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Ordinal, nonlinear context dependence

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  • O'Callaghan, Patrick
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    Abstract

    Prospect theory [KT79] and its more recent formalizations [KR06, KR07] prescribe "nonlinear" reference-dependence. The same may be said of other forms of context-dependence such as status quo bias [MO05]. Even in settings where there is a strong case for linear context-dependence such as Gilboa and Schmeidler's theory of case-based decisions, nonlinearity is typical in the absence of "diversity of preference". Furthermore, the hope of providing an axiomatic foundation for neuroscientific models of decision making, where context is interpreted as a physical state or "connectome" suggest a general, ordinal axiomatization of nonlinear context-dependence is called for. As with traditional, "context-free" models of ordinal utility (eg. Debreu [Deb54]), the issue of continuity is central: precise, yet simple and intuitive, conditions on the set of contexts are needed if preferences have a representation that is continuous across contexts. The continuity condition I employ is the obvious choice and is a generalisation of [GS03a]. There are interesting connections with literature on jointly continuous utility [Lev83, CCM09]. Finally, a promising feature of the present approach is it that may be used to axiomatise payoffs associated with discontinuous games (such as Bertrand oligopoly).

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    Paper provided by University of Queensland, School of Economics in its series Risk and Sustainable Management Group Working Papers with number 152450.

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    Date of creation: 18 May 2013
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    Handle: RePEc:ags:uqsers:152450

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    Keywords: Risk and Uncertainty;

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    1. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    2. Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, MIT Press, vol. 121(4), pages 1133-1165, November.
    3. Botond Koszegi & Matthew Rabin, 2006. "Reference-Dependent Risk Attitudes," Levine's Bibliography 122247000000001267, UCLA Department of Economics.
    4. Itzhak Gilboa & David Schmeidler, 2001. "A Derivation of Expected Utility Maximization in the Context of a Game," Cowles Foundation Discussion Papers 1342, Cowles Foundation for Research in Economics, Yale University.
    5. Barbos, Andrei, 2010. "Context effects: A representation of choices from categories," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1224-1243, May.
    6. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    7. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    8. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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