Question

consider following game the P2 A [213 PI B 166 8.5 4,2 strategies Find the Nash equilibrium in mixed

Answer 1

For Player 2, assume that the probability with which he selects D is p and the probability of choosing E is 1- p. Given this, Player l's expected payoff from choosing A is 2p +8(1 - p) = 8 - 6p and the expected payoff from choosing B is 6p + 4(1 - p) = 4 + 2p. Player 1 must be indifferent between these two payoffs if he is to randomize. This implies: 8-6P = 4 + 2P 4 = 8p p=1/2 = 0.5 Similarly, for Player 1, assume that the probability with which he selects A is q and the probability of choosing B is 1-q. Given this, Player 2’s expected payoff from choosing D is 3q + 6(1 – q) = 6 - 39 and the expected payoff from choosing E is 5q + 2(1 –q) = 2 + 3q. Player 2 must be indifferent between these two payoffs if he is to randomize. This implies: 6 - 39 = 2 + 3 6 = 4 q = 0.67 Under mixed strategy, Player 2 selects D with a probability of 0.5 and E with a probability of 0.5. Similarly, Player 1 selects A with a probability of 0.67 and B with a probability of 0.33