Matching pennies - Definition and Overview

Matching Pennies is the name for a simple example game used in game theory. It is played between two players, Player A and Player B. Each player has a penny and must secretly turn the penny to Heads or Tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), Player A receives one dollar from Player B (+1 for A, -1 for B). If the pennies do not match (one heads and one tails), Player B receives one dollar from Player A (-1 for A, +1 for B). This is an example of a zero-sum game, where one player's gain is exactly equal to the other player's loss.

The game can be written in a payoff matrix like the one below. Each cell of the matrix shows the two players' payoffs, with Player A's payoffs listed first.

This game has no pure strategy Nash equilibrium since there is no pure strategy (heads or tails) that is always best for either player. Instead, the Nash equilibrium of this game is in mixed strategies - each player's best strategy is to be as random as possible with their choice, choosing heads or tails with equal probability. In this way, the opponent has no way of predicting what the player will choose and will therefore have no way of taking advantage of any predictability.

See also

• Game theory
• Nash equilibrium