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Construction of Compromise Values for Cooperative Games

Author

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  • Robert P. Gilles

    (The Queen's University of Belfast)

  • Rene van den Brink

    (Vrije Universiteit Amsterdam and Tinbergen Institute)

Abstract

We explore a broad class of values for cooperative games in characteristic function form, known as compromise values. These values efficiently allocate payoffs by linearly combining well-specified upper and lower bounds on payoffs. We identify subclasses of games that admit non-trivial efficient allocations within the considered bounds, which we call bound-balanced games. Subsequently, we define the associated compromise value. We also provide an axiomatisation of this class of compromise values using a combination of the minimal-rights property and a variant of restricted proportionality. We construct and axiomatise various well-known and new compromise values based on these methods, including the ð œ -, the 𠜒-, the Gately, the CIS-, the PANSC-, the EANSC- and the new KM-values. We conclude that this approach establishes a common foundation for a wide range of different values.

Suggested Citation

  • Robert P. Gilles & Rene van den Brink, 2025. "Construction of Compromise Values for Cooperative Games," Tinbergen Institute Discussion Papers 25-017/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20250017
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    References listed on IDEAS

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    1. Julio Díaz & Peter Borm & Ruud Hendrickx & Marieke Quant, 2005. "A geometric characterisation of the compromise value," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 483-500, July.
    2. Gately, Dermot, 1974. "Sharing the Gains from Regional Cooperation: A Game Theoretic Application to Planning Investment in Electric Power," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 195-208, February.
    3. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, March.
    4. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    5. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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