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Preference for Randomization and Ambiguity Aversion

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  • Kaito Sato

Abstract

Raiffa (1961) criticizes ambiguity-averse preferences by claiming that hedging is possible with randomization of choices. We argue that the timing of randomization is crucial for hedging. Ex-ante randomizations, which are randomizations before a state is realized, could provide only ex-ante hedging but not ex-post hedging, in contrast to ex-post randomizations, which are randomizations after a state is realized. However, these two randomizations have been assumed to be indifferent under the reversal of order axiom proposed by Anscombe and Aumann (1963). We, therefore, propose a weaker axiom, the indifference axiom, which allows heterogeneous attitudes toward the timing of randomization. By using this new axiom as well as standard axioms, we provide an extension of Gilboa and Schmeidler’s (1989) Maxmin preferences that treats a preference for ex-ante randomizations separately from a preference for ex-post randomizations. In the representation, a single parameter characterizes a preference for ex-ante randomizations. By parsimoniously changing only the value of that single parameter, the representation can be consistent with Raiffa’s (1961) normative argument as well as recent experimental evidence. JEL Classification Numbers: D81, D03

Suggested Citation

  • Kaito Sato, 2011. "Preference for Randomization and Ambiguity Aversion," Discussion Papers 1524, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1524
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1524.pdf
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    References listed on IDEAS

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    1. Mukerji Sujoy & Shin Hyun Song, 2002. "Equilibrium Departures from Common Knowledge in Games with Non-Additive Expected Utility," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-30, June.
    2. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    3. Dwenger, Nadja & Kübler, Dorothea & Weizsäcker, Georg, 2013. "Preference for randomization: Empirical and experimental evidence," Discussion Papers, Research Unit: Market Behavior SP II 2013-201, Social Science Research Center Berlin (WZB).
    4. Adam Dominiak & Wendelin Schnedler, 2011. "Attitudes toward uncertainty and randomization: an experimental study," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 289-312, October.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    6. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    7. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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