Abstract
In this paper, we define the concept of the general nucleolus whose objective function is limited to the player complaint, to reflect the profit distribution more intuitively on the space of n-person cooperative games. An algorithm for calculating the general nucleolus under the case of linear complaint functions is given so that we can get an accurate allocation to pay for all players. A system of axioms are proposed to characterize the general nucleolus axiomatically and the Kohlberg Criterion is also given to characterize it in terms of balanced collections of coalitions. Finally, we prove the equivalence relationship of the general nucleolus, the least square general nucleolus and the p-kernel to normalize the different assignment criteria.
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Acknowledgements
The research has been supported by the National Natural Science Foundation of China (Grant Nos. 71571143 and 71671140) and sponsored by the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University (Grant No. Z2017043).
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Kong, Q., Sun, H., Xu, G. (2017). The General Nucleolus of n-Person Cooperative Games. In: Li, DF., Yang, XG., Uetz, M., Xu, GJ. (eds) Game Theory and Applications. China GTA China-Dutch GTA 2016 2016. Communications in Computer and Information Science, vol 758. Springer, Singapore. https://doi.org/10.1007/978-981-10-6753-2_15
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DOI: https://doi.org/10.1007/978-981-10-6753-2_15
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