Real Algebraic Tools in Stochastic Games
نویسنده
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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