Econ 402, penn state university, Ron Siegel

3. (40 points) Two players are playing a game in which player 1 chooses a nonnegative number :13 not exceeding 10, that is, 31 = [0, 10], and player 2 chooses a nonnegative number y not exceeding 10, that is, 82 = [0, 10]. Player 1's payoff function is u1($,y) = (x + 23} + my/Z) 332/2 and player 2's payoff function is 21.2 (1:, y) = (:1: + 23; + {By/2) 192/2. (a) (5 points) Find the bestreply functions, BR1(.32) and BR2(51). (b) (5 points) Describe players' strategies in R1, R2, and R3, that is, in the rst three rounds of iterated deletion of dominated strategies. (c) (5 points) Derive the rationalizable strategies (you may use any method you like, for example by deriving a formula for the upper bound and lower bound of the interval of strategies in Rk). (d) (5 points) Find the Nash equilibria. Now suppose that player 1's payoff function is ul (x, y) = (x+ 2y - xy/2) - 22/2 and player 2's payoff function is U2 (x, y) = (x+ 2y - xy/2) - 32/2. (e) (20 points) Repeat parts a, b, c, and d