Quasi-Cores in Bargaining sets (original) (raw)

Abstract

We propose a nonempty-valued subsolution of the_Mas-Colell Bargaining Set_ on the class of TU games satisfying_grand coalition zero-monotonicity_, a weaker condition than superadditivity, zero-monotonicity and balancedness. The subsolution is a slight modification of the_Shapley-Shubik Quasi-Core_. The_Zhou Bargaining Set_ is a refinement of the Mas-Colell Bargaining Set. We also give a nonempty-valued subsolution of the Zhou Bargaining Set on the class of all TU games satisfying_grand coalition superadditivity_, a weaker condition than superadditivity and balancedness. This subsolution is a modification of the Zhou Bargaining Set which is described by excesses. These results are examined for TU games with coalition structures.

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Authors and Affiliations

1. School of International Public Policy, Osaka University, Toyonaka, 560, Osaka, Japan
   Ken -Ichi Shimomura

Authors

1. Ken -Ichi Shimomura

Additional information

My first debt is to Rajiv Vohra, who has given detailed and useful comments on an earlier manuscript. Guidance and suggestions by William Thomson and Ryo-ichi Nagahisa are invaluable. Constructive comments by anonymous referees and an associate editor have greatly improved the contents and presentation of the paper. Thanks are also due to Jeffrey Banks, Marcus Berliant, Andreu Mas-Colell, Lin Zhou, and participants of seminars at Rochester, Toyama, Kyoto, Keio, Osaka ISER, Tsukuba, Osaka City University, and the 1992 Fall Midwest Conference at Pittsburgh, especially Jun Wako and Shmuel Zamir, for conversations and correspondence. This paper has grown out of an earlier one entitled “A Quasi-Core in a Bargaining Set” (1993). Part of the work was done during my subbatical at Brown University in 1994/1995. Their hospitality and funding from the Kyoto University Foundation are gratefully acknowledged. This research is partially supported by the Kikawada Foundation.

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Shimomura, K.I. Quasi-Cores in Bargaining sets.Int J Game Theory 26, 283–302 (1997). https://doi.org/10.1007/BF01263272

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• Received: 15 December 1993
• Revised: 15 December 1994
• Accepted: 15 February 1996
• Issue date: October 1997
• DOI: https://doi.org/10.1007/BF01263272

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