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On the equal treatment imputations subset in the bargaining set for smooth vector-measure games with a mixed measure space of players

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  • Avishay Aiche

    (Western Galilee College)

Abstract

This paper studies vector-measure games in which the set of players is represented by a mixed measure space with atoms and with an atom-less part. The bargaining set introduced in Mas-Colell (J Math Econ 18(2):129–139, 1989) for a continuum exchange economy is adapted and analyzed within this (TU) market game. It is shown that the equal treatment imputations in the bargaining set have some interesting properties. In particular, we prove an extension of the budgetary exploitation property of core allocations in mixed markets to equal-treatment imputations in the Mas-Colell bargaining set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:2:d:10.1007_s00182-018-0632-z
    DOI: 10.1007/s00182-018-0632-z
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    References listed on IDEAS

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    1. Shitovitz, Benyamin, 1989. "The bargaining set and the core in mixed markets with atoms and an atomless sector," Journal of Mathematical Economics, Elsevier, vol. 18(4), pages 377-383, September.
    2. 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.
    3. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    4. Sondermann, Dieter, 1974. "Economies of scale and equilibria in coalition production economies," Journal of Economic Theory, Elsevier, vol. 8(3), pages 259-291, July.
    5. Jiuqiang Liu, 2017. "Existence of competitive equilibrium in coalition production economies with a continuum of agents," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 941-955, November.
    6. Gabszewicz, Jean J. & Shitovitz, Benyamin, 1992. "The core in imperfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 15, pages 459-483, Elsevier.
    7. Shitovitz, Benyamin, 1982. "Some notes on the core of a production economy with some large traders and a continuum of small traders," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 99-105, January.
    8. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    9. SONDERMANN, Dieter, 1974. "Economies of scale and equilibria in coalition production economies," LIDAM Reprints CORE 172, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Jiuqiang Liu & Huihui Zhang, 2016. "Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1095-1109, November.
    11. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1997. "Core Equivalence Theorems for Infinite Convex Games," Journal of Economic Theory, Elsevier, vol. 76(1), pages 1-12, September.
    12. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667, Elsevier.
    13. Shitovitz, Benyamin, 1973. "Oligopoly in Markets with a Continuum of Traders," Econometrica, Econometric Society, vol. 41(3), pages 467-501, May.
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    Cited by:

    1. Maria Gabriella Graziano & Marialaura Pesce & Niccolo Urbinati, 2023. "The Equitable Bargaining Set," CSEF Working Papers 676, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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