Abstract
In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results.
Highlights
Stochastic games introduced by Shapley in Reference [1] which have been actively pursued over the last few decades because of several applications mainly in economics and queueing system; see, for instance, References [2,3,4,5]
By the properties of w-weak convergence, we study the asymptotic properties of average occupation measures and expected average costs, which are used to establish the upper-continuity of the multifunction
We have studied the discrete-time constrained stochastic games with denumerable state space under the average cost criteria
Summary
Stochastic games introduced by Shapley in Reference [1] which have been actively pursued over the last few decades because of several applications mainly in economics and queueing system; see, for instance, References [2,3,4,5]. In Reference [6], the authors present an existence condition of stationary Nash equilibria for the constrained average games. Different from the framework of game model considered in this paper, References [2,8,9] study the so-called centralized stochastic games in which all players jointly control a single Markov chain and the one-stage costs of each player are influenced by the actions of all players. Considers the game model with expected discounted cost criteria and expected average cost criteria and yields the existence of stationary Nash equilibria in the context of finite state space and compact action spaces. In this paper, we use fixed-point method directly because the existence of discounted Nash equilibria for stochastic games with independent state process has not been established.
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