Intelligent Players in a Fictitious Play Framework

• 成果类型: Article
• 署名作者: Vundurthy, Bhaskar; Kanellopoulos, Aris; Gupta, Vijay; Vamvoudakis, Kyriakos G.
• 署名单位: Carnegie Mellon University; Royal Institute of Technology; Purdue University System; Purdue University; University System of Georgia; Georgia Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3266505
• 发表日期: 2024
• 页码: 479-486
• 关键词: games; IP networks; Nash equilibrium; CONVERGENCE; absorption; trajectory; STANDARDS; Fragility of algorithms; learning in games; Multi-agent systems

摘要

Fictitious play is a popular learning algorithm in which players that utilize the history of actions played by the players and the knowledge of their own payoff matrix can converge to the Nash equilibrium under certain conditions on the game. We consider the presence of an intelligent player that has access to the entire payoff matrix for the game. We show that by not conforming to fictitious play, such a player can achieve a better payoff than the one at the Nash Equilibrium. This result can be viewed both as a fragility of the fictitious play algorithm to a strategic intelligent player and an indication that players should not throw away additional information they may have, as suggested by classical fictitious play.