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Strategic Experimentation with Exponential Bandits

(by Sven Rady, with Godfrey Keller) and Martin Cripps)


Econometrica 73(1), January 2005, pp. 39-68

Previously circulated as:
Oxford Department of Economics Discussion Paper No. 134
Munich Department of Economics Discussion Paper No. 03-02
CEPR Discussion Paper No. 3814

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We analyse a game of strategic experimentation with two-armed bandits whose risky arm might yield payoffs after exponentially distributed random times. Free-riding causes an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with beliefs as the state variable. We construct the unique symmetric Markovian equilibrium of the game, followed by various asymmetric ones. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between experimenting and free-riding all yield a similar pattern of information acquisition, greater efficiency being achieved when the players share the burden of experimentation more equitably. When players switch roles infinitely often, they can acquire an approximately efficient amount of information, but still at an inefficient rate. In terms of aggregate payoffs, all these asymmetric equilibria dominate the symmetric one wherever the latter prescribes simultaneous use of both arms.

Keywords: Strategic Experimentation, Two-Armed Bandit, Exponential Distribution
JEL Classification: C73, D83, H41, O32

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