p-dominance and equilibrium selection under perfect foresight dynamics

• 成果类型: Article
• 署名作者: Oyama, D
• 署名单位: University of Tokyo
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1006/jeth.2001.2955
• 发表日期: 2002
• 页码: 288-310
• 关键词: Equilibrium selection; perfect foresight dynamics; linear stability; p-Dominance

摘要

This paper studies equilibrium selection based on a class of perfect foresight dynamics and relates it to the notion of p-dominance. A continuum of rational players is repeatedly and randomly matched to play a symmetric n x n game. There are frictions: opportunities to revise actions follow independent Poisson processes. The dynamics has stationary states, each of which corresponds to a Nash equilibrium of the static game. A strict Nash equilibrium is linearly stable under the perfect foresight dynamics if, independent of the current action distribution, there exists a consistent belief that any player necessarily plays the Nash equilibrium action at every revision opportunity. It is shown that a strict Nash equilibrium is linearly stable under the perfect foresight dynamics with a small degree of friction if and only if it is the p-dominant equilibrium with p < 1/2. It is also shown that if a strict Nash equilibrium is the p-dominant equilibrium with p < 1/2, then it is uniquely absorbing (and globally accessible) for a small friction (but not vice versa). Set-valued stability concepts are introduced and their existence is shown. (C) 2002 Elsevier Science (USA).