We show that many results on the structure and stability of equilibria in finite games extend to Poisson games. In particular, the set of Nash equilibria of a Poisson game consists of finitely many connected components and at least one of them contains a stable set (De Sinopoli et al., 2014). In a similar vein, we prove that the number of Nash equilibria in Poisson voting games under plurality, negative plurality, and (when there are at most three candidates) approval rule, as well as in Poisson coordination games, is generically finite. As in finite games, these results are obtained exploiting the geometric structure of the set of Nash equilibria which, in the case of Poisson games, is shown to be semianalytic.

The structure of Nash equilibria in Poisson games / C. Meroni, C. Pimienta. - In: JOURNAL OF ECONOMIC THEORY. - ISSN 0022-0531. - 169(2017 May), pp. 128-144. [10.1016/j.jet.2017.02.003]

The structure of Nash equilibria in Poisson games

C. Meroni;
2017

Abstract

We show that many results on the structure and stability of equilibria in finite games extend to Poisson games. In particular, the set of Nash equilibria of a Poisson game consists of finitely many connected components and at least one of them contains a stable set (De Sinopoli et al., 2014). In a similar vein, we prove that the number of Nash equilibria in Poisson voting games under plurality, negative plurality, and (when there are at most three candidates) approval rule, as well as in Poisson coordination games, is generically finite. As in finite games, these results are obtained exploiting the geometric structure of the set of Nash equilibria which, in the case of Poisson games, is shown to be semianalytic.
generic determinacy of equilibria; o-Minimal structures; Poisson games; stable sets; voting
Settore SECS-P/01 - Economia Politica
mag-2017
20-feb-2017
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/712686
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