Learning in games with unstable equilibria

• 成果类型: Article
• 署名作者: Benaim, Michel; Hofbauer, Josef; Hopkins, Ed
• 署名单位: University of Edinburgh; University of Neuchatel; University of Vienna
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2008.09.003
• 发表日期: 2009
• 页码: 1694-1709
• 关键词: games; learning; best response dynamics; Stochastic fictitious play; Mixed strategy equilibria; TASP

摘要

We propose a new concept for the analysis of games, the TASP, which gives a precise prediction about non-equilibrium play in games whose Nash equilibria are mixed and are unstable under fictitious play-like learning. We show that, when players learn using weighted stochastic fictitious play and so place greater weight on recent experience, the time average of play often converges in these unstable games, even while mixed strategies and beliefs continue to cycle. This time average, the TASP, is related to the cycle identified by Shapley [L.S. Shapley, Some topics in two person games, in: M. Dresher, et al. (Eds.), Advances in Game Theory, Princeton University Press, Princeton, 1964]. The TASP can be close to or quite distinct from Nash equilibrium. (C) 2008 Elsevier Inc. All rights reserved.