Game Expectation

Let the elements in a payoff matrix be denoted a_(ij), where the is are player A's strategies and the js are player B's strategies. Player A can get at least


for strategy i. Player B can force player A to get no more than max_(j<=m)a_(ij) for a strategy j. The best strategy for player A is therefore


and the best strategy for player B is


In general,


Equality holds only if a game saddle point is present, in which case the quantity is called the value of the game.

See also

Game, Game Saddle Point, Payoff Matrix, Strategy, Value

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Game Expectation." From MathWorld--A Wolfram Web Resource.

Subject classifications