Imperfect Information, Social Norms, and Beliefs in Networks

We develop a simple Bayesian network game in which players, embedded in a network of social interactions, bear a cost from deviating from the social norm of their peers. All agents face uncertainty about the private benefits and the private and social costs of their actions. We prove the existence and uniqueness of a Bayesian Nash equilibrium and characterize players’ optimal actions. We then show that denser networks do not necessary increase agents’ actions and welfare. We also find that, in some cases, it is optimal for the planner to affect the payoffs of selected individuals rather than all agents in the network. We finally show that having more information is not always beneficial to agents and can, in fact, reduce their welfare. We illustrate all our results in the context of criminal networks in which offenders do not know with certitude the probability of being caught and do not want to be different from their peers in terms of criminal activities.