General conditions for the existence of maximal elements via the uncovered set

John Duggan

Journal of Mathematical Economics, 2011, vol. 47, issue 6, 755-759

Abstract: This paper disentangles the topological assumptions of classical results (e.g.,Walker, 1977 on the existence of maximal elements from rationality conditions. It is known from the social choice literature that under the standard topological conditions—with no rationality assumptions on preferences—there is an element such that the upper section of strict preference at that element is minimal in terms of set inclusion, i.e., the uncovered set is nonempty. Assuming the finite subordination property, a condition that weakens known acyclicity and convexity assumptions, each such uncovered alternative is in fact maximal. Implications are a generalization of a result of Yannelis and Prabhakar (1983) on semi-convexity, an extension of Fan’s (1961) lemma on KKM correspondences, and the existence of fixed points for subordinate convex correspondences generalizing the work of Browder (1968).

Keywords: Maximal element; Existence; Uncovered set; Fixed point (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:47:y:2011:i:6:p:755-759

DOI: 10.1016/j.jmateco.2011.09.008

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