For what values of x does Player 1 have a strictly dominant

For what values of x does Player 1 have a strictly dominant strategy? Name the strategy.

For what values of x does Player 1 have a weakly but not strictly dominant strategy? Name the strategy

Are there values of y for which Player 2 has a weakly dominant strategy?

Consider the following game ( and y can be any r the following game (r and y can be any non-negative real numbers): Player 2 A2,4 2, 3 3, 4 4 , 2 3 , 4 3 , 2 0, 3 2, y 0,1 C3, 2 Dx . 3

Solution

For x<3,Player 1 has strictly dominant strategy .Strategy C strictly dominates all other strategies for player 1 because payoff from strategy C is higher than all other strategy\'s payoffs of player 1. For x=3,Player 1 has weakly dominant strategy,C weakly dominates all other strategies for player 1 beacuse payoffs from strategy C will be equal to greater than all other strategy\'s payoffs of player 1. Player 2 has no dominant strategy,no matter what value y takes beacuse no strategy has payoffs that are equal or greater than all other strategy\'s payoff.