Overcoming Free-Riding in Bandit Games

TL;DR

This paper demonstrates that in experimentation games with Levy bandits, efficient equilibria exist under certain conditions, highlighting the importance of the solution concept rather than the model's intrinsic nature.

Contribution

It shows that efficient perfect Bayesian equilibria exist in Levy bandit games with diffusion components, and these equilibria can be approximated in discrete time.

Findings

Efficient equilibria exist when payoffs have a diffusion component.

Equilibria in discrete-time games converge to continuous-time equilibria.

Relaxing to strongly symmetric equilibrium suffices for efficiency.

Abstract

This paper considers a class of experimentation games with L\'{e}vy bandits encompassing those of Bolton and Harris (1999) and Keller, Rady and Cripps (2005). 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 (MPE). This is not an artifact 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.