Learning in unprofitable games

• 成果类型: Article
• 署名作者: Gaunersdorfer, Andrea; Hofbauer, Josef
• 署名单位: University of Vienna; University of Vienna
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2025.03.001
• 发表日期: 2025
• 页码: 108-126
• 关键词: Unprofitable games; Nash equilibrium; Maximin strategy; Quantal response equilibrium; Replicator dynamics; best response dynamics; Logit dynamics

摘要

A game is unprofitable if equilibrium payoffs do not exceed the maximin payoff for each player. In an unprofitable game, Nash equilibrium play has been notoriously difficult to justify. For a class of 3x3 games we analyze whether evolutionary and learning processes lead to Nash play. We find that neither the pure Nash equilibrium nor the pure maximin strategy are stable rest points under the studied dynamics whereas the mixed Nash equilibrium and the quantal response equilibrium may be attractors, repellors or surrounded by periodic orbits.