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Econ Theory (2011) 48:399424
DOI 10.1007/s00199-011-0641-7
SYMPOSIUM
Received: 7 December 2010 / Accepted: 16 May 2011 / Published online: 10 June 2011 Springer-Verlag 2011
Abstract We examine a variety of preference-based definitions of ambiguous events in the context of the smooth ambiguity model. We rst consider the definition proposed in Klibanoff et al. (Econometrica 73(6):18491892, 2005) based on the classic Ellsberg two-urn paradox (Ellsberg Q J Econ 75:643669, 1961) and show that it satises several desirable properties. We then compare this definition with those of Nehring (Math Soc Sci 38(2):197213, 1999), Epstein and Zhang (Econometrica 69:265306, 2001), Zhang (Econ Theory 20:159181, 2002), and Ghirardato and Marinacci (J Econ Theory 102:251289, 2002). Within the smooth ambiguity model, we show that Ghirardato and Marinacci (J Econ Theory 102:251289, 2002) would identify the same set of ambiguous and unambiguous events as our definition while Epstein and Zhang (Econometrica 69:265306, 2001) and Zhang (Econ Theory 20:159181, 2002) would yield a different classication. Moreover, we discuss and formally identify two key sources of the differences compared to Epstein and Zhang (Econometrica 69:265 306, 2001) and Zhang (Econ Theory 20:159181, 2002). The more interesting source
We thank Simone Cerreia-Vioglio, Paolo Ghirardato, Mark Machina and Marciano Siniscalchi for helpful discussions.
P. Klibanoff (B)
Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208, USAe-mail: [email protected]
M. Marinacci
Department of Decision Sciences and IGIER, Universit Bocconi, Milano, Italy e-mail: [email protected]
S. Mukerji
Department of Economics, University of Oxford, Oxford, UK e-mail: [email protected]
Definitions of ambiguous events and the smooth ambiguity model
Peter Klibanoff Massimo Marinacci
Sujoy Mukerji
123
400 P. Klibanoff et al.
is that these two definitions can confound non-constant ambiguity attitude and the ambiguity of an event.
Keywords Ambiguity Uncertainty Knightian uncertainty Ambiguity aversion
Uncertainty aversion Ellsberg paradox
JEL Classication D800 D810
1 Introduction
There are a variety of preference-based definitions of ambiguous events in the literature. In Klibanoff et al. (2005), we proposed one such definition based on the classic Ellsberg two-urn paradox (Ellsberg 1961). We showed, in the context of the smooth ambiguity model of decision making developed in Klibanoff et al. (2005), that this definition is characterized by, roughly, disagreement in the probability assigned to an event by the...