Stochastic Games for Continuous-Time Jump Processes Under Finite-Horizon Payoff Criterion

Journal Article · Sat Oct 15 04:00:00 EDT 2016 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-015-9314-4· OSTI ID:22617198

Wei, Qingda ^[1]; Chen, Xian ^[2]

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1. Huaqiao University, School of Economics and Finance (China)
2. Peking University, School of Mathematical Sciences (China)

In this paper we study two-person nonzero-sum games for continuous-time jump processes with the randomized history-dependent strategies under the finite-horizon payoff criterion. The state space is countable, and the transition rates and payoff functions are allowed to be unbounded from above and from below. Under the suitable conditions, we introduce a new topology for the set of all randomized Markov multi-strategies and establish its compactness and metrizability. Then by constructing the approximating sequences of the transition rates and payoff functions, we show that the optimal value function for each player is a unique solution to the corresponding optimality equation and obtain the existence of a randomized Markov Nash equilibrium. Furthermore, we illustrate the applications of our main results with a controlled birth and death system.

• OSTI ID: 22617198
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 74; ISSN 0095-4616
• Country of Publication: United States
• Language: English

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