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

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  • 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.
    Mathematics Subject Classification: Primary: 47H05, 90A40, 26A51; Secondary: 90A10, 52A01.

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