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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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    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp546rev.pdf
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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. 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.
    3. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    4. 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.
    5. 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.
    6. Epstein, Larry G, 1981. "Generalized Duality and Integrability," Econometrica, Econometric Society, vol. 49(3), pages 655-678, May.
    7. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    8. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
    9. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    10. A. Kovalenkov & M. Holtz Wooders, 1999. "An explicit bound on e for nonemptiness of e-cores of games," THEMA Working Papers 99-37, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    11. A. Kovalenkov & M. Holtz Wooders, 1999. "An explicit bound on e for nonemptiness of e-cores of games," THEMA Working Papers 99-37, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    12. 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.
    13. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
    14. Scotchmer, S. & Wooders, M.H., 1988. "Monotonicity in games that Exhaust Gains to Scale," Papers 525, Stanford - Institute for Thoretical Economics.
    15. Alexander Kovalenkov & Myrna Holtz Wooders, 1997. "An explicit bound on," Working Papers mwooders-98-04, University of Toronto, Department of Economics.
    16. 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.
    17. 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.
    18. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
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    Cited by:

    1. 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.
    2. 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.
    3. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    4. 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.
    5. 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.

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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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