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Act-Similarity in Case-Based Decision Theory

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  • Itzhak Gilboa
  • David Schmeidler

Abstract

Case-Based Decision Theory (CBDT) postulates that decision making under uncertainty is based on analogies to past cases. In its original version, it suggests that each of the available acts is ranked according to its own performance in similar decision problems encountered in the past. The purpose of this paper is to extend CBDT to deal with cases in which the evaluation of an act may also depend on past performance of different, but similar acts. To this end we provide a behavioral axiomatic definition of the similarity function over problem-act pairs (and not over problem pairs alone, as in the original model). We propose a model in which preferences are context-dependent. For each conceivable history of outcomes (to be thought of as the "context" of decision) there is a preference order over acts. If these context-dependent preference relations satisfy our consistency-across-contexts axioms, there is an essentially unique similarity function that represents these preferences via the (generalized) CBDT functional.
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Suggested Citation

  • Itzhak Gilboa & David Schmeidler, 1994. "Act-Similarity in Case-Based Decision Theory," Discussion Papers 1081, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1081
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1081.pdf
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    References listed on IDEAS

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    1. Itzhak Gilboa & David Schmeidler, 1993. "Case-Based Knowledge Representation," Discussion Papers 1053, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Itzhak Gilboa & David Schmeidler, 1993. "Case-Based Consumer Theory," Discussion Papers 1025, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Citations

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    Cited by:

    1. Matsui, Akihiko, 2000. "Expected utility and case-based reasoning," Mathematical Social Sciences, Elsevier, vol. 39(1), pages 1-12, January.
    2. Fioretti, Guido, 2006. "Recognising investment opportunities at the onset of recoveries," Research in Economics, Elsevier, vol. 60(2), pages 69-84, June.
    3. Bisin, Alberto & Verdier, Thierry, 1998. "On the cultural transmission of preferences for social status," Journal of Public Economics, Elsevier, vol. 70(1), pages 75-97, October.
    4. O'Callaghan, Patrick, 2016. "Parametric continuity from preferences when the topology is weak and actions are discrete," MPRA Paper 72356, University Library of Munich, Germany.
    5. Kent, Christopher John, 2011. "Two depressions, one banking collapse: Lessons from Australia," Journal of Financial Stability, Elsevier, vol. 7(3), pages 126-137, August.
    6. Brit Grosskopf & Rajiv Sarin & Elizabeth Watson, 2015. "An experiment on case-based decision making," Theory and Decision, Springer, vol. 79(4), pages 639-666, December.
    7. Guerdjikova, Ani, 2004. "A note on case-based optimization with a non-degenerate similarity function," Papers 04-46, Sonderforschungsbreich 504.
    8. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Case-based expected utility : preferences over actions and data," Papers 08-32, Sonderforschungsbreich 504.
    9. Eichberger, Jürgen & Guerdjikova, Ani, 2008. "Multiple Priors as Similarity Weighted Frequencies," Papers 08-07, Sonderforschungsbreich 504.
    10. 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.
    11. O'Callaghan, Patrick, 2016. "Minimal conditions for parametric continuity and stable policy in extreme settings," MPRA Paper 70989, University Library of Munich, Germany.
    12. Guerdjikova, Ani, 2006. "Portfolio Choice and Asset Prices in an Economy Populated by Case-Based Decision Makers," Working Papers 06-13, Cornell University, Center for Analytic Economics.
    13. Rustichini, A., 1998. "Sophisticated Players and Sophisticated Agents," Discussion Paper 1998-110, Tilburg University, Center for Economic Research.
    14. Han Bleichrodt & Martin Filko & Amit Kothiyal & Peter P. Wakker, 2017. "Making Case-Based Decision Theory Directly Observable," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 123-151, February.
    15. Easley, David & Rustichini, Aldo, 2005. "Optimal guessing: Choice in complex environments," Journal of Economic Theory, Elsevier, vol. 124(1), pages 1-21, September.
    16. Guerdjikova, Ani, 2004. "Preference for diversification with similarity considerations," Papers 04-48, Sonderforschungsbreich 504.
    17. Itzhak Gilboa & David Schmeidler, 1995. "Case-Based Knowledge and Planning," Discussion Papers 1127, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    18. Chambers, Christopher P. & Hayashi, Takashi, 2012. "Choice and individual welfare," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1818-1849.
    19. David Schmeidler & Itzhak Gilboa, 1996. "Cumulative Utility Consumer Theory," Working Papers 025, Ohio State University, Department of Economics.

    More about this item

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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