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Core and Coalitional Fairness: The Case of Information Sharing Rule

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  • Bhowmik, Anuj

Abstract

We investigate two of the most extensively studied cooperative notions in a pure exchange economy with asymmetric information. One of them is the core and the other is known as coalitional fairness. The set of agents is modelled by a mixed market consisting of some large agents and an ocean of small agents; and the commodity space is an ordered Banach space whose positive cone has an interior point. The information system in our framework is the one introduced by Allen in [1]. Thus, the same agent can have common, private or pooled information when she becomes member of different coalitions. It is shown that the main results in Grodal [20], Schmeidler [26] and Vind [31] can be established when the economy consists of a continuum of small agents. We also focus on the information mechanism based on size of coalitions introduced in [18] and obtain a result similar to the main result in [18]. Finally, we examine the concept of coalitional fairness proposed in [21]. We prove that the core is contained in the set of coalitionally fair allocations under some assumptions. This result provides extensions of Theorem 2 in [21] to an economy with asymmetric information as well as a deterministic economy with infinitely many commodities. Although we consider a general commodity space, all our results were so far unsolved to the case of information sharing rule with finitely many commodities.

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  • Bhowmik, Anuj, 2014. "Core and Coalitional Fairness: The Case of Information Sharing Rule," MPRA Paper 56644, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:56644
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    References listed on IDEAS

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    1. Beth Allen, 2006. "Market games with asymmetric information: the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 465-487, October.
    2. Einy, Ezra & Moreno, Diego & Shitovitz, Benyamin, 2000. "On the Core of an Economy with Differential Information," Journal of Economic Theory, Elsevier, vol. 94(2), pages 262-270, October.
    3. Gabszewicz, Jean Jaskold, 1975. "Coalitional Fairness of Allocations in Pure Exchange Economies," Econometrica, Econometric Society, vol. 43(4), pages 661-668, July.
    4. repec:dau:papers:123456789/2344 is not listed on IDEAS
    5. Bhowmik, Anuj & Graziano, Maria Gabriella, 2015. "On Vind’s theorem for an economy with atoms and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 26-36.
    6. Herves-Beloso, Carlos & Moreno-Garcia, Emma & Nunez-Sanz, Carmelo & Rui Pascoa, Mario, 2000. "Blocking Efficacy of Small Coalitions in Myopic Economies," Journal of Economic Theory, Elsevier, vol. 93(1), pages 72-86, July.
    7. Schmeidler, David, 1972. "A Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 579-580, May.
    8. Anuj Bhowmik & Jiling Cao, 2013. "On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 537-560, August.
    9. Yannelis, Nicholas C, 1991. "The Core of an Economy with Differential Information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 183-197, April.
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    11. Ezra Einy & Diego Moreno & Benyamin Shitovitz, 2001. "Competitive and core allocations in large economies with differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(2), pages 321-332.
    12. Evren, Özgür & Hüsseinov, Farhad, 2008. "Theorems on the core of an economy with infinitely many commodities and consumers," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1180-1196, December.
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    24. Koutsougeras, Leonidas C & Yannelis, Nicholas C, 1993. "Incentive Compatibility and Information Superiority of the Core of an Economy with Differential Information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 195-216, April.
    25. Bhowmik, Anuj & Cao, Jiling, 2013. "Robust efficiency in mixed economies with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 49-57.
    26. Luciano Castro & Marialaura Pesce & Nicholas Yannelis, 2011. "Core and equilibria under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 519-548, October.
    27. Carlos Hervés-Beloso & Emma Moreno-García & Nicholas Yannelis, 2005. "Characterization and incentive compatibility of Walrasian expectations equilibrium in infinite dimensional commodity spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 361-381, August.
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    29. Herves-Beloso, Carlos & Moreno-Garcia, Emma & Yannelis, Nicholas C., 2005. "An equivalence theorem for a differential information economy," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 844-856, November.
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    Cited by:

    1. He, Wei & Yannelis, Nicholas C., 2015. "Equilibrium theory under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 86-95.
    2. Bhowmik, Anuj & Graziano, Maria Gabriella, 2015. "On Vind’s theorem for an economy with atoms and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 26-36.
    3. Bhowmik, Anuj & Centrone, Francesca & Martellotti, Anna, 2016. "Coalitional Extreme Desirability in Finitely Additive Economies with Asymmetric Information," MPRA Paper 71084, University Library of Munich, Germany.
    4. Achille Basile & Maria Gabriella Graziano & Ciro Tarantino, 2018. "Coalitional fairness with participation rates," Journal of Economics, Springer, vol. 123(2), pages 97-139, March.
    5. Anuj Bhowmik & Maria Gabriella Graziano, 2018. "Blocking Coalitions and Fairness in Asset Markets and Asymmetric Information Economies," CSEF Working Papers 510, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

    More about this item

    Keywords

    Asymmetric information economy; coalitional fairness; core; information sharing rule.;

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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