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

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  • Wooders, Myrna

Abstract

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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  • 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.
  • Handle: RePEc:eee:mateco:v:44:y:2008:i:7-8:p:888-906
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 245-258.
    4. Ichiishi, Tatsuro, 1981. "A Social Coalitional Equilibrium Existence Lemma," Econometrica, Econometric Society, vol. 49(2), pages 369-377, March.
    5. 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.
    6. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
    7. 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.
    8. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    9. 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, pages 84-92.
    10. Alexander Kovalenkov & Myrna H. Wooders, 1999. "A law of scarcity for games," Working Papers mwooders-00-05, University of Toronto, Department of Economics.
    11. Kovalenkov, Alexander & Wooders, Myrna Holtz, 2001. "Epsilon Cores of Games with Limited Side Payments: Nonemptiness and Equal Treatment," Games and Economic Behavior, Elsevier, vol. 36(2), pages 193-218, August.
    12. 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.
    13. 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.
    14. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    15. 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.
    16. Wooders, Myrna Holtz & Zame, William R, 1984. "Approximate Cores of Large Games," Econometrica, Econometric Society, vol. 52(6), pages 1327-1350, November.
    17. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, pages 313-327.
    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.
    19. Aliprantis, Charalombos & Burkinshaw, Owen, 1991. "When Is the Core Equivalence Theorem Valid?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 169-182, April.
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    Cited by:

    1. 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), pages 191-209.
    2. R. Arribillaga, 2015. "Convergence of the approximate cores to the aspiration core in partitioning games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 521-534, July.
    3. Askoura, Y., 2011. "The weak-core of a game in normal form with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 43-47, January.
    4. Jean-François Caulier, 2009. "A note on the monotonicity and superadditivity of TU cooperative games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633612, HAL.
    5. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    6. repec:eee:matsoc:v:89:y:2017:i:c:p:32-42 is not listed on IDEAS
    7. Hideo Konishi & Ryusuke Shinohara, 2011. "Voluntary Participation and the Provision of Public Goods in Large Finite Economies," Boston College Working Papers in Economics 776, Boston College Department of Economics.
    8. Caulier, Jean-François & Mauleon, Ana & Vannetelbosch, Vincent, 2015. "Allocation rules for coalitional network games," Mathematical Social Sciences, Elsevier, pages 80-88.
    9. Myrna Wooders, 2010. "Cores of many-player games; nonemptiness and equal treatment," Review of Economic Design, Springer;Society for Economic Design, pages 131-162.
    10. 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.
    11. repec:hal:wpaper:hal-00633612 is not listed on IDEAS

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