On the Existence of Equilibria in Games with Arbitrary Strategy Spaces and Preferences∗
نویسنده
چکیده
This paper provides necessary and sufficient conditions for the existence of pure strategy Nash equilibria by replacing the assumptions concerning continuity and quasiconcavity with a unique condition, passing strategy space from topological vector spaces to arbitrary topological spaces. Preferences may also be nontotal/nontransitive, discontinuous, nonconvex, or nonmonotonic. We define a single condition, recursive diagonal transfer continuity (RDTC) for aggregator payoff function and recursive weak transfer quasi-continuity (RWTQC) for individuals’ preferences, respectively, which establishes the existence of pure strategy Nash equilibria in games with arbitrary (topological) strategy spaces and preferences without imposing any kind of quasiconcavity-related conditions.
منابع مشابه
Existence of Equilibria in Games with Arbitrary Strategy Spaces and Preferences: A Full Characterization∗
This paper studies the existence of Nash equilibria when strategy spaces are arbitrary topological spaces and preferences may be nontotal/nontransitive, discontinuous, nonconvex, or nonmonotonic. We define a single condition, recursive diagonal transfer continuity for aggregate payoffs or recursive weak transfer quasi-continuity for individuals’ preferences, which establishes the existence of N...
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