DP14046 Undiscounted Bandit Games

Author(s): R Godfrey Keller, Sven Rady
Publication Date: October 2019
Keyword(s): HJB Equation, Markov perfect equilibrium, strategic experimentation, Strong Long-Run Average Criterion, Two-Armed Bandit, Viscosity Solution
JEL(s): C73, D83
Programme Areas: Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=14046

We analyze undiscounted continuous-time games of strategic experimentation with two-armed bandits. The risky arm generates payoffs according to a Lévy 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.