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A law of scarcity for games

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  • Kovalenkov, Alexander
  • Wooders, Myrna Holtz

Abstract

The “law of scarcity” is that scarceness is rewarded ; recall, for example, the diamonds and water paradox. In this paper, furthering research initiated in Kelso and Crawford (1982, Econometrica 50, 1483-1504) for matching models, we demonstrate a law of scarcity for cores and approximate cores of games.

Suggested Citation

  • Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "A law of scarcity for games," The Warwick Economics Research Paper Series (TWERPS) 546, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:546
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    References listed on IDEAS

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    1. Engl, Greg & Scotchmer, Suzanne, 1996. "The core and the hedonic core: Equivalence and comparative statics," Journal of Mathematical Economics, Elsevier, vol. 26(2), pages 209-248.
    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. Greg Engl & Suzanne Scotchmer, 1997. "The law of supply in games, markets and matching models (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 539-550.
    4. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882.
    5. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
    6. Scotchmer, S. & Wooders, M.H., 1988. "Monotonicity in games that Exhaust Gains to Scale," Papers 525, Stanford - Institute for Thoretical Economics.
    7. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on," Working Papers mwooders-98-04, University of Toronto, Department of Economics.
    8. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    9. 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.
    10. 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.
    11. Kovalenkov, Alexander & Wooders, Myrna Holtz, 1999. "An Explicit Bound on E For Nonemptimess of E-Cores of Games," The Warwick Economics Research Paper Series (TWERPS) 537, University of Warwick, Department of Economics.
    12. Wooders, Myrna Holtz & Zame, William R., 1987. "Large games: Fair and stable outcomes," Journal of Economic Theory, Elsevier, vol. 42(1), pages 59-93, June.
    13. 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.
    14. Epstein, Larry G, 1981. "Generalized Duality and Integrability," Econometrica, Econometric Society, vol. 49(3), pages 655-678, May.
    15. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
    16. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
    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. 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.
    2. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    3. Myrna Wooders & Edward Cartwright, 2001. "On the theory of equalizing differences Increasing abundances of types of workers may increase their earnings," Economics Bulletin, AccessEcon, vol. 4(4), pages 1-10.
    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. Scotchmer, Suzanne, 2002. "The core and hedonic core: reply to Wooders (2001), with counterexamples," Journal of Mathematical Economics, Elsevier, vol. 37(4), pages 341-353, July.

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    More about this item

    Keywords

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

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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