There is a dollar on the table, which each player can try to grab. If only one p

Question

There is a dollar on the table, which each player can try to grab. If only one player grabs, G, and the other does not, D, the player who grabs gets the dollar and his payoff is 1, while the other player's payoff is 0. If both players try to grab at the same time, the dollar is destroyed and each player pays a penalty of 1. If neither player grabs, the dollar remains on the table and each player's payoff is 0.

Let p denote the probability that 1 plays D and let q denote the probability that 2 plays D.

The minmax strategy profile is (p, q) =(_,_) Enter answer to two decimal places, e.g., 0.00

Explanation / Answer

Player 2

G D

player 1 G -1,-1 1,0

D 0,1 0,0

p= probability that 1 plays D

q = probability that 2 plays D

Player 1 will play D, 0(q) + 0(1-q) >-1q + (1-q)1

1-2q<0

q>1/2

Player 2 will play D if, -p + 1-p < 0(p) + 0(1-p)

1 - 2p <0

p>1/2

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