Negatively Correlated Bandits∗

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. ∗We are grateful to Philippe Aghion, Patrick Bolton, Kalyan Chatterjee, Martin Cripps, Matthias Dewatripont, Jan Eeckhout, Florian Englmair, Eduardo Faingold, Philipp Kircher, George Mailath, Timofiy Mylovanov, Stephen Ryan, Klaus Schmidt, Larry Samuelson, as well as seminar participants at Bonn, Munich, UPenn, Yale, HEC Paris, the 2007 SFB/TR 15 Summer School in Bronnbach, the 2007 SFB/TR 15 Workshop for Young Researchers in Bonn, the 2008 SFB/TR 15 Meeting in Gummersbach, the 2008 North American Summer Meetings of the Econometric Society, the 2008 Meeting of the Society for Economic Dynamics and the European Summer Symposium in Economic Theory (ESSET) 2008 for helpful comments and suggestions. We thank the Department of Economics at the University of Bonn, the Business and Public Policy Group at the Wharton School, the UPenn Economics Department and the Studienzentrum Gerzensee for their hospitality. Financial support from the Deutsche Forschungsgemeinschaft through SFB/TR 15 and GRK 801 is gratefully acknowledged. †Munich Graduate School of Economics, Kaulbachstr. 45, D-80539 Munich, Germany; email: [email protected]. ‡Department of Economics, University of Munich, Kaulbachstr. 45, D-80539 Munich, Germany; email: [email protected].