Learning in repeated stochastic network aggregative games

We consider a repeated network aggregative game where agents are unsure about a parameter that weights their neighbors' actions in their utility function. We consider simple learning dynamics where agents iteratively play their best response, given previous information, and update their estimate of the network weight parameter according to ordinary least squares. We derive a sufficient condition dependent on the network and on the agents' utility function to guarantee that, under these dynamics, the agents' strategies converge almost surely to the full information Nash equilibrium. We illustrate our theoretical results on a local public good game where agents are uncertain about the level of substitutability of their goods.