Strategic experimentation with Poisson bandits

• 成果类型: Article
• 署名作者: Keller, Godfrey; Rady, Sven
• 署名单位: University of Oxford; University of Munich
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE595
• 发表日期: 2010-05-01
• 页码: 275-311
• 关键词: Strategic experimentation; two-armed bandit; Poisson process; Bayesian learning; piecewise deterministic process; Markov perfect equilibrium; differential-difference equation

摘要

We study a game of strategic experimentation with two-armed bandits where the risky arm distributes lump-sum payoffs according to a Poisson process. Its intensity is either high or low, and unknown to the players. We considerMarkov perfect equilibria with beliefs as the state variable and show that all such equilibria exhibit an encouragement effect relative to the single-agent optimum. There is no equilibrium in which all players use cutoff strategies. Owing to the encouragement effect, asymmetric equilibria in which players take turns playing the risky arm before all experimentation stops Pareto dominate the unique symmetric equilibrium. Rewarding the last experimenter with a higher continuation value increases the range of beliefs where players experiment, but may reduce the intensity of experimentation at more optimistic beliefs. This suggests that there is no equilibrium that uniformly maximizes the players' average payoff.