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The bargaining set and coalition formation

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  • Ken‐Ichi Shimomura

Abstract

We study solution concepts for nontransferable utility games according to which the coalition structure and the payoff allocations are simultaneously determined. The steady bargaining set is a refinement of the Zhou bargaining set, which is included in the Mas‐Colell bargaining set. We prove the nonemptiness and partial efficiency of the steady bargaining set for at least one coalition structure under the restrictive non‐crossing condition. Without this condition, the Zhou bargaining set may be empty and the Mas‐Colell bargaining set is nonempty but may not be efficient.

Suggested Citation

  • Ken‐Ichi Shimomura, 2022. "The bargaining set and coalition formation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 16-37, March.
    • Handle: RePEc:bla:ijethy:v:18:y:2022:i:1:p:16-37
    DOI: 10.1111/ijet.12320
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    References listed on IDEAS

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    1. Vohra, Rajiv, 1991. "An existence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 19-34.
    2. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
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    4. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
    5. Chang, Chih & Lee, Yuh Jye, 1993. "A non-weakly balanced game with non-empty bargaining set," Journal of Mathematical Economics, Elsevier, vol. 22(2), pages 195-198.
    6. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    7. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    8. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    9. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
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    Cited by:

    1. Chiara Donnini & Marialaura Pesce, 2023. "Fairness and formation rules of coalitions," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(4), pages 933-960, December.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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