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Aggregate monotonic stable single-valued solutions for cooperative games

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  • Pedro Calleja
  • Carles Rafels
  • Stef Tijs

Abstract

This article considers single-valued solutions of transferable utility cooperative games that satisfy core selection and aggregate monotonicity, defined either on the set of all games, G N , or on the set of essential games, E N (those with a non-empty imputation set). The main result is that for an arbitrary set of players, core selection and aggregate monotonicity are compatible with individual rationality, the dummy player property and symmetry for single-valued solutions defined on both G N and E N . This result solves an open question in the literature (see for example Young et al. Water Resour Res 18:463–475, 1982 ). Copyright Springer-Verlag Berlin Heidelberg 2012

Suggested Citation

  • Pedro Calleja & Carles Rafels & Stef Tijs, 2012. "Aggregate monotonic stable single-valued solutions for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 899-913, November.
    • Handle: RePEc:spr:jogath:v:41:y:2012:i:4:p:899-913
    DOI: 10.1007/s00182-012-0355-5
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    References listed on IDEAS

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    1. 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.
    2. Calleja, Pedro & Rafels, Carles & Tijs, Stef, 2009. "The aggregate-monotonic core," Games and Economic Behavior, Elsevier, vol. 66(2), pages 742-748, July.
    3. Kleppe, J., 2010. "Modelling interactive behaviour, and solution concepts," Other publications TiSEM b9b96884-5761-48f0-9ee4-4, Tilburg University, School of Economics and Management.
    4. Hans Haller & Jean Derks, 1999. "Weighted nucleoli," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 173-187.
    5. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Kannai, Yakar, 1992. "The core and balancedness," 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 12, pages 355-395, Elsevier.
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    Citations

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    Cited by:

    1. Calleja, Pedro & Llerena, Francesc, 2020. "Consistency, weak fairness, and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 28-33.
    2. Calleja, Pere & Llerena Garrés, Francesc, 2018. "Weak fairness and the Shapley value," Working Papers 2072/306979, Universitat Rovira i Virgili, Department of Economics.
    3. Dietzenbacher, Bas, 2019. "The Procedural Egalitarian Solution and Egalitarian Stable Games," Discussion Paper 2019-007, Tilburg University, Center for Economic Research.
    4. Pedro Calleja & Francesc Llerena, 2017. "Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 197-220, January.
    5. Calleja, Pere & Llerena Garrés, Francesc, 2015. "On the (in)compatibility of rationality, monotonicity and consistency for cooperative games," Working Papers 2072/247807, Universitat Rovira i Virgili, Department of Economics.
    6. Segal-Halevi, Erel & Sziklai, Balázs R., 2018. "Resource-monotonicity and population-monotonicity in connected cake-cutting," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 19-30.
    7. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2019. "Welfare egalitarianism in surplus-sharing problems and convex games," Discussion Papers on Economics 6/2019, University of Southern Denmark, Department of Economics.
    8. Erel Segal-Halevi & Balázs R. Sziklai, 2019. "Monotonicity and competitive equilibrium in cake-cutting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 363-401, September.
    9. Balazs Sziklai & Erel Segal-Halevi, 2015. "Resource-monotonicity and Population-monotonicity in Cake-cutting," CERS-IE WORKING PAPERS 1552, Institute of Economics, Centre for Economic and Regional Studies.

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    More about this item

    Keywords

    Cooperative games; Core; Aggregate monotonicity; Individual rationality; Dummy player property; Symmetry; C71;
    All these keywords.

    JEL classification:

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

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