Strategic Experimentation with Exponential Bandits

40 Pages Posted: 2 May 2003  

Martin Cripps

University College London - Department of Economics; Washington University in St. Louis - John M. Olin Business School

Godfrey Keller

University of Oxford - Department of Economics

Sven Rady

University of Bonn

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Date Written: March 2003

Abstract

This Paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a pay-off 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; moreover, the expected pay-off 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 pay-offs.

Keywords: Strategic experimentation, two-armed bandits, exponential distribution, Bayesian learning, Markov perfect equilibrium, public goods

JEL Classification: C73, D83, H41, O32

Suggested Citation

Cripps, Martin and Keller, Godfrey and Rady, Sven, Strategic Experimentation with Exponential Bandits (March 2003). CEPR Discussion Paper No. 3814. Available at SSRN: https://ssrn.com/abstract=401481

Martin Cripps

University College London - Department of Economics ( email )

Gower Street
London
London, WC1E 6BT
United Kingdom

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-4580 (Phone)
314-935-6359 (Fax)

Godfrey Keller

University of Oxford - Department of Economics ( email )

Manor Road Building
Manor Road
Oxford, OX1 3BJ
United Kingdom
+44 20 1865 281173 (Phone)

Sven Rady (Contact Author)

University of Bonn ( email )

Regina-Pacis-Weg 3
Postfach 2220
Bonn, D-53012
Germany

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