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Small group effectiveness, per capita boundedness and nonemptiness of approximate cores

  • Wooders, Myrna

Small groups of players of a cooperative game with side payments are "effective" if almost all gains to group formation can be realized by groups of players bounded in absolute size. Per capita payoffs are bounded if the average payoff to players has a uniform upper bound, independent of the size of the total player set. It is known that in the context of games with side payments derived from pregames (which induce a common underlying structure on the potential gains to groups of players from cooperation in any game) small group effectiveness implies nonemptiness of approximate cores and the approximation can be made arbitrarily close as the player set is increased in size. Moreover, per capita boundedness, along with thickness (implying that there are many substitutes for each player) yields the same result. In this paper, using extensions of the concepts of small group effectiveness and per capita boundedness to games without side payments (NTU games), we obtain results analogous to those for games with side payments. As the prior results, the results of the current paper can be applied to economies with non-convexities, non-monotonicities, production, indivisibilities, clubs, and local public goods.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 7-8 (July)
Pages: 888-906

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Handle: RePEc:eee:mateco:v:44:y:2008:i:7-8:p:888-906
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Aliprantis, Charalombos & Burkinshaw, Owen, 1991. "When Is the Core Equivalence Theorem Valid?," Economic Theory, Springer, vol. 1(2), pages 169-82, April.
  2. Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "Approximate Cores Of Games And Economies With Clubs," The Warwick Economics Research Paper Series (TWERPS) 535, University of Warwick, Department of Economics.
  3. Wooders, Myrna Holtz, 1992. "Inessentiality of Large Groups and the Approximate Core Property: An Equivalence Theorem," Economic Theory, Springer, vol. 2(1), pages 129-47, January.
  4. Conley, John P. & Wooders, Myrna H., 2001. "Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics," Journal of Economic Theory, Elsevier, vol. 98(2), pages 261-294, June.
  5. Shubik, Martin & Wooders, Myrna Holtz, 1983. "Approximate cores of replica games and economies. Part I: Replica games, externalities, and approximate cores," Mathematical Social Sciences, Elsevier, vol. 6(1), pages 27-48, October.
  6. Myrna Wooders & Alexander Kovalenkov, 2001. "Epsilon cores of games with limited side payments Nonemptiness and equal treatment," Economics Bulletin, AccessEcon, vol. 28(5), pages A0.
  7. Reny, Philip J. & Holtz Wooders, Myrna, 1996. "The Partnered Core of a Game without Side Payments," Journal of Economic Theory, Elsevier, vol. 70(2), pages 298-311, August.
  8. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
  9. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-50, November.
  10. 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.
  11. Jean-Marc Bonnisseau & Vincent Iehle, 2004. "Payoffs-dependent Balancedness and Cores," Game Theory and Information 0403004, EconWPA.
  12. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-77, March.
  13. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
  14. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  15. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer, vol. 25(2), pages 245-58.
  16. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
  17. Wooders, Myrna Holtz, 1988. "Stability of jurisdiction structures in economies with local public goods," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 29-49, February.
  18. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
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