Definition:Matching Pennies

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Definition

Matching pennies is a two-person game whose mechanics are as follows.

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.


Payoff Table

The payoff table of Matching Pennies is as follows:

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


Analysis

Analysis of Matching Pennies

Solution

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