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Using oriented volume to prove Sperner’s lemma

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  • Yakar Kannai

    (Weizmann Institute of Science)

Abstract

An elementary proof of Sperner’s lemma, using only oriented volumes of simplices, is provided. Several generalizations are indicated.

Suggested Citation

  • Yakar Kannai, 2013. "Using oriented volume to prove Sperner’s lemma," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 11-19, May.
    • Handle: RePEc:spr:etbull:v:1:y:2013:i:1:d:10.1007_s40505-013-0013-5
    DOI: 10.1007/s40505-013-0013-5
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Andrew McLennan & Rabee Tourky, 2008. "Using volume to prove Sperner’s Lemma," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 593-597, June.
    3. Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 108-116, January.
    4. Kannai, Yakar, 1992. "The core and balancedness," 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 12, pages 355-395, Elsevier.
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    More about this item

    Keywords

    Sperner’s lemma; Oriented volume;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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