Towards a taxonomy of learning dynamics in 2 x 2 games

• 成果类型: Article
• 署名作者: Pangallo, Marco; Sanders, James B. T.; Galla, Tobias; Farmer, J. Doyne
• 署名单位: Scuola Superiore Sant'Anna; Scuola Superiore Sant'Anna; University of Manchester; University of Oxford; University of Oxford; The Santa Fe Institute
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.11.015
• 发表日期: 2022
• 页码: 1-21
• 关键词: Behavioural game theory; EWA learning; CONVERGENCE; equilibrium; chaos

摘要

Do boundedly rational players learn to choose equilibrium strategies as they play a game repeatedly? A large literature in behavioral game theory has proposed and experimentally tested various learning algorithms, but a comparative analysis of their equilibrium convergence properties is lacking. In this paper we analyze Experience-Weighted Attraction (EWA), which generalizes fictitious play, best-response dynamics, reinforcement learning and also replicator dynamics. Studying 2 x 2 games for tractability, we recover some wellknown results in the limiting cases in which EWA reduces to the learning rules that it generalizes, but also obtain new results for other parameterizations. For example, we show that in coordination games EWA may only converge to the Pareto-efficient equilibrium, never reaching the Pareto-inefficient one; that in Prisoner Dilemma games it may converge to fixed points of mutual cooperation; and that limit cycles or chaotic dynamics may be more likely with longer or shorter memory of previous play. (C) 2021 Elsevier Inc. All rights reserved.