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Coalitionally Monotonic Set-solutions for Cooperative TU Games

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  • Josep Maria Izquierdo Aznar
  • Carlos Rafels Pallarola

    (Universitat de Barcelona)

Abstract

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the trade-off between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core- selection requirement by the core-extension property.

Suggested Citation

  • Josep Maria Izquierdo Aznar & Carlos Rafels Pallarola, 2002. "Coalitionally Monotonic Set-solutions for Cooperative TU Games," Working Papers in Economics 75, Universitat de Barcelona. Espai de Recerca en Economia.
  • Handle: RePEc:bar:bedcje:200275
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    References listed on IDEAS

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    1. TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 229-240.
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    3. Rafels, C. & Tijs, S.H., 1997. "On the cores of cooperative games and the stability of the Weber set," Other publications TiSEM 14435da8-14ce-4845-8e54-4, Tilburg University, School of Economics and Management.
    4. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    5. Derks, J J M, 1992. "A Short Proof of the Inclusion of the Core in the Weber Set," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 149-150.
    6. Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 133-137.
    7. Daniel Granot & Michael Maschler, 1997. "The Reactive Bargaining Set: Structure, Dynamics and Extension to NTU Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 75-95.
    8. Maschler, Michael, 1976. "An advantage of the bargaining set over the core," Journal of Economic Theory, Elsevier, vol. 13(2), pages 184-192, October.
    9. David Housman & (*), Lori Clark, 1998. "Note Core and monotonic allocation methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 611-616.
    10. Izquierdo, Josep M. & Rafels, Carles, 2001. "Average Monotonic Cooperative Games," Games and Economic Behavior, Elsevier, vol. 36(2), pages 174-192, August.
    11. Rafels, Carles & Ybern, Neus, 1995. "Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 113-126.
    12. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667 Elsevier.
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    JEL classification:

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

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