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The asymptotic core, nucleolus and Shapley value of smooth market games with symmetric large players

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  • Avishay Aiche
  • Anna Rubinchik
  • Benyamin Shitovitz

Abstract

We examine the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector in a transferable utility (TU) market game. We provide sufficient conditions for the asymptotic core and the nucleolus to coincide with the unique TU competitive payoff distribution. This equivalence results from nucleolus of a finite TU market game belonging to its core, the core equivalence in a symmetric oligopoly with identical atoms and single-valuedness of the core in the limiting smooth game. In some cases (but not always), the asymptotic Shapley value is more favourable for the large traders than the nucleolus, in contrast to the monopoly case (Einy et al. in J Econ Theory 89(2):186–206, 1999 ), where the nucleolus allocation is larger than the Shapley value for the atom. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Avishay Aiche & Anna Rubinchik & Benyamin Shitovitz, 2015. "The asymptotic core, nucleolus and Shapley value of smooth market games with symmetric large players," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 135-151, February.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:1:p:135-151
    DOI: 10.1007/s00182-014-0422-1
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    References listed on IDEAS

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    1. Abraham Neyman & Rann Smorodinsky, 2004. "Asymptotic Values of Vector Measure Games," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 739-775, November.
    2. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
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    9. 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).
    10. Trockel, Walter, 1976. "A limit theorem on the core," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 247-264, December.
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    Cited by:

    1. Avishay Aiche, 2019. "On the equal treatment imputations subset in the bargaining set for smooth vector-measure games with a mixed measure space of players," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 411-421, June.
    2. Aiche, Avishay & Griskin, Vladimir & Shitovitz, Benyamin, 2019. "The asymptotic kernel in TU production market games with symmetric big players and a uniform ocean of small players," Economics Letters, Elsevier, vol. 181(C), pages 107-110.

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    More about this item

    Keywords

    Mixed games; Oligopoly; Asymptotic nucleolus; Asymptotic Shapley value; C71; D40; D43;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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