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a-reduced game a^-stationary distributions a^-stationary strategies absorbing set ai(dilci best response correlated equilibrium dominated pure strategies dominated strategies dual constraints dual problem elementary game elementary incentives equilibria with elementary equilibrium refinements existence of correlated finite strategic-form game full dual reduction implement the correlated incentive constraints iterative dual reduction Lemma linear programming problem Markov chains Matching Pennies game matrix for player mediator mediator's recommendations minimal a^-absorbing set minimal a^-absorbing subset Nash equilibria Nau and McCardle nontrivial dual vector number of pure obey the mediator's original game Player 2 x2 positive probability probability 1/2 probability distribution proof Proposition pure-strategy profiles random deviation strategy randomized strategy reduced game T/a REDUCTION AND ELEMENTARY satisfies the dual SceC SCHOOL OF MANAGEMENT Sd eC set of pure stationary distribution stationary strategies strategic incentive problem strategic transition matrix strategies for player strategies in C^/a strategy profile trivial dual vector VceC VcieCi Vi€N x2 y2 Player