Question

1. There are two players: A government, G, and a firm, F . The firm can choose to invest in a Research and Development project, action R, or not, action N . If the firm chooses R, it gets a payoff of pπ − c, where p is the level of patent protection given to the firm, π are the profits generated by the invention to a monopolist, and c is the cost of research. So if p = 1, the firm’s invention is fully protected against competition, while if p = 0, the firm receives no protection. If the firm chooses N , it gets a payoff of zero. The government would like to maximize consumer welfare from the invention, given by (1 − p) π if research takes place and 0 else. In solving the following game, focus on pure strategies only.

(a) Suppose the firm decides whether to research or not and the government decides p simultaneously. Find one Nash equilibrium of the game.

(b) Suppose the firm moves first in deciding whether to invest or not, and then the government decides p. What is the subgame perfect Nash equilibrium?

(c) Invert now the timing with respect to (b). Hence, suppose the government moves first and decides p, and then the firm decides whether to invest or not. What is the subgame perfect Nash equilibrium?

(d) Explain briefly how your results in parts b and c differ. What implications does this question have for patent policy?

Answer 1

(a) Suppose the firm decides whether to research or not and the government decides p simultaneously. Find one Nash equilibrium of the game.

Thus for the firm it is optimal to undertake a Research with or without government intervention. Thus the payoff for the firm is (p pi -c),(1-p)pi or (p pi -c,0).