Journal of the Operations Research Society of China
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This paper studies the policy iteration algorithm (PIA) for zero-sum stochastic differential games with the basic long-run average criterion, as well as with its more selective version, the so-called bias criterion. The system is assumed to be a nondegenerate diffusion. We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation. We also ensure the convergence of a sequence of such solutions, of the corresponding sequence of policies, and, ultimately, of the PIA.
Key words: Ergodic payoff criterion, Zero-sum stochastic differential games, Policy iteration algorithm, Nondegenerate diffusions , Poisson equation , Scha¨lconvergence , Bias game
Jose Daniel Lopez-Barrientos. Policy Iteration Algorithms for Zero-Sum Stochastic Differential Games with Long-Run Average Payoff Criteria[J]. Journal of the Operations Research Society of China, doi: 10.1007/s40305-014-0061-z.
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URL: https://www.jorsc.shu.edu.cn/EN/10.1007/s40305-014-0061-z
https://www.jorsc.shu.edu.cn/EN/Y2014/V2/I4/395