Definable utility in o-minimal structures. (Q1587385)

The authors obtain definable utility representations for both continuous and upper semi-continuous definable preferences in the tame topology of \(o\)-minimal expansious of real closed ordered fields \textit{A. Pillay} and \textit{C. Steinhorn} [Am. Math. Soc. 295, 565--592 (1986; Zbl 0662.03023)], \textit{J. E. Knight}, \textit{A. Pillay} and \textit{C. Steinhorn} [ibid. 295, 593--605 (1986; Zbl 0662.03024)]. The applications of such preferences provided are in establishing local determinacy of competitive equilibrium and in modeling bounded rationality. The proofs are based on geometric properties of definable sets and provide alternative methods to the classical methods of Debreu, Rader and Arrow and Hahn. Finally, the results are shown to extend Theorem I in [\textit{L. Blume} and \textit{W. Zame}. The algebraic geometry of competitive equilibrium, In: W. Neuefeind and R. G. Riezman (eds.), Economic theory and International trade: Essays in Memoriam J. Trout Rader, Springer-Verlag Berlin (1992)].