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Pareto Optimality in Infinite Horizon Cooperative Difference 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 discusses Pareto optimality in infinite horizon cooperative difference games. Under an assumption about the Lagrange multipliers, necessary conditions for the existence of Pareto solutions are put forward. Furthermore, two conditions are introduced to ensure that the assumption on the Lagrange multipliers is set up. In addition, it is shown that necessary conditions are also sufficient under a convexity assumption and a transversality condition. Next, the LQ case is studied. By the discussion of the convexity of the cost functionals, the characterization of Pareto solutions is explored. If the system is stabilizable, then the solvability of the related ARE provides a sufficient condition under which all Pareto solutions can be obtained based on the solutions of an introduced ALE.

Suggested Citation

  • Yaning Lin & Weihai Zhang, 2022. "Pareto Optimality in Infinite Horizon Cooperative Difference Games," Springer Books, in: Essays on Pareto Optimality in Cooperative Games, chapter 0, pages 139-157, Springer.
    • Handle: RePEc:spr:sprchp:978-981-19-5049-0_8
    DOI: 10.1007/978-981-19-5049-0_8
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