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Strongly Symmetric Equilibria in Bandit Games

(by Sven Rady, with Johannes Hörner and Nicholas Klein)

SFB/TR 15 Discussion Paper No. 469, August 2014

This paper has been superseded by "Overcoming Free-Riding in Bandit Games" No. 135


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.


Keywords: Two-Armed Bandit, Bayesian Learning, Strategic Experimentation,

Strongly Symmetric Equilibrium.

JEL Classification Numbers: C73, D83.

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