The repeated interaction of rational agents in networked environments with uncertainty where agents' payoffs depend on behavior of the whole society is called a Bayesian Network game. The rational strategy of an agent is determined by the Bayesian Nash equilibrium. We discuss asymptotic properties of these games.  For the particular case of quadratic payoffs we introduce the Quadratic Network Game filter that agents can run locally to update their beliefs, select corresponding optimal actions, and eventually learn a sufficient statistic of the network's state. Lastly, we present an application of the class of games considered and the game filter to a demand side management model in smart grids with heterogeneous users and renewable energy supply uncertainty.