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Monotonic core solutions: Beyond Young's theorem

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  • Arin Aguirre, Francisco Javier

Abstract

We introduce two new monotonicity properties for core concepts: single-valued solution concepts that always select a core allocation whenever the game is balanced (has a nonempty core). We present one result of impossibility for one of the properties and we pose several open questions for the second property. The open questions arise because the most important core concepts (the nucleolus and the per capita nucleolus) do not satisfy the property even in the class of convex games.

Suggested Citation

  • Arin Aguirre, Francisco Javier, 2010. "Monotonic core solutions: Beyond Young's theorem," IKERLANAK 6373, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    • Handle: RePEc:ehu:ikerla:6373
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    References listed on IDEAS

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    1. J. Arin & V. Feltkamp, 2005. "Monotonicity properties of the nucleolus on the domain of veto balanced games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 331-341, December.
    2. 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).
    3. Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 133-137.
    4. Arin Aguirre, Francisco Javier & Feltkamp, Vincent, 2007. "On monotonic core allocations for coalitional games whith veto players," IKERLANAK 6480, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
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