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Remarks concerning concave utility functions on finite sets

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  • Yakar Kannai

Abstract

A direct construction of concave utility functions representing convex preferences on finite sets is presented. An alternative construction in which at first directions of supergradients (“prices”) are found, and then utility levels and lengths of those supergradients are computed, is exhibited as well. The concept of a least concave utility function is problematic in this context. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Yakar Kannai, 2005. "Remarks concerning concave utility functions on finite sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 333-344, August.
    • Handle: RePEc:spr:joecth:v:26:y:2005:i:2:p:333-344
    DOI: 10.1007/s00199-004-0545-x
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    Cited by:

    1. Yashiv, Eran & Perets, Gadi, 2018. "Lie Symmetries and Essential Restrictions in Economic Optimization," CEPR Discussion Papers 12611, C.E.P.R. Discussion Papers.
    2. ,, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    3. Apartsin, Yevgenia & Kannai, Yakar, 2006. "Demand properties of concavifiable preferences," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 36-55, December.
    4. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
    5. Christopher Connell & Eric Rasmusen, 2012. "Concavifying the Quasiconcave," Working Papers 2012-10, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.

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