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