Question

In the matching pennies game, each player reveals a penny flipped to either heads or tails (pennies are a discontinued copper-plated currency worth $0.01 ). If both players reveal that same result, Player 1 gets both pennies. If they both reveal different results, Player 2 gets both pennies. In table form:

(a) How many pure-strategy Nash equilibria exist? What are they?

Answer 1

The matching pennies game has no pure-strategy Nash equilibria because each player's best response changes depending on the other player's actions, leading to a symmetric and cyclical pattern without stability in pure strategies.

Step-by-step explanation:

The question asks about the pure-strategy Nash equilibria in the game of matching pennies. In this game, there are two players, each player selects either heads or tails without knowing the choice of the other player. Player 1 wins if both pennies are the same side, and Player 2 wins if the pennies are different.

For each player, there are two strategies available - selecting heads or tails. However, since players have opposite objectives, there is constant conflict, and no player has an incentive to unilaterally change their strategy once the opponent's strategy is known.

This leads us to the conclusion that in a matching pennies game, there are no pure-strategy Nash equilibria because the game is zero-sum and completely symmetric. Each player's best response constantly changes in reaction to the other player's strategy, creating a cyclical pattern without any stable equilibrium in pure strategies.