The Role of Heterogeneity in a model of Strategic Experimentation

In this paper, I examine a situation where economic agents facing a trade-off between exploring a new option and exploiting their existing knowledge about a safe option, are heterogeneous with respect to their innate abilities in exploring the new option. I consider a two-armed bandit framework in continuous time with one safe arm and one risky arm. There are two players and each has access to an identical safe arm and a risky arm. A player using the safe arm experiences a safe flow payoff whereas the payoff from a bad risky arm is worse than the safe arm and that of 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. I show that if the degree of heterogeneity between the players is high enough, then there exists a Markov perfect equilibrium in simple cutoff strategies. For any degree of heterogeneity, there always exist equilibria where at least one player uses a non-cutoff strategy. When the equilibrium in cutoff strategies exists, it strictly dominates any other equilibria. When there does not exist any equilibrium in cutoff strategies, for some range of heterogeneity we can identify the welfare maximising equilibrium. For very low range of heterogeneity, the ranking among the equilibria is ambiguous.