Definition of a game; Two-person zero-sum games; Linear programming; Infinite games; Multistage games; Utility theory; Two-person general-sum games; n-Person games; Stable sets; Indices of power; The bargaining set and related concepts; Nonatomic games; Games without side payments.
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TWOPERSON ZEROSUM GAMES
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Annals assume axioms balancing vector Banzhaf-Coleman index bargaining set characteristic function choose column commodity constant-sum game constraint set continuous convex hull convex set counterobjection defined Definition domination entry equations equilibrium n-tuple equilibrium pairs Example exists fact finite number following theorem game element game in 0,1 give given Hence imputation kernel Lemma Let us suppose linear program lottery matrix game Maximize minimal balanced collections minimax theorem mixed strategies Moreover multilinear n-person game n-tuple nonempty core nonnegative normalization nucleolus objective function obtain optimal strategies Pareto-optimal perfect information pivot play player set polynomial positive possible primitive set problem Proof prove pure strategies S C N saddle point satisfying seen sequence Shapley value Show side payments Similarly simple game solve space stable set stable set solution stochastic game strategies x subset superadditivity symmetric Symmetric Games tableau terminal three-person game two-person unique vertex winning coalition xAyT zero