Question

(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure) strategies for each of the players. Make sure to write down which (pure) strategies strictly dominate them. • (7) b) Which (pure) strategies survive the process of iterated elimination of strictly dominated strate- gies? (6) c) Find the pure-strategy Nash equilibria of this game.

Answer 1

. for player ; u is strictly dominateated strateg, dominated by strategy M. Because, u (ki)<H(*;) Player a does not have a strictly dominated strategy, because for strict dominance the payoffs of one strateg must be greater than payoff of dominant Strategy. less b) As u is to in strictly eliminate dominated, first step u . Then the game ni layer 2 Player I M8,29,49,5 In reduced form c is dominated by R. Player 2 Player 1 - R 9,5 8,2 M8, 2 D 8,10 6,7 l Dis weakly dominated by M player-2 Player 1 LR M1 8,2 9,5 is stricty dominated by R R M4,5

1. c) For pure strateg NE ; underline each element that denotes highest payoff given payoff of other player Player - 2 . LTER Player I u 6,8/2,6/8,2 | D 3,104,66,7) Pure strategy. NE: {M,R} = {9,5} {D, L } = {8, 10}