Multipermutation-Based Intersection Theorem and Its Applications |
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Authors: | Yang Z. F. |
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Affiliation: | (1) Faculty of Business Administration, Yokohama National University, Yokohama, Japan |
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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. |
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Keywords: | intersection theorem fixed-point theorem combinatorial theorem equilibrium problem indivisibility equilibrium theorem |
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