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Assignment games with population monotonic allocation schemes

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  • Tamás Solymosi

    (Corvinus University of Budapest)

Abstract

We characterize the assignment games which admit a population monotonic allocation scheme (PMAS) in terms of efficiently verifiable structural properties of the nonnegative matrix that induces the game. We prove that an assignment game is PMAS-admissible if and only if the positive elements of the underlying nonnegative matrix form orthogonal submatrices of three special types. In game theoretic terms it means that an assignment game is PMAS-admissible if and only if it contains either a veto player or a dominant veto mixed pair, or the game is a composition of these two types of special assignment games. We also show that in PMAS-admissible assignment games all core allocations can be extended to a PMAS, and the nucleolus coincides with the tau-value.

Suggested Citation

  • Tamás Solymosi, 2024. "Assignment games with population monotonic allocation schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(1), pages 67-88, February.
    • Handle: RePEc:spr:sochwe:v:62:y:2024:i:1:d:10.1007_s00355-023-01477-z
    DOI: 10.1007/s00355-023-01477-z
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    1. S. Miquel & M. Núñez, 2011. "The maximum and the addition of assignment games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 189-212, July.
    2. 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.
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    5. Han Xiao & Qizhi Fang, 2022. "Population monotonicity in matching games," Journal of Combinatorial Optimization, Springer, vol. 43(4), pages 699-709, May.
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    7. 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).
    8. Takaaki Abe & Shuige Liu, 2019. "Monotonic core allocation paths for assignment games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 557-573, December.
    9. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
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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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