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Transformation of Characteristic Function in Dynamic Games

Author

Listed:
  • Gao Hongwei

    (College of Mathematics, Qingdao University, Qingdao, 266071, China)

  • Petrosyan Leon

    (Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg, 198504, Russia)

  • Qiao Han

    (Management School, University of Chinese Academy of Sciences, Beijing, 100190, China)

  • Sedakov Artem

    (Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, Saint Petersburg, 198504, Russia)

  • Xu Genjiu

    (Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China)

Abstract

The problem of transformation of characteristic function, using a transformation matrix and connected with associated consistency of a solution concept, was investigated for the class of so-called “one-shot” games. The same problem also arises in dynamic games when players move step by step along the cooperative trajectory. In this case the evolution of characteristic function is, in general, unpredictable and may lead to time-inconsistency of a fixed cooperative solution concept. There are different approaches to overcome this problem based on transformation of characteristic function. In this paper, the step-wise transformation is used, which is a generalization of similar transformation of characteristic function for dynamic games with perfect information, and it leads to the time-consistent solution. The general form of such transformation is proposed.

Suggested Citation

  • Gao Hongwei & Petrosyan Leon & Qiao Han & Sedakov Artem & Xu Genjiu, 2013. "Transformation of Characteristic Function in Dynamic Games," Journal of Systems Science and Information, De Gruyter, vol. 1(1), pages 22-37, February.
    • Handle: RePEc:bpj:jossai:v:1:y:2013:i:1:p:22-37:n:2
    DOI: 10.1515/JSSI-2013-0022
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    References listed on IDEAS

    as
    1. Andrea Galeotti & Sanjeev Goyal, 2010. "The Law of the Few," American Economic Review, American Economic Association, vol. 100(4), pages 1468-1492, September.
    2. Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 279-289.
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