Strategic Experimentation with Poisson Bandits
AbstractWe 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 â€˜encouragement effectâ€™ 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 â€˜anticipation effectâ€™: 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.
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Bibliographic InfoPaper provided by Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich in its series Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems with number 260.
Date of creation: May 2009
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Strategic Experimentation; Two-Armed Bandit; Poisson Process; Bayesian Learning; Piecewise Deterministic Process; Markov Perfect Equilibrium; Differential-Difference Equation;
Other versions of this item:
- Sven Rady & Godfrey Keller, 2007. "Strategic Experimentation with Poisson Bandits," 2007 Meeting Papers 332, Society for Economic Dynamics.
- Keller, R Godfrey & Rady, Sven, 2009. "Strategic Experimentation with Poisson Bandits," CEPR Discussion Papers 7270, C.E.P.R. Discussion Papers.
- Keller, Godfrey & Rady, Sven, 2009. "Strategic Experimentation with Poisson Bandits," Discussion Papers in Economics 10575, University of Munich, Department of Economics.
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
- O32 - Economic Development, Technological Change, and Growth - - Technological Change; Research and Development; Intellectual Property Rights - - - Management of Technological Innovation and R&D
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- Cripps, Martin & Keller, Godfrey & Rady, Sven, 2003.
"Strategic Experimentation with Exponential Bandits,"
Discussion Papers in Economics
4, University of Munich, Department of Economics.
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