Strategic Experimentation with Poisson Bandits

Keller, Godfrey and Rady, Sven (09. April 2009): Strategic Experimentation with Poisson Bandits. Discussion Papers in Economics 2009-5

Abstract

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 consider Markov perfect equilibria with beliefs as the state variable. As the belief process is piecewise deterministic, payoff functions solve differential-difference equations. There is no equilibrium where all players use cut-off strategies, and all equilibria exhibit an `encouragement effect' relative to the single-agent optimum. We construct asymmetric equilibria in which players have symmetric continuation values at sufficiently optimistic beliefs yet take turns playing the risky arm before all experimentation stops. Owing to the encouragement effect, these equilibria Pareto dominate the unique symmetric one for sufficiently frequent turns. Rewarding the last experimenter with a higher continuation value increases the range of beliefs where players experiment, but may reduce average payoffs at more optimistic beliefs. Some equilibria exhibit an `anticipation effect': as beliefs become more pessimistic, the continuation value of a single experimenter increases over some range because a lower belief means a shorter wait until another player takes over.

• Item Type: Paper (Discussion Paper)
• Keywords: Strategic Experimentation, Two-Armed Bandit, Poisson Process, Bayesian Learning, Piecewise Deterministic Process, Markov Perfect Equilibrium, Differential-Difference Equation
• Subjects: Economics; Economics > Discussion Papers in Economics; Economics > Discussion Papers in Economics > Economics of Information; Economics > Discussion Papers in Economics > Mathematical Methods; Economics > Discussion Papers in Economics > Game Theory
• Dewey Classification: 300 Social sciences; 300 Social sciences > 330 Wirtschaft
• Journal of Economic Literature classification: C73, D83, O32
• Language: English