Abstract
Khmelnitskaya and Yanovskaya (Math Methods Oper Res 66(2):255–261, 2007) characterized the Owen value for TU games with a coalition structure by the axioms of efficiency, marginality, symmetry across coalitions and symmetry within coalitions. Symmetry across components requires that components with equally productive in the game between components obtain the same total payoffs of their members. In this note, inspired by Casajus (Econ Lett 169:59–62, 2018), we weaken the symmetry across components to the sign symmetry across components, which requires only that equally productive components obtain the same sign of total payoffs. We extend the Khmelnitskaya-Yanovskaya’s characterization by using efficiency, marginality, sign symmetry across coalitions, and sign symmetry within coalitions, similarly as it was done by Casajus (Econ Lett 169:59–62, 2018) for the Shapley value for general TU games. At last, we extend the main result to the Winter value for games with level structure
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By using this claim to \(\phi =Ow\), one can get \(\sum _{j\in P}Ow_j(w)=\sum _{j\in P{\setminus } T}Ow_j(v)\), and hence \(\sum _{j\in P}\phi _j(w)= \sum _{j\in P} Ow_j(w)\). This is an analog of the efficiency property for (P, w).
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This work is supported by the National Social Science Foundation of China (Grant Nos. 21 &ZD113).
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Chen, X., Zhan, M. & Zhao, Z. A characterization of the Owen value via sign symmetries. Theory Decis (2024). https://doi.org/10.1007/s11238-024-09985-9
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DOI: https://doi.org/10.1007/s11238-024-09985-9