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Convergence of the approximate cores to the aspiration core in partitioning games

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  • R. Arribillaga

Abstract

The approximate core and the aspiration core are two non-empty solutions for cooperative games that have emerged in order to give an answer to cooperative games with an empty core. Although the approximate core and the aspiration core come from two different ideas, we show that both solutions are related in a very interesting way in partitioning games (or superadditive games). In fact, we prove that the approximate core converges to the aspiration core in partitioning games (or superadditive games). Copyright Sociedad de Estadística e Investigación Operativa 2015

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  • R. Arribillaga, 2015. "Convergence of the approximate cores to the aspiration core in partitioning games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 521-534, July.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:2:p:521-534
    DOI: 10.1007/s11750-014-0351-y
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    References listed on IDEAS

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    1. Camelia Bejan & Juan Gómez, 2012. "Axiomatizing core extensions," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 885-898, November.
    2. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(4), pages 425-440, December.
    3. Pulido, Manuel A. & Sanchez-Soriano, Joaquin, 2006. "Characterization of the core in games with restricted cooperation," European Journal of Operational Research, Elsevier, vol. 175(2), pages 860-869, December.
    4. Kovalenkov, Alexander & Wooders, Myrna, 2003. "Approximate cores of games and economies with clubs," Journal of Economic Theory, Elsevier, vol. 110(1), pages 87-120, May.
    5. Shubik, Martin, 1971. "The "Bridge Game" Economy: An Example of Indivisibilities," Journal of Political Economy, University of Chicago Press, vol. 79(4), pages 909-912, July-Aug..
    6. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    7. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
    8. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
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    Cited by:

    1. Camelia Bejan & Juan Camilo Gómez, 2018. "Equal treatment without large numbers," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1239-1259, November.

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