Collective Experimentation with Correlated Payoffs

Abstract: This paper studies an exponential bandit model in which a group of agents collectively decide whether to undertake a risky action $R$. This action is implemented if the fraction of agents voting for it exceeds a predetermined threshold $k$. Building on Strulovici (2008), which assumes the agents' payoffs are independent, we explore the case in which the agents' payoffs are correlated. During experimentation, each agent learns individually whether she benefits from $R$; in this way, she also gains information about its overall desirability. Furthermore, each agent is able to learn indirectly from the others, because in making her decisions, she conditions on being pivotal (i.e., she assumes her vote will determine the collective outcome). We show that, when the number of agents is large, increasing the threshold $k$ for implementing $R$ leads to increased experimentation. However, information regarding the overall desirability of $R$ is effectively aggregated only if $k$ is sufficiently low.