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

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Abstract

We study the asymptotic nucleolus of a smooth and symmetric oligopoly with an atomless sector. We show that under appropriate assumptions, the asymptotic nucleolus of the TU market game coincides with the unique TU competitive payoff distribution. This equivalence results from nucleolus of a finite game belonging to its core and the Aumann Core Equivalence, which holds for this economy due to the cut-throat competition among the identical large players. A comparison with the Shapley value yields that in some cases, the asymptotic Shapley value is more favorable for the large traders than the asymptotic nucleolus. This may be interpreted by the `fairness property' of Shapley Value which does not reflect the intense competition among the large traders, accounting for the relative importance of their marginal contribution.

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  • Aiche, Avishay & Rubinchik, Anna & Shitovitz, Benyamin, "undated". "The asymptotic core, nucleolus and Shapley value of smooth market games with symmetric large players," Working Papers WP2012/8, University of Haifa, Department of Economics.
    • Handle: RePEc:haf:huedwp:wp201208
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    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;

    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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