Strategic experimentation with asymmetric players

Abstract

We examine a two-player game with two-armed exponential bandits à la (Keller et al. in Econometrica 73:39–68, 2005), where players operate different technologies for exploring the risky option. We characterise the set of Markov perfect equilibria and show that there always exists an equilibrium in which the player with the inferior technology uses a cut-off strategy. All Markov perfect equilibria imply the same amount of experimentation but differ with respect to the expected speed of the resolution of uncertainty. If and only if the degree of asymmetry between the players is high enough, there exists a Markov perfect equilibrium in which both players use cut-off strategies. Whenever this equilibrium exists, it welfare dominates all other equilibria. This contrasts with the case of symmetric players, where there never exists a Markov perfect equilibrium in cut-off strategies.