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Strategic Experimentation with Exponential Bandits

R Keller (), Martin Cripps, Olin School of Business, Washington University, Sven Rady, Department of Economics and University of Munich

No 143, Economics Series Working Papers from University of Oxford, Department of Economics

Abstract: This paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a payoff only after some exponentially distributed random time. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with posterior beliefs as the state variable. After characterizing the unique symmetric Markovian equilibrium of the game, which is in mixed strategies, we construct a variety of pure-strategy equilibria. There is no equilibrium where all players use simple cut-off strategies. 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. 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; moreoever, the expected payoff of an experimenter exhibits the novel feature that it rises as players become more pessimistic. Finally, over the range of beliefs where players use both arms a positive fraction of the time, the symmetric equilibrium is dominated by any asymmetric one in terms of aggregate payoffs.

Keywords: strategic experimentation; two-armed bandit; exponential distribution; Bayesian learning; Markov perfect equilibrium; public goods (search for similar items in EconPapers)
JEL-codes: C73 D83 H41 O32 (search for similar items in EconPapers)
Date: 2003-01-01
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Journal Article: Strategic Experimentation with Exponential Bandits (2005) Downloads
Working Paper: Strategic Experimentation with Exponential Bandits (2003) Downloads
Working Paper: Strategic Experimentation with Exponential Bandits (2003) Downloads
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