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Approximate Cores Of Games And Economies With Clubs

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  • Kovalenkov, Alexander

    (Department of Economics, University of North Carolina)

  • Wooders, Myrna Holtz

    (Department of Economics, University of Warwick)

Abstract

We introduce the framework of parameterized collections of games with and without sidepayments and provide three nonemptiness of approximate core theorems. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. Our theorems are based on a new notion of partitionbalanced profiles and approximately partition-balanced profiles. The results are applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results.

Suggested Citation

  • Kovalenkov, Alexander & Wooders, Myrna Holtz, 2002. "Approximate Cores Of Games And Economies With Clubs," The Warwick Economics Research Paper Series (TWERPS) 634, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:634
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Cartwright, Edward & Conley, John & Wooders, Myrna, 2005. "The Law of Demand in Tiebout Economies," The Warwick Economics Research Paper Series (TWERPS) 734, University of Warwick, Department of Economics.
    2. 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.
    3. 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.
    4. Meseguer-Artola, Antoni & Wooders, Myrna Holtz & Martinez-Legaz, Juan-Enrique, 2003. "Representing Games As Coalition Production Economies With Public Goods," The Warwick Economics Research Paper Series (TWERPS) 669, University of Warwick, Department of Economics.
    5. Cartwright, Edward & Wooders, Myrna, 2005. "Correlated equilibrium and behavioural conformity," The Warwick Economics Research Paper Series (TWERPS) 732, University of Warwick, Department of Economics.
    6. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    7. Allouch, Nizar & Conley, John P. & Wooders, Myrna, 2009. "Anonymous price taking equilibrium in Tiebout economies with a continuum of agents: Existence and characterization," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 492-510, September.
    8. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "Epsilon cores of games and economies with limited side payments," Working Papers mwooders-98-03, University of Toronto, Department of Economics.
    9. Arnold, Tone & Wooders, Myrna, 2002. "Dynamic Club Formation With Coordination," The Warwick Economics Research Paper Series (TWERPS) 640, University of Warwick, Department of Economics.
    10. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 137-153, March.
    11. 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.
    12. 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.
    13. 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.
    14. Page Jr., Frank H. & Wooders, Myrna, 2007. "Networks and clubs," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 406-425.
    15. repec:eee:matsoc:v:89:y:2017:i:c:p:50-60 is not listed on IDEAS
    16. Alexander Kovalenkov & Myrna Wooders, 2003. "Advances in the theory of large cooperative games and applications to club theory; the side payments case," Chapters,in: The Endogenous Formation of Economic Coalitions, chapter 1 Edward Elgar Publishing.
    17. Allouch, Nizar & Wooders, Myrna, 2002. "Competitive Pricing In Socially Networked Economies," The Warwick Economics Research Paper Series (TWERPS) 639, University of Warwick, Department of Economics.
    18. 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.
    19. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
    20. Alexander Kovalenkov & Myrna H. Wooders, 1999. "A law of scarcity for games," Working Papers mwooders-00-05, University of Toronto, Department of Economics.
    21. Edward Cartwright & Myrna Wooders, 2003. "Social Conformity and Bounded Rationality in Arbitrary Games with Incomplete Information: Some First Results," Working Papers 2003.119, Fondazione Eni Enrico Mattei.
    22. Kung, Fan-chin, 2008. "Voluntary contributions to multiple public goods in a production economy with widespread externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1364-1378, December.
    23. Anne Van den nouweland & Myrna Wooders, 2016. "Existence of Share Equilibrium in Symmetric Local Public Good Economies∗," Vanderbilt University Department of Economics Working Papers 16-00008, Vanderbilt University Department of Economics.

    More about this item

    Keywords

    cooperative games ; clubs ; approximate cores ; effective small groups ; parameterized collections of games ; NTU games;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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