The Game
Players I and II each choose a number, and respectively, with ; the payoff to I is
(i.e. player II pays to player I;the game is zero-sum). Sometimes player I is referred to as the maximizing player and player II the minimizing player.
If is interpreted as a point on the unit square, the figure shows the payoff to player I. Now suppose that player I adopts a mixed strategy: choosing a number from probability density function (pdf) ; player II chooses from . Player I seeks to maximize the payoff, player II to minimize the payoff. Note that each player is aware of the other's objective.
Read more about this topic: Example Of A Game Without A Value
Famous quotes containing the word game:
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—Finley Peter Dunne (18671936)
“Art is a concrete and personal and rather childish thing after allno matter what people do to graft it into science and make it sociological and psychological; it is no good at all unless it is let alone to be itselfa game of make-believe, or re-production, very exciting and delightful to people who have an ear for it or an eye for it.”
—Willa Cather (18731947)