Sudipta Sarangi (Virginia Tech) – Games Under Network Uncertainty

We consider an incomplete information network game in which agents are only aware of the identity of their immediate neighbors. They form beliefs about the links of their neighbors (the rest of the network) and play a linear-quadratic effort game to maximize interim payoffs. We establish the existence and uniqueness of Bayesian-Nash equilibria in pure strategies. In equilibrium, agents use local knowledge of their direct connections to make inferences about the complementarity strength of their actions with other agents given by their updated beliefs regarding their walks in the network. Using this and an example we show that under incomplete information, besides network architecture, agent identity plays a crucial role in determining strategic behavior. We also characterize equilibrium behavior under different forms of ex-ante prior beliefs like uniform priors, Erdos-Renyi network generation, and homophilic linkage. Not surprisingly, uniform priors provide similar results similar to degree-based models of incomplete information.