Journal Article

Negatively Correlated Bandits

Nicolas Klein and Sven Rady

in The Review of Economic Studies

Published on behalf of Review of Economic Studies Ltd

Volume 78, issue 2, pages 693-732
Published in print April 2011 | ISSN: 0034-6527
Published online February 2011 | e-ISSN: 1467-937X | DOI: http://dx.doi.org/10.1093/restud/rdq025
Negatively Correlated Bandits

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  • Information, Knowledge, and Uncertainy
  • Game Theory and Bargaining Theory
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We analyse a two-player game of strategic experimentation with two-armed bandits. Either player has to decide in continuous time whether to use a safe arm with a known pay-off or a risky arm whose expected pay-off per unit of time is initially unknown. This pay-off can be high or low and is negatively correlated across players. We characterize the set of all Markov perfect equilibria in the benchmark case where the risky arms are known to be of opposite type and construct equilibria in cut-off strategies for arbitrary negative correlation. All strategies and pay-offs are in closed form. In marked contrast to the case where both risky arms are of the same type, there always exists an equilibrium in cut-off strategies, and there always exists an equilibrium exhibiting efficient long-run patterns of learning. These results extend to a three-player game with common knowledge that exactly one risky arm is of the high pay-off type.

Keywords: Strategic experimentation; Two-armed bandit; Exponential distribution; Poisson process; Bayesian learning; Markov perfect equilibrium; C73; D83; O32

Journal Article.  19873 words.  Illustrated.

Subjects: Information, Knowledge, and Uncertainy ; Game Theory and Bargaining Theory ; Technological Change; Research and Development

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