Strategic Experimentation with Competition and Private Arrival of Information

This paper considers a two-armed bandit problem with one safe arm and one risky arm. The risky arm if good, can potentially experience two kinds of arrivals. One is publicly observable and the other is private to the agent who experiences it. The safe arm experiences publicly observable arrivals according to a given intensity. Private arrivals yield no payoff. Only the first publicly observed arrival(in any of the arms) yields a payo of 1 unit. Players start with a common prior about the quality of the risky arm. It has been shown that in a particular kind symmetric equilibrium, conditional on no arrival players tend to experiment too much along the risky arm if they start with too high a prior and experiment too less if they start with a low prior.