Constrained average stochastic games with continuous-time independent state processes

ABSTRACT

This paper attempts to study nonzero-sum continuous-time constrained average stochastic games with independent state processes. In these game models, each player independently controls a continuous-time Markov chain, but players are coupled by the immediate cost functions. The transition rates and immediate cost functions are allowed to be unbounded. Each player wants to minimize certain expected average cost, but constraints are imposed on other expected average costs. By introducing the average occupation measures, we establish the one-to-one relationship of constrained Nash equilibria and the fixed points of certain multifunction defined on the product space of average occupation measures. Then, by using the fixed point theorem, we show the existence of constrained Nash equilibria. Finally, we show that each stationary Nash equilibrium corresponds to a global minimizer of a certain mathematical program.

Keywords:

• Constrained Nash equilibrium
• expected average criterion
• average occupation measure

Mathematics Subject Classifications:

• 90C40
• 91A15

Acknowledgements

We are greatly indebted to the editors and the anonymous referees for their constructive comments. The first author was funded by National Natural Science Foundation of China (Grant No.11801080). The research of the second author was supported by National Natural Science Foundation of China (Grant No.61673019, 61973096).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author was funded by National Natural Science Foundation of China [grant number 11801080]. The research of the second author was supported by National Natural Science Foundation of China [grant numbers 61673019, 61973096].