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Population Lorenz-monotonic allocation schemes for TU-games

Author

Listed:
  • Josep M. Izquierdo

    (Universitat de Barcelona)

  • Jesús Montes

    (Universitat de Barcelona
    Universitat Abat Oliba CEU)

  • Carlos Rafels

    (Universitat de Barcelona)

Abstract

Sprumont (Games Econ Behav 2:378–394, 1990) introduces population monotonic allocation schemes (PMAS) and proves that every assignment game with at least two sellers and two buyers, where each buyer-seller pair derives a positive gain from trade, lacks a PMAS. In particular glove games lacks PMAS. We propose a new cooperative TU-game concept, population Lorenz-monotonic allocation schemes (PLMAS), which relaxes some population monotonicity conditions by requiring that the payoff vector of any coalition is Lorenz dominated by the corresponding restricted payoff vector of larger coalitions. We show that every TU-game having a PLMAS is totally balanced, but the converse is not true in general. We obtain a class of games having a PLMAS, but no PMAS in general. Furthermore, we prove the existence of PLMAS for every glove game and for every assignment game with at most five players. Additionally, we also introduce two new notions, PLMAS-extendability and PLMAS-exactness, and discuss their relationships with the convexity of the game.

Suggested Citation

  • Josep M. Izquierdo & Jesús Montes & Carlos Rafels, 2024. "Population Lorenz-monotonic allocation schemes for TU-games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(2), pages 417-436, September.
    • Handle: RePEc:spr:sochwe:v:63:y:2024:i:2:d:10.1007_s00355-024-01538-x
    DOI: 10.1007/s00355-024-01538-x
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    References listed on IDEAS

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    1. Kristof Bosmans & Luc Lauwers, 2011. "Lorenz comparisons of nine rules for the adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 791-807, November.
    2. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    3. Dutta, Bhaskar & Ray, Debraj, 1991. "Constrained egalitarian allocations," Games and Economic Behavior, Elsevier, vol. 3(4), pages 403-422, November.
    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. 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.
    7. Mitra, Tapan & Ok, Efe A., 1997. "On the Equitability of Progressive Taxation," Journal of Economic Theory, Elsevier, vol. 73(2), pages 316-334, April.
    8. Juan D. Moreno‐Ternero & Antonio Villar, 2006. "On the Relative Equitability of a Family of Taxation Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(2), pages 283-291, May.
    9. Norde, Henk & Reijnierse, Hans, 2002. "A dual description of the class of games with a population monotonic allocation scheme," Games and Economic Behavior, Elsevier, vol. 41(2), pages 322-343, November.
    10. Traub, Stefan & Seidl, Christian & Schmidt, Ulrich, 2003. "Lorenz, Pareto, Pigou: Who Scores Best? Experimental Evidence on Dominance Relations of Income Distributions," Economics Working Papers 2003-04, Christian-Albrechts-University of Kiel, Department of Economics.
    11. William Thomson, 2012. "Lorenz rankings of rules for the adjudication of conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 547-569, August.
    12. Miguel Ángel Mirás Calvo & Iago Núñez Lugilde & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2023. "Deviation from proportionality and Lorenz-domination for claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 439-467, June.
    13. V. Feltkamp & Javier Arin, 2002. "Lorenz undominated allocations for TU-games: The weighted Coalitional Lorenz Solutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 869-884.
    14. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 187-193.
    15. L. S. Shapley & Martin Shubik, 1967. "Ownership and the Production Function," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 81(1), pages 88-111.
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