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 equi\-libria 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.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
Publisher Info
Paper provided by University of Munich, Department of Economics in its series Discussion Papers in Economics with number
10575.
Godfrey Keller & Sven Rady, 2009.
"Strategic Experimentation with Poisson Bandits,"
Discussion Papers
260, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
[Downloadable!]
Find related papers by JEL classification: 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 - - - Management of Technological Innovation and R&D
This paper has been announced in the following NEP Reports:
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.: