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Annals assuming Axioms bottom row chance moves choice clear coalition structure commodity Consider the game constraint set continuous converge convex hull convex set defined Definition dF(x differential game dominated equal to zero equilibrium n-tuple equilibrium pairs Example exist expected payoff fact finite games finite number game element game matrix game theory give given Hence imputation infeasible information set integral interval kernel Lemma Let us suppose linear program lottery matrix game Maximize minimax theorem Minimize mixed strategies Moreover n-person game non-basic non-negative non-positive objective function obtain optimal strategies payoff function perfect information pivot step play positive possible problem proof prove pure strategies recursive game represent respectively saddle point satisfying seen sequence Shapley value Show Similarly simplex algorithm solve stable set solution stochastic game strategy for player strategy x subset symmetric symmetric games terminal two-person unique utility variables vector vertex