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The structure of Nash equilibria in Poisson games

Claudia Meroni () and Carlos Pimienta ()

No 25/2015, Working Papers from University of Verona, Department of Economics

Abstract: In finite games, the graph of the Nash equilibrium correspondence is a semialgebraic set (i.e. it is defined by finitely many polynomial inequal- ities). This fact implies many game theoretical results about the structure of equilibria. We show that many of these results can be readily exported to Poisson games even if the expected utility functions are not polynomials. We do this proving that, in Poisson games, the graph of the Nash equilibrium correspondence is a globaly subanalytic set. Many of the properties of semialgebraic sets follow from a set of axioms that the collection of globaly subanalytic sets also satisfy. Hence, we easily show that every Poisson game has finitely many connected components and that at least one of them contains a stable set of equilibria. By the same reasoning, we also show how generic determinacy results in finite games can be extended to Poisson games.

Keywords: Poisson games; voting; stable sets; o-minimal structures; globaly subanalytic sets. (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
Date: 2015-10
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Journal Article: The structure of Nash equilibria in Poisson games (2017) Downloads
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