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Population monotonic solutions on convex games

Author

Listed:
  • Toru Hokari

    (Institute of Economic Research, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, JAPAN)

Abstract

The Dutta-Ray solution and the Shapley value are two well-known examples of population-monotonic solutions on the domain of convex games. We provide a new formula for the Dutta-Ray solution from which population-monotonicity immediately follows. Then we define a new family of population-monotonic solutions, which we refer to as "sequential Dutta-Ray solutions." We also show that it is possible to construct several symmetric and population-monotonic solutions by using the solutions in this family.

Suggested Citation

  • Toru Hokari, 2000. "Population monotonic solutions on convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 327-338.
    • Handle: RePEc:spr:jogath:v:29:y:2000:i:3:p:327-338
    Note: Received September 1998/Revised version: December 1999
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    Citations

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    Cited by:

    1. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2002. "Convex Fuzzy Games and Participation Monotonic Allocation Schemes," Other publications TiSEM ad3fc093-38be-4802-aa35-a, Tilburg University, School of Economics and Management.
    2. Dietzenbacher, Bas, 2019. "The Procedural Egalitarian Solution and Egalitarian Stable Games," Discussion Paper 2019-007, Tilburg University, Center for Economic Research.
    3. Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2004. "Egalitarianism in convex fuzzy games," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 313-325, May.
    4. Ehlers, Lars, 2003. "Multiple public goods, lexicographic preferences, and single-plateaued preference rules," Games and Economic Behavior, Elsevier, vol. 43(1), pages 1-27, April.
    5. Dietzenbacher, Bas, 2020. "Monotonicity and Egalitarianism (revision of CentER DP 2019-007)," Discussion Paper 2020-003, Tilburg University, Center for Economic Research.
    6. Francesc Llerena & Carles Rafels & Cori Vilella, 2008. "A simple procedure for computing strong constrained egalitarian allocations," Working Papers 327, Barcelona School of Economics.
    7. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
    8. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Egalitarianism in Multi-Choice Games," Other publications TiSEM bfbd67a5-701f-4be7-a1c9-0, Tilburg University, School of Economics and Management.
    9. Hans Keiding, 2011. "Maximizing selections from the core of a cooperative game," Journal of Global Optimization, Springer, vol. 50(1), pages 107-118, May.
    10. Brânzei, R. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2007. "Egalitarianism in Multi-Choice Games," Discussion Paper 2007-55, Tilburg University, Center for Economic Research.
    11. Dietzenbacher, Bas, 2021. "Monotonicity and egalitarianism," Games and Economic Behavior, Elsevier, vol. 127(C), pages 194-205.

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