April  2007, 3(2): 233-255. doi: 10.3934/jimo.2007.3.233

Existence of closed graph, maximal, cyclic pseudo-monotone relations and revealed preference theory

1. 

School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology, G.P.O. Box 2476V, Melbourne, Australia 3001, Australia

2. 

LIMOS, Université Blaise Pascal, Boite Postale 206, F-63174 AUBIERE Cedex, France

Received  August 2006 Revised  October 2006 Published  April 2007

We investigate a multifunction $x$→Ñ f $(x)$ derived via normal cones to the level sets Š $(x)$ := { $x^$' | $f(x^$') $ < f(x)$} for an important class of pseudo--convex functions. It is shown that $x$→Ñ f $(x)$ is simultaneously both a maximally cyclically pseudo--monotone and a maximally pseudo-monotone relation within neighbourhoods on which $f$ is nonconstant. The relevance of this work to the problem of construction of a utility function from observations of revealed preferences of a consumer is discussed.
Citation: A. C. Eberhard, J-P. Crouzeix. Existence of closed graph, maximal, cyclic pseudo-monotone relations and revealed preference theory. Journal of Industrial & Management Optimization, 2007, 3 (2) : 233-255. doi: 10.3934/jimo.2007.3.233
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