Average stochastic games for continuous-time jump processes

We consider nonzero-sum games for continuous-time jump processes with unbounded transition rates under expected average payoff criterion. The state and action spaces are Borel spaces and reward rates are unbounded. We introduce an approximating sequence of stochastic game models with extended state space, for which the uniform exponential ergodicity is obtained. Moreover, we prove the existence of a stationary almost Markov Nash equilibrium by introducing auxiliary static game models. Finally, a cash flow model is employed to illustrate the results. (c) 2020 Elsevier B.V. All rights reserved.

Automated summary

In this study, nonzero-sum games for continuous-time jump processes with unbounded transition rates under expected average payoff criterion are considered. An approximating sequence of stochastic game models with extended state space is introduced to achieve uniform exponential ergodicity. Additionally, the existence of a stationary almost Markov Nash equilibrium is proven by introducing auxiliary static game models.