. The cost of investment is F > 0. Firm 2 does not have this in- vestment opportunity. a. Find the value F' for which the unique subgame-perfect equilibrium involves rm I investing. b. Assume that F > F". Find a Nash equilibrium of the game that is not subgame perfect