Undiscounted bandit games

Working paper

We analyze undiscounted continuous-time games of strategic experimentation with two-armed bandits. The risky arm generates payoffs according to a Le´vy process with an unknown average payoff per unit of time which nature draws from an arbitrary finite set. Observing all actions and realized payoffs, players use Markov strategies with the common posterior belief about the unknown parameter as the state variable. We show that the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the payoff of the safe arm, the expected current payoff of the risky arm, and the expected full-information payoff, given the current belief. In particular, the equilibrium does not depend on the precise specification of the payoff-generating processes.

Authors: Keller, G; Rady, S

• Publication status: Published
• Publisher: University of Oxford
• Series: Department of Economics Discussion Paper Series
• Publication date: 2019-10-10
• Paper number: 882
• Keywords: Markov Perfect equilibrium; strategic experimentation; viscosity solution; two-armed bandit; HJb equation; strong long-run average criterion