Strategic Experimentation with Private Payoffs

We consider two players facing identical discrete-time bandit
problems with a safe and a risky arm. In any period, the risky arm
yields either a success or a failure, and the first success reveals
the risky arm to dominate the safe one. When payoffs are public
information, the ensuing free-rider problem is so severe that the
equilibrium number of experiments is at most one plus the number of
experiments that a single agent would perform. When payoffs are
private information and players can communicate via cheap talk, the
socially optimal symmetric experimentation profile can be supported
as a perfect Bayesian equilibrium for sufficiently optimistic prior
beliefs. These results generalize to more than two players whenever
the success probability per period is not too high. In particular,
this is the case when successes occur at the jump times of a
Poisson process and the period length is sufficiently small.