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The asymptotic kernel in TU production market games with symmetric big players and a uniform ocean of small players

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  • Aiche, Avishay
  • Griskin, Vladimir
  • Shitovitz, Benyamin

Abstract

We apply the mixed measure space model of players to the analysis of smooth oligopolies with two types of players. Following Kannai (1966) and others, we use the asymptotic approach to obtain the structure of the asymptotic kernel for smooth Transferable Utility production market games with symmetric big players and a uniform ocean of small players. We show that in the case of a duopoly, the asymptotic kernel is a nondegenerate interval that strictly contains the asymptotic nucleolus, which in turn coincides with the unique Transferable Utility Competitive Equilibrium being the upper end-point of the interval (from the point of view of the uniform ocean).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecolet:v:181:y:2019:i:c:p:107-110
    DOI: 10.1016/j.econlet.2019.05.016
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    References listed on IDEAS

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    1. 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.
    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. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    4. Guesnerie, Roger, 1977. "Monopoly, syndicate, and shapley value: About some conjectures," Journal of Economic Theory, Elsevier, vol. 15(2), pages 235-251, August.
    5. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    6. Einy, Ezra & Moreno, Diego & Shitovitz, Benyamin, 1999. "The Asymptotic Nucleolus of Large Monopolistic Market Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 186-206, December.
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    More about this item

    Keywords

    Asymptotic solution concepts; Kernel; Vector measure games;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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