Solution to Matching Pennies

Solution to Matching Pennies

There are two players: $A$ and $B$.

Each player puts down a coin, traditionally a penny, either head or tail up, without showing it to the other player.

The coins are then uncovered.

If they both show the same side, $A$ is deemed to have won, and he takes both coins.

If they show different sides, $B$ is deemed to have won, and he takes both coins.

Proof

From the payoff table:

		$\text B$
$\text A$		$\begin{array}{r {{|}} c {{|}} } & \text{H} & \text{T} \\ \hline \text{H} & 1, -1 & -1, 1 \\ \hline \text{T} & -1, 1 & 1, -1 \\ \hline \end{array}$

The game of Matching Pennies has no Nash equilibrium.

Sources

• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $2.3$: Examples: Example $17.1$