Let the elements in a payoff matrix be denoted , where the s are player A's strategies and
are player B's strategies. Player A can get at least
for strategy . Player B can force player A to get no more than for a strategy . The best strategy
for player A is therefore
and the best strategy for player B is
Equality holds only if a game saddle point is present, in which case the quantity is called the value
of the game.
, Game Saddle Point
, Payoff Matrix
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Cite this as:
Weisstein, Eric W. "Game Expectation."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GameExpectation.html