Negatively Correlated Bandits

31 Pages Posted: 2 Dec 2008

See all articles by Nicolas A. Klein

Nicolas A. Klein

University of Bonn - Institute of Economic Theory II

Sven Rady

University of Bonn

Multiple version iconThere are 2 versions of this paper

Date Written: October 2008

Abstract

We analyze a two-player game of strategic experimentation with two-armed bandits. Each player has to decide in continuous time whether to use a safe arm with a known payoff or a risky arm whose likelihood of delivering payoffs is initially unknown. The quality of the risky arms is perfectly negatively correlated between players. In marked contrast to the case where both risky arms are of the same type, we find that learning will be complete in any Markov perfect equilibrium if the stakes exceed a certain threshold, and that all equilibria are in cutoff strategies. For low stakes, the equilibrium is unique, symmetric, and coincides with the planner's solution. For high stakes, the equilibrium is unique, symmetric, and tantamount to myopic behavior. For intermediate stakes, there is a continuum of equilibria.

Keywords: Bayesian Learning, Exponential Distribution, Markov Perfect Equilibrium, Poisson Process, Strategic Experimentation, Two-Armed Bandit

JEL Classification: C73, D83, O32

Suggested Citation

Klein, Nicolas A. and Rady, Sven, Negatively Correlated Bandits (October 2008). CEPR Discussion Paper No. DP6983, Available at SSRN: https://ssrn.com/abstract=1308054

Nicolas A. Klein

University of Bonn - Institute of Economic Theory II ( email )

Lennestrasse 37
53113 Bonn
Germany

Sven Rady (Contact Author)

University of Bonn ( email )

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

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