Strongly Symmetric Equilibria in Bandit Games
This paper studies strongly symmetric equilibria (SSE) in continuous-time games of strategic experimentation with Poisson bandits. SSE payoﬀs can be studied via two functional equations similar to the HJB equation used for Markov equilibria. This is valuable for three reasons. First, these equations retain the tractability of Markov equilibrium, while allowing for punishments and rewards: the best and worst equilibrium payoﬀ are explicitly solved for. Second, they capture behavior of the discrete-time game: as the period length goes to zero in the discretized game, the SSE payoﬀ set converges to their solution. Third, they encompass a large payoﬀ set: there is no perfect Bayesian equilibrium in the discrete-time game with frequent interactions with higher asymptotic eﬀiciency.
Hörner, Johannes; Klein, Nicolas; and Rady, Sven, "Strongly Symmetric Equilibria in Bandit Games" (2014). Cowles Foundation Discussion Papers. 2364.