Distributed filters for Bayesian network games

We consider a repeated network game where agents' utilities are quadratic functions of the state of the world and actions of all the agents. The state of the world is represented by a vector on which agents receive private signals with Gaussian noise. We define the solution concept as Bayesian Nash equilibrium and present a recursion to compute equilibrium strategies locally if an equilibrium exists at all stages. We further provide conditions under which a unique equilibrium exists. We conclude with an example of the proposed recursion in a repeated Cournot competition game and discuss properties of convergence such as efficient learning and convergence rate.