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Ambiguous events and maxmin expected utility

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  • Amarante, Massimiliano
  • Filiz, Emel

Abstract

We study the properties associated to various definitions of ambiguity ([8], [9], [18] and [23]) in the context of Maximin Expected Utility (MEU). We show that each definition of unambiguous events produces certain restrictions on the set of priors, and completely characterize each definition in terms of the properties it imposes on the MEU functional. We apply our results to two open problems. First, in the context of MEU, we show the existence of a fundamental incompatibility between the axiom of "Small unambiguous event continuity" ([8]) and the notions of unambiguous event due to Zhang [23] and Epstein-Zhang [8]. Second, we show that, in the context of MEU, the classes of unambiguous events according to either Zhang [23] or Epstein-Zhang [8] are always -systems. Finally, we reconsider the various definitions in light of our findings, and identify some new objects (Z-filters and EZ-filters) corresponding to properties which, while neglected in the current literature, seem relevant to us.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 134 (2007)
Issue (Month): 1 (May)
Pages: 1-33

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Handle: RePEc:eee:jetheo:v:134:y:2007:i:1:p:1-33

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Jiankang Zhang, 2002. "Subjective ambiguity, expected utility and Choquet expected utility," Economic Theory, Springer, vol. 20(1), pages 159-181.
  2. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  4. Massimo Marinacci & Paolo Ghirardato, 2001. "Risk, ambiguity, and the separation of utility and beliefs," ICER Working Papers - Applied Mathematics Series 21-2001, ICER - International Centre for Economic Research.
  5. Klaus Nehring, . "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Department of Economics 97-08, California Davis - Department of Economics.
  6. Massimo Marinacci & Fabio Maccheroni & Alain Chateauneuf & Jean-Marc Tallon, 2003. "Monotone Continuous Multiple Priors," ICER Working Papers - Applied Mathematics Series 30-2003, ICER - International Centre for Economic Research.
  7. Larry G. Epstein & Jiankang Zhang, 1999. "Subjective Probabilities on Subjectively Unambiguous Events," Carleton Economic Papers 99-18, Carleton University, Department of Economics.
  8. Massimiliano Amarante, 2005. "Ambiguity, measurability and multiple priors," Economic Theory, Springer, vol. 26(4), pages 995-1006, November.
  9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  10. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
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Cited by:
  1. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010. "Rational Preferences under Ambiguity," Carlo Alberto Notebooks 169, Collegio Carlo Alberto.
  2. Klaus Nehring, 2006. "Is it Possible to Define Subjective Probabilities in Purely Behavioral Terms? A Comment on Epstein-Zhang (2001)," Economics Working Papers 0067, Institute for Advanced Study, School of Social Science.
  3. Dominiak, Adam & Dürsch, Peter & Lefort, Jean-Philippe, 2009. "A Dynamic Ellsberg Urn Experiment," Working Papers 0487, University of Heidelberg, Department of Economics.
  4. Alain Chateauneuf & Luciano De Castro, 2011. "Ambiguity Aversion and Absence of Trade," Discussion Papers 1535, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Massimiliano Amarante, 2013. "Conditional Expected Utility," Cahiers de recherche 02-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Qu, Xiangyu, 2013. "Maxmin expected utility with additivity on unambiguous events," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 245-249.

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