The game of Matching Pennies
A)has no Nash equilibrium.
B)has a pure-strategy Nash equilibrium.
C)has a mixed strategy Nash equilibrium.
D)has multiple Nash equilibria.

Question

Quizplus · Accepted Answer

Matching Pennies has a mixed strategy Nash equilibrium. In this game, both players have two options - to place their penny heads-up or tails-up. The payoffs for each player depend on whether or not their pennies match. If the pennies match, Player 1 wins and Player 2 loses. If the pennies do not match, Player 2 wins and Player 1 loses. Since both players have two options, there are four possible outcomes. If both players play strictly one strategy, they have a 50-50 chance of winning. Thus, neither player has an incentive to stick to one strategy. Instead, the best strategy for each player is to randomly choose between heads and tails with equal probability. Therefore, the mixed strategy Nash equilibrium for Matching Pennies is for both players to play each strategy with a probability of 0.5.

The Game of Matching Pennies