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Convergence of strong time-consistent payment schemes in dynamic games

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  • Petrosyan, Leon
  • Sedakov, Artem
  • Sun, Hao
  • Xu, Genjiu

Abstract

The problem of consistency of a solution over time remains an important issue in cooperative dynamic games. Payoffs to players prescribed by an inconsistent solution may not be achievable since such a solution is extremely sensitive to its revision in the course of a game developing along an agreed upon cooperative behavior. The paper proposes a strong time-consistent payment scheme which is stable to a revision of cooperative set solutions, e.g., the core. Using a linear transformation of the solution, it becomes possible to obtain non-negative payments to players. In the paper, we also deal with a limit linear transformation of the solution whose convergence is proved. Developing a non-negative strong time-consistent payment scheme in a closed form, we guarantee that the solution supported by the scheme will not be revised over time.

Suggested Citation

  • Petrosyan, Leon & Sedakov, Artem & Sun, Hao & Xu, Genjiu, 2017. "Convergence of strong time-consistent payment schemes in dynamic games," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 96-112.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:96-112
    DOI: 10.1016/j.amc.2017.07.030
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    References listed on IDEAS

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    Cited by:

    1. Artem Sedakov & Hao Sun, 2020. "The Relationship between the Core and the Modified Cores of a Dynamic Game," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    2. Liu Cui & Gao Hongwei & Petrosian Ovanes & Xue Juan & Wang Lei, 2018. "Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions," Journal of Systems Science and Information, De Gruyter, vol. 7(1), pages 1-16, March.

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