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Distributed strategic learning has been getting attention in recent years. Assystems become distributed finding Nash equilibria in a distributed fashion isbecoming more important for various applications. In this paper, we develop adistributed strategic learning framework for seeking Nash equilibria understochastic state-dependent payoff functions. We extend the work of Krsticet.al. in [1] to the case of stochastic state dependent payoff functions. Wedevelop an iterative distributed algorithm for Nash seeking and examine itsconvergence to a limiting trajectory defined by an Ordinary DifferentialEquation (ODE). We show convergence of our proposed algorithm for vanishingstep size and provide an error bound for fixed step size. Finally, we conduct astability analysis and apply the proposed scheme in a generic wirelessnetworks. We also present numerical results which corroborate our claim.

On The Convergence of a Nash Seeking Algorithm with Stochastic State Dependent Payoff