Discrete-time constrained stochastic games with the expected average payoff criteria

ABSTRACT

In this paper we consider nonzero-sum discrete-time constrained stochastic games under the expected average payoff criteria. The state space is a countable set, the action spaces of the players are Borel spaces and the cost functions can be possibly unbounded. Under reasonable conditions, we first construct an approximating sequence of the auxiliary constrained stochastic game models and obtain the ergodicity of the approximating transition laws. Then basing on the properties of the invariant probability measures, we introduce a suitable multifunction and show the existence of constrained Nash equilibria for these approximating game models by a fixed point approach. Moreover, we prove the existence of a stationary constrained Nash equilibrium for the original game model via an approximation technique. Furthermore, we use a controlled population system to illustrate our results.

KEYWORDS:

• Nonzero-sum games
• expected average payoff criterion
• optimality conditions
• constrained Nash equilibrium

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 91A15
• 91A25

Acknowledgments

I am greatly indebted to the referees for the valuable comments and suggestions which have greatly improved the presentation.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The research was supported by National Natural Science Foundation of China (Grant No.11601166).