On the Arrow-Hahn utility representation method
In this paper we characterize metric spaces used in Beardon's generalization of Arrow-Hahn utility representation method as generalized Peano continua. For continuous preference relations defined on such metric spaces, we further construct an upper semi-continuous utility function which explicitly depends on the distance.
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- Monteiro, Paulo Klinger, 1987. "Some results on the existence of utility functions on path connected spaces," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 147-156, April.
- Jose C. R. Alcantud & Ghanshyam B. Mehta, 2005. "Constructive Utility Functions on Banach spaces," Microeconomics 0502003, EconWPA.
- A. F. Beardon, 1997. "Utility representation of continuous preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 369-372.
- Candeal, Juan C. & Indurain, Esteban & Mehta, Ghanshyam B., 2004. "Utility functions on locally connected spaces," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 701-711, September.
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