More strategies, more Nash equilibria

Sophie Bade; Guillaume Haeringer; Ludovic Renou

doi:10.1016/j.jet.2005.08.009

More strategies, more Nash equilibria

Sophie Bade, Guillaume Haeringer, Ludovic Renou

Department of Economics and Economic History

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

Abstract

We show in this paper that for the class of two-player games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions there exists a monotone relation between the size of strategy spaces and the number of Nash equilibria. These sufficient conditions for our theorem to hold are shown to be tight. © 2006 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	551-557
Journal	Journal of Economic Theory
Volume	135
Issue number	1
DOIs	https://doi.org/10.1016/j.jet.2005.08.009
Publication status	Published - 1 Jul 2007

Keywords

Nash equilibrium
Number of Nash equilibria
Strategic-form games
Strategy spaces

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abstract = "We show in this paper that for the class of two-player games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions there exists a monotone relation between the size of strategy spaces and the number of Nash equilibria. These sufficient conditions for our theorem to hold are shown to be tight. {\textcopyright} 2006 Elsevier Inc. All rights reserved.",

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AB - We show in this paper that for the class of two-player games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions there exists a monotone relation between the size of strategy spaces and the number of Nash equilibria. These sufficient conditions for our theorem to hold are shown to be tight. © 2006 Elsevier Inc. All rights reserved.

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KW - Number of Nash equilibria

KW - Strategic-form games

KW - Strategy spaces

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