Abstract
This paper devotes to the study of the equal allocation of nonseparable costs value for cooperative games. On the one hand, we show that the equal allocation of nonseparable costs value is the unique optimal solution that minimizes the total complaints for individual players over the pre-imputation set. On the other hand, analogously to the way of determining the Nucleolus, we obtain the equal allocation of nonseparable costs value by applying the lexicographic order over the individual complaints. Moreover, we offer alternative characterizations of the equal allocation of nonseparable costs value by proposing several new properties such as dual nullifying player property, dual dummifying player property and grand marginal contribution monotonicity.
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Acknowledgements
We are very grateful to the associate editor and two anonymous referees. Their valuable comments and suggestions contributed to a substantial improvement of the paper. We are also very grateful to Dr. Harry Aarts from University of Twente and Dr. Artem Sedakov from St. Petersburg State University who help us improve the use of the language. This work is supported by National Science Foundation of China (NSFC) through Grant Nos. 71601156, 71671140 and 71571143 as well as Shaanxi Province Science and Technology Research and Development Program (No. 2016JQ7008).
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Communicated by Kyriakos G. Vamvoudakis.
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Sun, P., Hou, D., Sun, H. et al. Optimization Implementation and Characterization of the Equal Allocation of Nonseparable Costs Value. J Optim Theory Appl 173, 336–352 (2017). https://doi.org/10.1007/s10957-017-1092-5
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DOI: https://doi.org/10.1007/s10957-017-1092-5
Keywords
- Cooperative games
- The equal allocation of nonseparable costs value
- Optimization
- Complaint
- Characterization