Real Algebraic Tools in Stochastic Games

نویسنده

  • ABRAHAM NEYMAN
چکیده

In game theory and in particular in the theory of stochastic games, we encounter systems of polynomial equalities and inequalities. We start with a few examples. The first example relates to the minmax value and optimal strategies of a two-person zero-sum game with finitely many strategies. Consider a twoperson zero-sum game represented by a k ×m matrix A = (aij), 1 ≤ i ≤ k and 1 ≤ j ≤ m. The necessary conditions for the variables v, x1, . . . , xk and y1, . . . , ym to be the minmax value and optimal strategies of player 1 (the maximizer and row player) and player 2, respectively, are given by the following list of polynomial inequalities and equalities in the variables v, x1, . . . , xk, y1, . . . , ym:

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تاریخ انتشار 2003