Ambiguous events and maxmin expected utility
AbstractWe study the properties associated to various definitions of ambiguity (, ,  and ) 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" () and the notions of unambiguous event due to Zhang  and Epstein-Zhang . Second, we show that, in the context of MEU, the classes of unambiguous events according to either Zhang  or Epstein-Zhang  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 InfoArticle provided by Elsevier in its journal Journal of Economic Theory.
Volume (Year): 134 (2007)
Issue (Month): 1 (May)
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Web page: http://www.elsevier.com/locate/inca/622869
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- Jiankang Zhang, 2002.
"Subjective ambiguity, expected utility and Choquet expected utility,"
Springer, vol. 20(1), pages 159-181.
- Jiankang Zhang, 1999. "Subjective Ambiguity, Expected Utility and Choquet Expected Utility," Carleton Economic Papers 99-19, Carleton University, Department of Economics, revised Aug 2002.
- Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-87, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- 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.
- Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
- Ghirardato, Paolo & Marinacci, Massimo, 2000. "Risk, Ambigity and the Separation of Utility and Beliefs," Working Papers 1085, California Institute of Technology, Division of the Humanities and Social Sciences.
- Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society.
- Klaus Nehring, .
"Capacities And Probabilistic Beliefs: A Precarious Coexistence,"
Department of Economics
97-08, California Davis - Department of Economics.
- Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
- Klaus Nehring & Michael Magill & Julian R. Betts, 2003. "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Working Papers 978, University of California, Davis, Department of Economics.
- 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.
- Larry G. Epstein & Jiankang Zhang, 1999.
"Subjective Probabilities on Subjectively Unambiguous Events,"
Carleton Economic Papers
99-18, Carleton University, Department of Economics.
- Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
- Massimiliano Amarante, 2005.
"Ambiguity, measurability and multiple priors,"
Springer, vol. 26(4), pages 995-1006, November.
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
- Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010.
"Rational Preferences under Ambiguity,"
Carlo Alberto Notebooks
169, Collegio Carlo Alberto.
- 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.
- Dominiak, Adam & Dürsch, Peter & Lefort, Jean-Philippe, 2009.
"A Dynamic Ellsberg Urn Experiment,"
0487, University of Heidelberg, Department of Economics.
- Lefort, Jean-Philippe & Dominiak, Adam & Dürsch, Peter, 2012. "A Dynamic Ellsberg Urn Experiment," Economics Papers from University Paris Dauphine 123456789/7357, Paris Dauphine University.
- Dominiak, Adam & Dürsch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Economics Papers from University Paris Dauphine 123456789/7333, Paris Dauphine University.
- 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.
- Massimiliano Amarante, 2013.
"Conditional Expected Utility,"
Cahiers de recherche
02-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- 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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