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Irrational-Behavior-Proof Conditions Based on Limit Characteristic Functions

Author

Listed:
  • Liu Cui

    (School of Mathematics and Statistics, Qingdao University, Qingdao266071, China)

  • Gao Hongwei

    (School of Mathematics and Statistics, Institute of Applied Mathematics of Shandong, Qingdao University, Qingdao266071, China)

  • Petrosian Ovanes

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

  • Xue Juan

    (School of Mathematics and Statistics, Qingdao University, Qingdao266071, China)

  • Wang Lei

    (School of Mathematics and Statistics, College of Automation and Electrical Engineering, Qingdao University, Qingdao266071, China)

Abstract

Irrational-behavior-proof (IBP) conditions are important aspects to keep stable cooperation in dynamic cooperative games. In this paper, we focus on the establishment of IBP conditions. Firstly, the relations of three kinds of IBP conditions are described. An example is given to show that they may not hold, which could lead to the fail of cooperation. Then, based on a kind of limit characteristic function, all these conditions are proved to be true along the cooperative trajectory in a transformed cooperative game. It is surprising that these facts depend only upon the individual rationalities of players for the Shapley value and the group rationalities of players for the core. Finally, an illustrative example is given.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:jossai:v:7:y:2018:i:1:p:1-16:n:1
    DOI: 10.21078/JSSI-2019-001-16
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    References listed on IDEAS

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    3. Gérard Hamiache, 2010. "A Matrix Approach To The Associated Consistency With An Application To The Shapley Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 175-187.
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