Game theory

1. Miscellaneous questions related to mixed strategy equilibria. (a) In the game of Exercise 1 of problem set 1, find a mixed-strategy equilibrium where no player uses a weakly dominated strategy with positive probability. (b) Calculate all the mixed-strategy Nash Equilibria for the following three games: G1,G2 and G3. (Hint for Game G3, each player has a strictly dominated strategy which you can eliminate!) Col: Col: h L R. Row: H 4,4 1,6 Row: 1. 10 0, 4 T 1, 10 15, 2 0, 14 2, 24 Game GI Game G2 Col: b1 b2 b3 2,2 0.3 4.7 Row: 02 0, 1 1,4 2,7 03 1,3 3,9 1,7 Game G3 (c) Suppose we play the following zero-sum game. You write down a number from the set {1, 2,3, ..., 100} without me seeing it, and I try to guess it. If I guess correctly, you pay me the number in dollars. If I don't guess correctly, no money changes hands. Find a Nash equilibrium in mixed strategies of this game, so that every number from {1, 2, 3, ..., 100} is played with positive probability by both players