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Comparative statics and laws of scarcity for games

In: Rationality and Equilibrium

Author

Listed:
  • Alexander Kovalenkov

    (University of North Carolina)

  • Myrna Wooders

    (Vanderbilt University
    University of Warwick)

Abstract

Summary A “law of scarcity” is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we demonstrate conditions under which all payoffs in the core of any game in a parameterized collection have an equal treatment property and show that equal treatment core payoff 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 payoff 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. Results are compared to the developments in the literature on matching markets, pregames, and general equilibrium. This paper expands on results published in Kovalenkov and Wooders, Economic Theory (26, 383–396, 2005).

Suggested Citation

  • Alexander Kovalenkov & Myrna Wooders, 2006. "Comparative statics and laws of scarcity for games," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 141-167, Springer.
    • Handle: RePEc:spr:steccp:978-3-540-29578-5_8
    DOI: 10.1007/3-540-29578-X_8
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    Cited by:

    1. 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.
    2. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    3. Edward Cartwright & Myrna Wooders, 2005. "The Law od Demand in Tiebout Economies," Vanderbilt University Department of Economics Working Papers 0527, Vanderbilt University Department of Economics.

    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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