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

Stochastic Games for Continuous-Time Jump Processes Under Finite-Horizon Payoff Criterion 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. Applied Mathematics and Optimization Springer Journals

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

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Springer US
Copyright © 2015 by Springer Science+Business Media New York
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
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