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On the Structural Stability of Values for Cooperative Games

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Abstract

It is generally assumed that any set of players can form a feasible coalition for classical cooperative games. But, in fact, some players may withdraw from the current game and form a union, if this makes them better paid than proposed. Based on the principle of coalition split, this paper presents an endogenous procedure of coalition formation by levels and bargaining for payoffs simultaneously, where the unions formed in the previous step continue to negotiate with others in the next step as “individuals,” looking for maximum share of surplus by organizing themselves as a partition. The structural stability of the induced payoff configuration is discussed, using two stability criteria of core notion for cooperative games and strong equilibrium notion for noncooperative games.

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Acknowledgements

The research has been supported by Science Foundation of Henan University of Technology (Grant No. 2019BS049), the Innovative Funds Plan of Henan University of Technology (Grant No. 2020ZKCJ08), the National Social Science Foundation of China (Grant No. 20CGL017), and the National Natural Science Foundation of China (Grant Nos. 71571143, 71671140).

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Authors and Affiliations

  1. Department of Mathematics, School of Sciences, Henan University of Technology, Zhengzhou, 450001, Henan, People’s Republic of China

    Xianghui Li

  2. School of Sciences, Henan University of Technology, Zhengzhou, 450001, Henan, People’s Republic of China

    Yang Li

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  1. Xianghui Li
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  2. Yang Li
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Correspondence to Xianghui Li.

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Communicated by Kyriakos G. Vamvoudakis.

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Li, X., Li, Y. On the Structural Stability of Values for Cooperative Games. J Optim Theory Appl 189, 873–888 (2021). https://doi.org/10.1007/s10957-021-01863-6

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  • DOI: https://doi.org/10.1007/s10957-021-01863-6

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