Homework 7 1. Two firms can perform joint research on two products, a fancy one and plain one, and each make a profit of three million. Firm one has the opportunity to make an offer to firm two regarding the project as its facilities are set up and its staff is hired. If the firm one decides to tell firm two it has no interest in doing business with it, both firms must decide to research the fancy product or the plain product. (Neither firm has the capacity to research both alone.) The payoffs in this second round decision making are as follows (in millions): 2 f F 1,1 4,2 1 P 2,4 0.0 Each firm would prefer to research the fancy product while the other firm researches the plain product; however, both firms do not want to research the same product. a. Draw the extensive-form game of the two round game described above. b. Find the subgame perfect pure strategy Nash equilibria. c. Can forward induction be used to eliminate any of the equilibrium found in b? 2. A wife and husband play the game of battle of the sexes. Before playing, the husband has the opportunity to burn a hundred dollars. (The wife observes the burning.) The payoffs to the battle of the sexes game are as follows (assume the payoffs are represented in dollars): 2 b F 400, 200 0,0 1 B 0,0 200, 400 a) Draw the extensive-form game. b) Find all subgame perfect equilibria. Do any involve burning money? c) Can forward induction reduce the set of equilibria? Homework 7 1. Two firms can perform joint research on two products, a fancy one and plain one, and each make a profit of three million. Firm one has the opportunity to make an offer to firm two regarding the project as its facilities are set up and its staff is hired. If the firm one decides to tell firm two it has no interest in doing business with it, both firms must decide to research the fancy product or the plain product. (Neither firm has the capacity to research both alone.) The payoffs in this second round decision making are as follows (in millions): 2 f F 1,1 4,2 1 P 2,4 0.0 Each firm would prefer to research the fancy product while the other firm researches the plain product; however, both firms do not want to research the same product. a. Draw the extensive-form game of the two round game described above. b. Find the subgame perfect pure strategy Nash equilibria. c. Can forward induction be used to eliminate any of the equilibrium found in b? 2. A wife and husband play the game of battle of the sexes. Before playing, the husband has the opportunity to burn a hundred dollars. (The wife observes the burning.) The payoffs to the battle of the sexes game are as follows (assume the payoffs are represented in dollars): 2 b F 400, 200 0,0 1 B 0,0 200, 400 a) Draw the extensive-form game. b) Find all subgame perfect equilibria. Do any involve burning money? c) Can forward induction reduce the set of equilibria