Matching Pennies is Strictly Competitive
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Theorem
The game of Matching Pennies is strictly competitive.
Proof
By definition, a strictly competitive game is a game in which the interests of each player are diametrically opposed.
Recall the payoff table of Matching Pennies:
$\text B$ | ||
$\text A$ | $\begin{array}{r {{|}} c {{|}} } & \text{H} & \text{T} \\ \hline \text{H} & 1, -1 & -1, 1 \\ \hline \text{T} & -1, 1 & 1, -1 \\ \hline \end{array}$ |
It can be seen by inspection that exchanging $\text A$ and $\text B$ results in exactly the same entries in the payoff table.
From the nature of a payoff table it follows that the fortunes of each player are opposite and equal.
Hence the result.
$\blacksquare$
Sources
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $2.3$: Examples: Example $17.1$