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Existence Conditions of Pareto Solutions in Infinite Horizon Stochastic Differential Games

In: Essays on Pareto Optimality in Cooperative Games

Author

Listed:
  • Yaning Lin

    (Shandong University of Technology, School of Mathematics and Statistics)

  • Weihai Zhang

    (Shandong University of Science and Technology, College of Electrical Engineering and Automation)

Abstract

This chapter investigates Pareto optimality in infinite horizon stochastic differential games. Employing the equivalent description of Pareto optimality, necessary conditions for the existence of Pareto solutions are presented under certain assumption on the Lagrange multiplier set. Furthermore, a condition is introduced to guarantee that the above assumption is established for the LQ case. In addition, the sufficient conditions for a control to be Pareto efficient are put forward in terms of the necessary conditions, a convexity condition as well as a transversality condition. For the LQ situation, the characterization of Pareto-efficient strategies and Pareto solutions are also studied. If the system is mean-square stabilizable, then the solvability of the related SARE provides a sufficient condition under which Pareto-efficient strategies are equivalent to the weighted sum optimal controls and all Pareto solutions can be derived based on the solutions of an introduced GALE.

Suggested Citation

  • Yaning Lin & Weihai Zhang, 2022. "Existence Conditions of Pareto Solutions in Infinite Horizon Stochastic Differential Games," Springer Books, in: Essays on Pareto Optimality in Cooperative Games, chapter 0, pages 31-48, Springer.
    • Handle: RePEc:spr:sprchp:978-981-19-5049-0_3
    DOI: 10.1007/978-981-19-5049-0_3
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