This article considers a class of experimentation games with Lévy bandits encompassing those of Bolton and Harris (1999, Econometrica, 67, 349–374) and Keller, Rady, and Cripps (2005, Econometrica, 73, 39–68). Its main result is that efficient (perfect Bayesian) equilibria exist whenever players’ payoffs have a diffusion component. Hence, the trade-offs emphasized in the literature do not rely on the intrinsic nature of bandit models but on the commonly adopted solution concept (Markov perfect equilibrium). This is not an artefact of continuous time: we prove that efficient equilibria arise as limits of equilibria in the discrete-time game. Furthermore, it suffices to relax the solution concept to strongly symmetric equilibrium.