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Subadditive and Homogeneous of Degree One Games Are Totally Balanced

Author

Listed:
  • Shoshana Anily

    (Tel Aviv University, Tel Aviv 69978, Israel)

  • Moshe Haviv

    (Department of Statistics and the Center for the Study of Rationality, Hebrew University of Jerusalem, 91905 Jerusalem, Israel)

Abstract

A cooperative game with transferable utility is said to be homogeneous of degree one if for any integer m , the value of cloning m times all players at any given coalition, leads to m times the value of the original coalition. We show that this property coupled with subadditivity, guarantees the nonemptyness of the core of the game and of all its subgames, namely, the game is totally balanced. Examples for games stemming from the areas of retailing and of facility location are given.

Suggested Citation

  • Shoshana Anily & Moshe Haviv, 2014. "Subadditive and Homogeneous of Degree One Games Are Totally Balanced," Operations Research, INFORMS, vol. 62(4), pages 788-793, August.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:4:p:788-793
    DOI: 10.1287/opre.2014.1283
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    References listed on IDEAS

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    4. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, March.
    5. Tijs, S.H. & Parthasarathy, T. & Potters, J.A.M. & Rajendra Prasad, V., 1984. "Permutation games : Another class of totally balanced games," Other publications TiSEM a7edfa18-6224-4be3-b677-5, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Shoshana Anily, 2018. "Full characterization of the nonnegative core of some cooperative games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 303-316, June.
    2. Frank Karsten & Marco Slikker & Geert-Jan van Houtum, 2015. "Resource Pooling and Cost Allocation Among Independent Service Providers," Operations Research, INFORMS, vol. 63(2), pages 476-488, April.
    3. Loe Schlicher & Marco Slikker & Willem van Jaarsveld & Geert-Jan van Houtum, 2020. "Core Nonemptiness of Stratified Pooling Games: A Structured Markov Decision Process Approach," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1445-1465, November.
    4. Frank Karsten & Marco Slikker & Peter Borm, 2017. "Cost allocation rules for elastic single‐attribute situations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 271-286, June.
    5. Bernardi Mauro & Roy Cerqueti & Arsen Palestini, 2016. "Allocation of risk capital in a cost cooperative game induced by a modified Expected Shortfall," Papers 1608.02365, arXiv.org.
    6. Zhi Chen & Weijun Xie, 2021. "Sharing the value‐at‐risk under distributional ambiguity," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 531-559, January.
    7. Ulaş Özen & Marco Slikker & Greys Sošić, 2022. "On the core of m$m$‐attribute games," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1770-1787, April.

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