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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.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 2 (1992)
Issue (Month): 1 (January)
Pages: 129-47

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Handle: RePEc:spr:joecth:v:2:y:1992:i:1:p:129-47

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Cited by:
  1. Myrna Wooders, 2009. "Market Games and Clubs," Vanderbilt University Department of Economics Working Papers 0919, Vanderbilt University Department of Economics.
  2. 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.
  3. 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.
  4. 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.
  5. 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).
  6. Alexander Kovalenkov & Myrna H. Wooders, 1999. "A law of scarcity for games," Working Papers mwooders-00-05, University of Toronto, Department of Economics.
  7. 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.
  8. Kovalenkov, Alexander & Wooders, Myrna, 2002. "Advances In The Theory Of Large Cooperative Games And Applications To Club Theory : The Side Payments Case," The Warwick Economics Research Paper Series (TWERPS) 641, University of Warwick, Department of Economics.
  9. 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.
  10. 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.

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