On extremal pure Nash equilibria for mixed extensions of normal-form games |
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Authors: | S. Heikkilä |
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Affiliation: | Department of Mathematical Sciences, University of Oulu, Box 3000, FIN-90014 University of Oulu, Finland |
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Abstract: | In this paper we derive conditions under which mixed extensions of normal-form games have least and greatest Nash equilibria in pure strategies, and either of them gives best utilities among all mixed Nash equilibria when strategy spaces are complete separable metric spaces equipped with closed partial orderings, and the values of utility functions are in separable ordered Banach spaces. The obtained results are applied to supermodular normal-form games whose strategy spaces are multidimensional. |
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Keywords: | Game Normal-form Supermodular Strategy Pure Mixed Nash equilibrium Greatest Least Ordered Polish space Ordered Banach space Generalized iteration method |
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