Existence of pure equilibria in symmetric two-player zero-sum games

Mehmet Ismail

Existence of pure equilibria in symmetric two-player zero-sum games

Political Economy

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

Abstract

This paper contributes to the literature on pure equilibria in symmetric zero-sum games in two main ways. First, we introduce new sufficient conditions, including interchangeability and weak quasiconcavity, for the existence of such equilibria. Second, we uncover relationships between these newly introduced conditions and existing ones. For instance, we demonstrate that the class of weakly quasiconcave games generalizes the class of quasiconcave games and ordinal potential games. Additionally, we show that exact potential games satisfy the interchangeability condition. However, no logical relationship exists between interchangeability and (weak) quasiconcavity.

Original language	English
Journal	INTERNATIONAL JOURNAL OF GAME THEORY
Publication status	Accepted/In press - 18 Mar 2025

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Existence_of_Pure_Equilibrium_March_2025Accepted author manuscript, 289 KB

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abstract = "This paper contributes to the literature on pure equilibria in symmetric zero-sum games in two main ways. First, we introduce new sufficient conditions, including interchangeability and weak quasiconcavity, for the existence of such equilibria. Second, we uncover relationships between these newly introduced conditions and existing ones. For instance, we demonstrate that the class of weakly quasiconcave games generalizes the class of quasiconcave games and ordinal potential games. Additionally, we show that exact potential games satisfy the interchangeability condition. However, no logical relationship exists between interchangeability and (weak) quasiconcavity.",

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AB - This paper contributes to the literature on pure equilibria in symmetric zero-sum games in two main ways. First, we introduce new sufficient conditions, including interchangeability and weak quasiconcavity, for the existence of such equilibria. Second, we uncover relationships between these newly introduced conditions and existing ones. For instance, we demonstrate that the class of weakly quasiconcave games generalizes the class of quasiconcave games and ordinal potential games. Additionally, we show that exact potential games satisfy the interchangeability condition. However, no logical relationship exists between interchangeability and (weak) quasiconcavity.

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