Answer to Question #181390 in Economics of Enterprise for Jennie

Question

Can a two-person game, in which each player has two actions, has infinitely many mixed strategy Nash equilibria? If yes, illustrate a game which has such a Nash equilibrium. If no, explain your argument.

Answer 1

The idea of a Mixed Strategy is that for P1 to be indifferent between her actions, she needs player 2 to play her actions with a probability such that P1 is indifferent between playing her actions with any probability. So, they simultaneously provide each other with a random strategy such that the other is indifferent between the two actions on expectation. In short, they are both indifferent between the two actions and therefore any random combination.