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Examples Definitions and State
Duality and prices
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activity algebraic amount assert assigned assume assumption basis called capacity Chap chapter choose column computation consider convex cone coordinate corresponding define definition demand denote diet dual problem duality theorem economic entries equilibrium prices equilibrium theorem equilibrium vector example exchange matrix Exercise exists fact feasible vector finding nonnegative finite cone flow game theory give given hence income independent subset inequality xA integers irreducible Lemma linear programming linear subspace m-vector mathematical matrix game maximize maximum problem maximum-flow problem minimax theorem minimize minimum mixed strategies nodes nonnegative numbers nonnegative solution optimal strategies optimal vector output payoff matrix Pi plays player polytope price vector production prove pure strategies rank reader replace result satisfy scalar simple simplex method solve strategies for Pi subspace suppose symmetric symmetric game tableau theory tion unit vectors verify zero