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Coping With Ignorance: Unforeseen Contingencies and Non-Additive Uncertainty

Ghirardato, Paolo (1996) Coping With Ignorance: Unforeseen Contingencies and Non-Additive Uncertainty. Social Science Working Paper, California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20170817-145148657

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Abstract

In real-life decision problems, decision makers are never provided with the necessary background structure: the set of states of the world, the outcome space, the set of actions. They have to devise all these by themselves. I model the (static) choice problem of a decision maker (DM) who is aware that her perception of the state space is too coarse, as for instance when there might be unforeseen contingencies. After making assumptions on the way the DM perceives the decision problem, I present a set of axioms on her preferences which imply that they can represented by a (generalized) expectation with respect to a non-additive measure, called a belief function. As it turns out, the very natural axioms presented have strong implications on the way the DM copes with the type of ignorance described above. I show how some decision rules that have been studied in the literature can be obtained as a special case of the model presented here (though they have to be interpreted differently). I then show that this formulation of the problem can yield very natural results on the comparative statics of beliefs as the DM's understanding of the decision problem becomes deeper, for instance when unforeseen events become foreseen. I present the implications of these results for a simple asset pricing model. Finally I argue that if we are willing to make assumptions on the faithfulness of the DM's perception with respect to reality, then the DM described here will, in the limit as her perception becomes finer and finer, resemble a Savage DM.


Item Type:Report or Paper (Working Paper)
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http://resolver.caltech.edu/CaltechAUTHORS:20170824-133956964Related ItemPublished Version
Additional Information:Revised version. Original dated to September 1995. This paper is a modified version of chapter 1 of my doctoral dissertation at UC Berkeley. I wish to thank my adviser Bob Anderson and Jeff Ely, Larry Epstein, Itzhak Gilboa, Peter Klibanoff, Piero La Mura, Alessandro Lizzeri, Mark Machina, Tom Marschak, Suzanne Scotchmer, Chris Shannon and Daniele Terlizzese for helpful and stimulating discussion. Eddie Dekel, Edi Kami, Debbie Minehart and patient audiences at a variety of Schools and Conferences provided helpful comments on earlier versions. Finally I am grateful to an Editor and two anonymous referees for comments which greatly helped improve the form and substance of the paper. The usual disclaimer applies. Support from an Alfred P. Sloan Doctoral Dissertation Fellowship is gratefully acknowledged. An earlier version was partially funded by Universita Bocconi. Published as Ghirardato, Paolo. "Coping with ignorance: unforeseen contingencies and non-additive uncertainty." Economic Theory 17, no. 2 (2001): 247-276.
Group:Social Science Working Papers
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Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:Unforeseen contingencies, Underspecified decision problem, Belief functions, Choquet integrals, Pessimism index.
Classification Code:JEL: D81, L22
Record Number:CaltechAUTHORS:20170817-145148657
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170817-145148657
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80577
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:21 Aug 2017 17:03
Last Modified:24 Aug 2017 23:16

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