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A note: characterizations of convex games by means of population monotonic allocation schemes

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  • Jesús Getán
  • Jesús Montes
  • Carles Rafels

Abstract

Convex cooperative games were first introduced by Shapley (Int J Game Theory 1:11–26, 1971 ) while population monotonic allocation schemes (PMAS) were subsequently proposed by Sprumont (Games Econ Behav 2:378–394, 1990 ). In this paper we provide several characterizations of convex games and introduce three new notions: PMAS-extendability, PMAS-exactness, and population monotonic set schemes, which imitate the classical concepts that they extend. We show that all of these notions provide new characterizations of the convexity of the game. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Jesús Getán & Jesús Montes & Carles Rafels, 2014. "A note: characterizations of convex games by means of population monotonic allocation schemes," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 871-879, November.
    • Handle: RePEc:spr:jogath:v:43:y:2014:i:4:p:871-879
    DOI: 10.1007/s00182-013-0408-4
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    References listed on IDEAS

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    1. Barış Çiftçi & Peter Borm & Herbert Hamers, 2010. "Population monotonic path schemes for simple games," Theory and Decision, Springer, vol. 69(2), pages 205-218, August.
    2. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    3. Josep Izquierdo & Carles Rafels, 2012. "A characterization of convex TU games by means of the Mas-Colell bargaining set (à la Shimomura)," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 381-395, May.
    4. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    5. Moulin, H, 1990. "Cores and Large Cores When Population Varies," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 219-232.
    6. J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 211-227.
    7. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
    8. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
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    Cited by:

    1. Dietzenbacher, Bas & Dogan, Emre, 2024. "Population monotonicity and egalitarianism," Research Memorandum 007, Maastricht University, Graduate School of Business and Economics (GSBE).

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