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
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
- 1956: Steven Vajda: The Theory of Games and Linear Programming ... (previous) ... (next): Chapter $\text{I}$: An Outline of the Theory of Games: $2$
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $2.3$: Examples: Example $17.1$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): game theory
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): game theory