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Laws of Scarcity for a Finite Game : Exact Bounds on Estimations

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Listed:
  • Kovalenkov, Alexander

    (Department of Economics, University of North Carolina)

  • Wooders, Myrna

    (Department of Economics, University of Warwick)

Abstract

A "law of scarcity" is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we show that equal treatment core payout vectors satisfy a condition of cyclic monotonicity. Our results are developed for parameterized collections of games and exact bounds on the maximum possible deviation of approximate core payo® vectors from satisfying a law of scarcity are stated in terms of the parameters describing the games. We note that the parameters can, in principle, be estimated.

Suggested Citation

  • Kovalenkov, Alexander & Wooders, Myrna, 2003. "Laws of Scarcity for a Finite Game : Exact Bounds on Estimations," The Warwick Economics Research Paper Series (TWERPS) 691, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:691
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    References listed on IDEAS

    as
    1. 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.
    2. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882.
    3. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
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    5. Scotchmer, S. & Wooders, M.H., 1988. "Monotonicity in games that Exhaust Gains to Scale," Papers 525, Stanford - Institute for Thoretical Economics.
    6. Mas-Colell, Andreu, 1975. "A further result on the representation of games by markets," Journal of Economic Theory, Elsevier, vol. 10(1), pages 117-122, February.
    7. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    8. Carlo Carraro (ed.), 2003. "The Endogenous Formation of Economic Coalitions," Books, Edward Elgar Publishing, number 2999.
    9. 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.
    10. Alexander Kovalenkov & Myrna Holtz Wooders, 2001. "An Exact Bound on Epsilon for Nonemptiness of Epsilon Cores of Games," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 654-678, November.
    11. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    12. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    13. 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.
    14. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    15. Alexander Kovalenkov & Myrna H. Wooders, 1999. "An explicit bound on epsilon for nonemptiness of Epsilon-cores of games," Working Papers mwooders-00-03, University of Toronto, Department of Economics.
    16. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
    17. 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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    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. 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.
    3. 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.
    4. Ehud Lehrer & Marco Scarsini, 2013. "On the Core of Dynamic Cooperative Games," Dynamic Games and Applications, Springer, vol. 3(3), pages 359-373, September.
    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).

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    More about this item

    Keywords

    monotonicity ; cooperative games ; clubs ; games with side payments (TU games) ; cyclic monotonicity ; law of scarcity ; law of demand ; approximate cores ; effective small groups ; parameterized collections of games;
    All these keywords.

    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
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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