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Ordinal, nonlinear context dependence

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  • O'Callaghan, Patrick

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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  • O'Callaghan, Patrick, 2013. "Ordinal, nonlinear context dependence," Risk and Sustainable Management Group Working Papers 152450, University of Queensland, School of Economics.
  • Handle: RePEc:ags:uqsers:152450
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    References listed on IDEAS

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    1. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 121(4), pages 1133-1165.
    2. Itzhak Gilboa & David Schmeidler, 2003. "Inductive Inference: An Axiomatic Approach," Econometrica, Econometric Society, vol. 71(1), pages 1-26, January.
    3. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
    4. Gilboa,Itzhak & Schmeidler,David, 2001. "A Theory of Case-Based Decisions," Cambridge Books, Cambridge University Press, number 9780521802345.
    5. Gilboa, Itzhak & Schmeidler, David, 2003. "A derivation of expected utility maximization in the context of a game," Games and Economic Behavior, Elsevier, vol. 44(1), pages 172-182, July.
    6. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    7. Botond Koszegi & Matthew Rabin, 2007. "Reference-Dependent Risk Attitudes," American Economic Review, American Economic Association, vol. 97(4), pages 1047-1073, September.
    8. Barbos, Andrei, 2010. "Context effects: A representation of choices from categories," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1224-1243, May.
    9. Itzhak Gilboa & D. Schmeidler, 2003. "Expected Utility in the Context of a Game," Post-Print hal-00752136, HAL.
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    Keywords

    Risk and Uncertainty;

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