EconPapers    
Economics at your fingertips  
 

Attitude toward imprecise information

Thibault Gajdos (), T. Hayashi, Jean-Marc Tallon () and Jean-Christophe Vergnaud ()

Journal of Economic Theory, 2008, vol. 140, issue 1, 27-65

Abstract: This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability-possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P and is assumed to rank pairs of the form (P,f) where f is an act mapping states into outcomes. The key representation result delivers maxmin expected utility (MEU) where the min operator ranges over a set of probability priors--just as in the MEU representation result of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141-153]. However, unlike the MEU representation, the representation here also delivers a mapping, [phi], which links the probability-possibility set, describing the available information, to the set of revealed priors. The mapping [phi] is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability-possibility set. This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability-possibility set, i.e., [phi] is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the "mean value" of the probability-possibility set, and (ii) shrinking the probability-possibility set toward the mean value to a degree determined by preferences.

Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (126) Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0022-0531(07)00120-2
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Attitude toward imprecise information (2008) Downloads
Working Paper: Attitude toward imprecise information (2006) Downloads
Working Paper: Attitude toward imprecise information (2006) Downloads
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:140:y:2008:i:1:p:27-65

Access Statistics for this article

Journal of Economic Theory is currently edited by A. Lizzeri and K. Shell

More articles in Journal of Economic Theory from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().

 
Page updated 2020-01-27
Handle: RePEc:eee:jetheo:v:140:y:2008:i:1:p:27-65