Network Games with Incomplete Information

We consider a network game with strategic complementarities where the individual reward or the strength of interactions is only partially known by the agents. Players receive different correlated signals and they make inferences about other players' information. We demonstrate that there exists a unique Bayesian-Nash equilibrium. We characterize the equilibrium by disentangling the information effects from the network effects and show that the equilibrium effort of each agent is a weighted combinations of different Katz-Bonacich centralities where the decay factors are the eigenvalues of the information matrix while the weights are its eigenvectors. We then study the impact of incomplete information on a network policy which aim is to target the most relevant agents in the network (key players). Compared to the complete information case, we show that the optimal targeting may be very different.