  Distributed strategic learning has been getting attention in recent years. As
systems become distributed finding Nash equilibria in a distributed fashion is
becoming more important for various applications. In this paper, we develop a
distributed strategic learning framework for seeking Nash equilibria under
stochastic state-dependent payoff functions. We extend the work of Krstic
et.al. in [1] to the case of stochastic state dependent payoff functions. We
develop an iterative distributed algorithm for Nash seeking and examine its
convergence to a limiting trajectory defined by an Ordinary Differential
Equation (ODE). We show convergence of our proposed algorithm for vanishing
step size and provide an error bound for fixed step size. Finally, we conduct a
stability analysis and apply the proposed scheme in a generic wireless
networks. We also present numerical results which corroborate our claim.
