Strategic Experimentation: The Case of Poisson Bandits
University College London - Department of Economics; Washington University in Saint Louis - John M. Olin Business School
University of Oxford - Department of Economics
University of Bonn; Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute for Economic Research)
CESifo Working Paper Series No. 737
This paper studies a game of strategic experimentation in which the players have access to two-armed bandits where the risky arm distributes lump-sum payoffs according to a Poisson process with unknown intensity. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies. We characterize the unique symmetric Markovian equilibrium of the game, which is in mixed strategies. A variety of asymmetric pure-strategy equilibria is then constructed for the special case where there are two players and the arrival of the first lump-sum fully reveals the quality of the risky arm. Equilibria where players switch finitely often between the roles of experimenter and free-rider all lead to the same pattern of information acquisition; the efficiency of these equilibria depends on the way players share the burden of experimentation among them. We show that at least for relatively pessimistic beliefs, even the worst asymmetric equilibrium is more efficient than the symmetric one. In equilibria where players switch roles infinitely often they can acquire an approximately efficient amount of information, but the rate at which it is acquired still remains inefficient.
Number of Pages in PDF File: 37
Keywords: Strategic Experimentation, Two-armed Bandit, Poisson Process, Bayesian Learning, Markov Perfect Equilibrium, Public Goods
JEL Classification: C73, D83, H41, O32working papers series
Date posted: September 19, 2002
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