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Inessentiality of Large Groups and the Approximate Core Property: An Equivalence Theorem

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  • Wooders, Myrna Holtz

Abstract

Inessentiality of large groups or, in other words, effectiveness of small groups, means that almost all gains to group formation can be realized by partitions of the players into groups bounded in absolute size. The approximate cores property is that all sufficiently large games have nonempty approximate cores. I consider these properties in a framework of games in characteristic function form satisfying a mild boundedness condition where, when the games have many players, most players have many substitutes. I show that large (finite) games satisfy inessentially of large groups if and only if they satisfy the approximate core property.

Suggested Citation

  • Wooders, Myrna Holtz, 1992. "Inessentiality of Large Groups and the Approximate Core Property: An Equivalence Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 129-147, January.
    • Handle: RePEc:spr:joecth:v:2:y:1992:i:1:p:129-47
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    Citations

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    Cited by:

    1. Flam, Sjur & Owen, Guillermo & Saboya, Martha, 2005. "The not-quite non-atomic game: Non-emptiness of the core in large production games," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 279-297, November.
    2. Yusuke Kamishiro & Roberto Serrano & Myrna Wooders, 2021. "Monopolists of scarce information and small group effectiveness in large quasilinear economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 801-827, December.
    3. Allouch, Nizar & Wooders, Myrna, 2008. "Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes," Journal of Economic Theory, Elsevier, vol. 140(1), pages 246-278, May.
    4. Myrna Wooders, 2010. "Cores of many-player games; nonemptiness and equal treatment," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 131-162, March.
    5. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
    6. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    7. Nizar Allouch & Myrna Wooders, 2017. "On the nonemptiness of approximate cores of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 191-209, January.
    8. Kovalenkov, Alexander & Wooders, Myrna, 2003. "Approximate cores of games and economies with clubs," Journal of Economic Theory, Elsevier, vol. 110(1), pages 87-120, May.
    9. Alexander Kovalenkov & Myrna Wooders, 2003. "Advances in the theory of large cooperative games and applications to club theory; the side payments case," Chapters, in: Carlo Carraro (ed.), The Endogenous Formation of Economic Coalitions, chapter 1, Edward Elgar Publishing.
    10. Alexander Kovalenkov & Myrna Wooders, 2005. "Laws of scarcity for a finite game - exact bounds on estimations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 383-396, August.
    11. Nizar Allouch & Myrna Wooders, 2004. "Price Taking Equilibrium in Club Economies with Multiple Memberships and Unbounded Club Sizes," Working Papers 513, Queen Mary University of London, School of Economics and Finance.
    12. Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "A law of scarcity for games," Economic Research Papers 269297, University of Warwick - Department of Economics.
    13. Yusuke Kamishiro & Roberto Serrano & Myrna Wooders, 2015. "Information and Small Group Effectiveness in Large Quasilinear Economies," Working Papers 2015-11, Brown University, Department of Economics.
    14. Nizar Allouch & Myrna Wooders, 2017. "On the nonemptiness of approximate cores of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 191-209, January.
    15. Wooders, Myrna H., 2001. "Some corrections to claims about the literature in Engl and Scotchmer (1996)," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 295-309, December.
    16. Yokota, Koji, 2012. "Time Discount and Convex Hiring Cost," ビジネス創造センターディスカッション・ペーパー (Discussion papers of the Center for Business Creation) 10252/4850, Otaru University of Commerce.
    17. Myrna Wooders, 2013. "Small improving coalitions and small group effectiveness," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 11-21, March.
    18. Myrna Wooders, 2008. "Games with Many Players and Abstract Economies Permitting Differentiated Commodities, Clubs, and Public Goods," Vanderbilt University Department of Economics Working Papers 0813, Vanderbilt University Department of Economics.
    19. Nizar Allouch & Myrna Wooders, 2004. "Price taking equilibrium in club economies with multiple memberships and unbounded club sizes," Cahiers de la Maison des Sciences Economiques b04109, Université Panthéon-Sorbonne (Paris 1).

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