Strategic Experimentation with Poisson Bandits

Keller, Godfrey and Rady, Sven (May 2009): Strategic Experimentation with Poisson Bandits. SFB/TR 15 Discussion Paper No. 260

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 piece-wise 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
• Keywords: Strategic Experimentation, Two-Armed Bandit, Poisson Process, Bayesian Learning, Piecewise Deterministic Process, Markov Perfect Equilibrium, Differential-Difference Equation
• Faculties: Special Research Fields > Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems; Special Research Fields > Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems > A8 - Strategische Erzeugung und Weitergabe von Informationen; Economics; Economics > Chairs > Chair of Dynamic Economic Theory (closed)
• Subjects: 300 Social sciences > 330 Economics
• JEL Classification: C73, D83, O32
• Language: English