Abstract.
We introduce a compromise value for non-transferable utility games: the Chi-compromise value. It is closely related to the Compromise value introduced by Borm, Keiding, McLean, Oortwijn, and Tijs (1992), to the MC-value introduced by Otten, Borm, Peleg, and Tijs (1998), and to the Ω-value introduced by Bergantiños, Casas-Méndez, and Vázquez-Brage (2000). The main difference being that the maximal aspiration a player may have in the game is his maximal (among all coalitions) marginal contribution. We show that it is well defined on the class of totally essential and non-level games. We propose an extensive-form game whose subgame perfect Nash equilibrium payoffs coincide with the Chi-compromise value.
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Manuscript received: May 2001/Final version received: January 2002
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ID="*" We thank Carles Rafels, Howard Petith, and a referee for their helpful comments. Financial support from the Spanish Ministry of Education and Culture (through grants PB98-0870 and PB98-0613-C02-01), from the Xunta de Galicia (through grant PGIDT00PXI30001PN), and from the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya (through grant 2000SGR-0054) is gratefully acknowledged. The paper was partially written while Jordi Massó was visiting the Universidad Nacional de San Luis (Argentina). He acknowledges the hospitality of its Instituto de Matemática Aplicada and the financial support through a sabbatical fellowship from the Spanish Ministry of Education and Culture.
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Bergantiños, G., Massó, J. The Chi-compromise value for non-transferable utility games. Mathematical Methods of OR 56, 269–286 (2002). https://doi.org/10.1007/s001860200193
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DOI: https://doi.org/10.1007/s001860200193