Question

Problem 1. (20 points) Consider a game with two players, Alice and Bob. Alice can choose A or B. The game ends if she chooses A while it continues to Bob if she chooses B. Bob then can choose C or D. If he chooses C the game ends, and if he chooses D the game continues to Alice. Finally, Alice can choose E or F and the game ends after each of these choices. a. Present this game as an extensive form game tree. b. How many leaves (terminal nodes) does the game have? c. How many pure strategies does each player have? d. Consider the following payoffs where the first index is Alice's payoff and the second index is Bob's payoff: Choice A by Alice gives (2,0), choice C by Bob gives (3,1), choice E by Alice gives (0,0) and choice F by Alice gives (1,2). What are the Nash equilibria of this game? e. Explain which equilibria is more appealing than the other? (Think about Pareto efficiency and subgame perfection).

Answer 1

a) Extensive form Game (b) Terminal Nodes e). Now pure strategies, S_A = {A, B} times {E, F} = {AE, AF, BE, BF} = 4 strategies of Alice S_Bob = {C, D} A implies 2 strategies to Bob. D) NE Alice 3NE: < AE, D > , < AF, D > , < BE, C > A e) Now SPNE rightarrow solving via Backward seduction so < AF, D > is More appealing < BF, C > is off the eqn path, as Alice always will choose F, & not E, But < BE, C > is pareto superior than < AF, D > & < AE, D > A