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On a covering theorem

Author

Listed:
  • Adam Idzik

    (Institute of Computer Science, Polish Academy of Sciences, ul. Ordona 21, 01-237 Warsaw, POLAND)

  • Tatsuro Ichiishi

    (Department of Economics, Ohio State University, Columbus, OH 43210-1172, USA)

Abstract

A simple proof of Reny and Wooders' recent strengthening of Shapley's extension of the Knaster-Kuratowski-Mazurkiewicz lemma on a closed cover of a simplex is given. The proof uses Ky Fan's coincidence theorem.

Suggested Citation

  • Adam Idzik & Tatsuro Ichiishi, 2002. "On a covering theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 833-838.
    • Handle: RePEc:spr:joecth:v:19:y:2002:i:4:p:833-838
    Note: Received: May 26, 2000; revised version: January 22, 2001
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    Citations

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    Cited by:

    1. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    2. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

    More about this item

    Keywords

    Shapley's generalization of the K-K-M lemma; Reny-Wooders' strengthening of Shapley's theorem; Ky Fan's coincidence theorem; Invulnerability; Core of a non-side-payment game.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • L20 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - General

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