Players A and B are engaged in a coinmatching game Each show

Players A and B are engaged in a coin-matching game. Each shows a coin as either heads or tails. If the coins match, B pays A $1. If they differ, A pays B $1.

a. Write down the payoff matrix for this game, and show that it does not contain a Nash equilibrium.

b. How might the players choose their strategies in this case?

Solution

B’s strategies

Head Tails

A’s strategies         Heads       +1, -1                 -1, +1

Tails         -1, +1                 +1, -1

The payoffs are based on the choices made by the players although this choice is unknown to the other player. The players’ payoffs or utility are balanced in the sense that one player’s gain in utility is an inverse of the second player.

The Nash equilibrium is not exhibited in this instance since there is no available channel for the players to maximize their payoffs. Though the players have adequate aptitude to deduce the solution, the equilibrium remains unknown owing to the intricacy of the game. A zero-sum game as depicted above can be solved by adopting linear optimization.