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Multipermutation-Based Intersection Theorem and Its Applications

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  • Z. F. Yang

    (Yokohama National University)

Abstract

In this paper, we introduce a multipermutation-based intersection theorem on the product space of several unit simplices, called the simplotope. This theorem gives a substantial generalization of an intersection result of Scarf on the unit simplex (Ref. 1). By using this new result, we also obtain a multipermutation-based generalization of the Brouwer fixed-point theorem on the simplotope. Furthermore, we apply this new result to an economic equilibrium model with indivisibilities and obtain an equilibrium existence theorem.

Suggested Citation

  • Z. F. Yang, 2000. "Multipermutation-Based Intersection Theorem and Its Applications," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 477-487, February.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:2:d:10.1023_a:1004626216810
    DOI: 10.1023/A:1004626216810
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    References listed on IDEAS

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    1. Talman, A.J.J., 1991. "Intersection theorems on the unit simplex and the simplotope," Discussion Paper 1991-57, Tilburg University, Center for Economic Research.
    2. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 1997. "Existence of an equilibrium in a competitive economy with indivisibilities and money," Journal of Mathematical Economics, Elsevier, vol. 28(1), pages 101-109, August.
    3. P. J. J. Herings & A. J. J. Talman, 1998. "Intersection Theorems with a Continuum of Intersection Points," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 311-335, February.
    4. Talman, A.J.J., 1991. "Intersection theorems on the unit simplex and the simplotope," Other publications TiSEM 3d9e52e1-2498-49ac-928b-2, Tilburg University, School of Economics and Management.
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