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Deriving Egalitarian and proportional principles from individual monotonicity

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  • Yukihiko Funaki

    (Waseda University)

  • Yukio Koriyama

    (CREST, Ecole Polytechnique, Institut Polytechnique de Paris)

Abstract

The problem of efficient allocation of the grand coalition worth in transferable-utility games boils down to specifying how the surplus is distributed among individuals, in the situation where the individual share is well-defined. We show that the Individual Monotonicity axiom for Equal Surplus, together with Efficiency and Equal Treatment, implies Egalitarian Surplus Sharing, while the same axiom for Equal Ratio implies Proportional Division. The results thus illustrate the common structure in deriving two principles of surplus distribution, egalitarian and proportional, from the Individual Monotonicity axioms. We further show that relaxation of Equal Treatment leads to Weighted Surplus Sharing and Shifted Proportional Division, highlighting the common structure in which Individual Monotonicity characterizes the allocations that can incorporate social objectives of a redistributive nature.

Suggested Citation

  • Yukihiko Funaki & Yukio Koriyama, 2025. "Deriving Egalitarian and proportional principles from individual monotonicity," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(1), pages 1-24, June.
    • Handle: RePEc:spr:jogath:v:54:y:2025:i:1:d:10.1007_s00182-025-00945-3
    DOI: 10.1007/s00182-025-00945-3
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    References listed on IDEAS

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