An axiomatic characterization of Nash equilibrium

• 成果类型: Article
• 署名作者: Brandl, Florian; Brandt, Felix
• 署名单位: University of Bonn; Technical University of Munich
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE5825
• 发表日期: 2024-11-01
• 页码: 1473-1504
• 关键词: Game theory; axiomatic characterization; Nash equilibrium; C72

摘要

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability, (ii) if a strategy profile is played in two games, it is also played in every convex combination of these games, and (iii) players can shift probability arbitrarily between two indistinguishable actions, and deleting one of these actions has no effect. Our theorem implies that every equilibrium refinement violates at least one of these axioms. Moreover, every solution concept that approximately satisfies these axioms returns approximate Nash equilibria, even in natural subclasses of games, such as two-player zero-sum games, potential games, and graphical games.