Multipermutation-Based Intersection Theorem and Its Applications

Z. F. Yang
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Z. F. Yang: Yokohama National University

Journal of Optimization Theory and Applications, 2000, vol. 104, issue 2, No 12, 477-487

Abstract: 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.

Keywords: intersection theorem; fixed-point theorem; combinatorial theorem; equilibrium problem; indivisibility; equilibrium theorem (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1004626216810

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