MATHEMATICAL ENGINEERING TECHNICAL REPORTS Sperner’s Lemma and the Existence of Zero on the Discrete Simplex and Simplotope
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چکیده
In this paper we show a zero point theorem for a certain meaningful class of correspondences on a discrete simplex, which is equivalent to Sperner’s lemma [Abh. Math. Sem. Univ. Hamburg 6 (1928) 265]. Also, we show a zero point theorem for correspondences on a discrete simplotope, which is derived from a Sperner-like theorem on the simplotope by van der Laan and Talman [Math. Oper. Res. 7 (1982) 1] and Freund [Math. Oper. Res. 11 (1986) 169]. The two discrete zero point theorems are closely related to the discrete fixed point theorem of Iimura, Murota and Tamura [J. Math. Econ. 41 (2005) 1030]. We also provide applications of the two theorems to economic and game models.
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تاریخ انتشار 2010