Proof of the Minimax Theorem
نویسنده
چکیده
Formalization of a 2 Person Zero-Sum Game 1. There are two players, P1 and P2. 2. P1 has a set A = {a1, a2, . . . , am} of m pure strategies (or actions). 3. P2 has a set B = {b1, b2, . . . , bn} of n pure strategies (or actions). 4. Each player has a utility for each (ai, bj) pair of actions. The utility for P1 is denoted U1(ai, bj) and the utility for P2 is denoted U2(ai, bj). Since this is a zero-sum game, U1(ai, bj) = −U2(ai, bj) for all i and j. To minimize the number of subscripts we will carry around, let M(ai, bj) = U1(ai, bj) denote the mutual utility for the game.
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