Stability and convergence of non-cooperative stochastic adaptive games

In this paper, we consider non-cooperative stochastic adaptive games defined by linear discrete-time stochastic systems with two players. The players are of `bounded rationality' and are purposed to design strategy profile to optimize their respective quadratic payoff functions. The strategy profile of the players has unknown parameters, which are estimated by the well-known LS algorithm on line. The resulting adaptive profile is shown to have some nice stability and convergence properties, for example, an asymptotic Nash equilibrium can be reached.