An Adjusted Payoff-Based Procedure for Normal Form Games

• 成果类型: Article
• 署名作者: Bravo, Mario
• 署名单位: Universidad de Santiago de Chile
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0785
• 发表日期: 2016
• 页码: 1469-1483
• 关键词: urn models; reinforcement; algorithms; DYNAMICS

摘要

We study a simple adaptive model in the framework of an N -player normal form game. The model consists of a repeated game where the players only know their own action space and their own payoff scored at each stage, not those of the other agents. Each player, in order to update her mixed action, computes the average vector payoff she has obtained by using the number of times she has played each pure action. The resulting stochastic process is analyzed via the ODE method from stochastic approximation theory. We are interested in the convergence of the process to rest points of the related continuous dynamics. Results concerning almost sure convergence and convergence with positive probability are obtained and applied to a traffic game. We also provide some examples where convergence occurs with probability zero.