The Role of Heterogeneity in a Model of Strategic Experimentation

In this paper, I examine the effect of introducing heterogeneity between players in a model of strategic experimentation. I consider a two-armed bandit problem in continuous time with one safe arm and a risky arm. There are two players and each has an access to such a bandit. A player using the safe arm experiences a safe flow payoff. The risky arm can either be good or bad. A bad risky arm is worse than the safe arm and the good risky arm is better than the safe arm. Players start with a common prior about the probability of the risky arm being good. At a time point, a player can choose only one of the arms. I show that if the degree of heterogeneity between the players is high enough, then there exists a unique Markov perfect equilibrium in simple cut-off strategies. The non-cooperative equilibrium in the heterogeneous model in terms of welfare, always gets a higher rank than any non-cooperative equilibrium of a homogeneous players model with same or more amount of experimentation in the benchmark.