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A geometric characterisation of the compromise value

Author

Listed:
  • Julio Díaz
  • Peter Borm
  • Ruud Hendrickx

  • Marieke Quant

Abstract

In this paper, we characterise the compromise value of a game as the barycentre of the edges of its core cover. For this, we introduce the τ* value, which extends the adjusted proportional rule for bankruptcy situations and coincides with the compromise value on a large class of games. Copyright Springer-Verlag 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:61:y:2005:i:3:p:483-500
    DOI: 10.1007/s001860400407
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    Cited by:

    1. Miguel Ángel Mirás Calvo & Iago Núñez Lugilde & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2024. "On properties of the set of awards vectors for a claims problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 137-167, April.
    2. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    3. Robert P. Gilles & Rene van den Brink, 2025. "Construction of Compromise Values for Cooperative Games," Tinbergen Institute Discussion Papers 25-017/II, Tinbergen Institute.
    4. Doudou Gong & Bas Dietzenbacher & Hans Peters, 2024. "Two-bound core games and the nucleolus," Annals of Operations Research, Springer, vol. 336(3), pages 1419-1433, May.
    5. Robert P. Gilles & Ren'e van den Brink, 2025. "Construction of Compromise Values for Cooperative Games," Papers 2503.05381, arXiv.org, revised Oct 2025.
    6. Julio González-Díaz & Estela Sánchez-Rodríguez, 2007. "A natural selection from the core of a TU game: the core-center," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 27-46, September.
    7. A. Estévez-Fernández & M. Fiestras-Janeiro & M. Mosquera & E. Sánchez-Rodríguez, 2012. "A bankruptcy approach to the core cover," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 343-359, December.
    8. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2022. "The average-of-awards rule for claims problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 863-888, November.
    9. Keyzer, Michiel & van Wesenbeeck, Cornelia, 2011. "Optimal coalition formation and surplus distribution: Two sides of one coin," European Journal of Operational Research, Elsevier, vol. 215(3), pages 604-615, December.

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