Undiscounted bandit games

• 成果类型: Article
• 署名作者: Keller, Godfrey; Rady, Sven
• 署名单位: University of Oxford; University of Bonn; University of Bonn
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2020.08.003
• 发表日期: 2020
• 页码: 43-61
• 关键词: Strategic experimentation; Bayesian two-armed bandit; Strong long-run average criterion; Markov perfect equilibrium; HJB equation; Viscosity solution

摘要

We analyze undiscounted continuous-time games of strategic experimentation with two armed bandits. The risky arm generates payoffs according to a Levy process with an unknown average payoff per unit of time which nature draws from an arbitrary finite set. Observing all actions and realized payoffs, plus a free background signal, players use Markov strategies with the common posterior belief about the unknown parameter as the state variable. We show that the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the payoff of the safe arm, the expected current payoff of the risky arm, and the expected full-information payoff, given the current belief. In particular, the equilibrium does not depend on the precise specification of the payoff-generating processes. (c) 2020 Elsevier Inc. All rights reserved.