Pivato, Marcus and Vergopoulos, Vassili (2018): Subjective expected utility with imperfect perception.
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Abstract
In many decisions under uncertainty, there are constraints on both the available information and the feasible actions. The agent can only make certain observations of the state space, and she cannot make them with perfect accuracy —she has imperfect perception. Likewise, she can only perform acts that transform states continuously into outcomes, and perhaps satisfy other regularity conditions. To incorporate such constraints, we modify the Savage decision model by endowing the state space S and outcome space X with topological structures. We axiomatically characterize a Subjective Expected Utility (SEU) representation of conditional preferences, involving a continuous utility function on X (unique up to positive affine transformations), and a unique probability measure on a Boolean algebra B of regular open subsets of S. We also obtain SEU representations involving a Borel measure on the Stone space of B — a “subjective” state space encoding the agent’s imperfect perception.
Item Type:  MPRA Paper 

Original Title:  Subjective expected utility with imperfect perception 
Language:  English 
Keywords:  Subjective expected utility; topological space; technological feasibility; continuous utility; regular open set; Borel measure. 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  85757 
Depositing User:  Marcus Pivato 
Date Deposited:  11 Apr 2018 13:34 
Last Modified:  03 Oct 2019 05:54 
References:  Aliev, R. A., Huseynov, O. H., 2014. Decision Theory with Imperfect Information. World Scientific Publishing Co., Inc., River Edge, NJ. Aliprantis, C. D., Border, K. C., 2006. Infinite dimensional analysis: A hitchhiker’s guide, 3rd Edition. Springer, Berlin. Arrow, K. J., 1970. Essays in the Theory of RiskBearing. NorthHolland. Caplin, A., Martin, D., 2015. A testable theory of imperfect perception. The Economic Journal 125, 184–202. Epstein, L. G., Zhang, J., 2001. Subjective probabilities on subjectively unambiguous events. Econometrica 69 (2), 265–306. Fremlin, D. H., 2004. Measure theory. Vol. 3: Measure Algebras. Torres Fremlin, Colchester, U.K. Ghirardato, P., August 2002. Revisiting savage in a conditional world. Economic Theory 20 (1), 83–92. Gollier, C., 2001. The Economics of Risk and Time. MIT Press. Hammond, P. J., 1988. Consequentialist foundations for expected utility. Theory and decision 25 (1), 25–78. Hammond, P. J., 1998. Objective expected utility: A consequentialist perspective. In: Barber`a, S., Ham mond, P. J., Seidl, C. (Eds.), Handbook of Utility Theory. Vol. 1. Kluwer, Ch. 5, pp. 143–211. Jaffray, J.Y., Wakker, P., 1993. Decision making with belief functions: Compatibility and incompatibility with the surething principle. Journal of Risk and Uncertainty 7 (3), 255–271. Johnstone, P., 1986. Stone Spaces. Cambridge Studies in Advanced Mathematics. Cambridge University Press. Kopylov, I., 2007. Subjective probabilities on “small” domains. J. Econom. Theory 133 (1), 236–265. Kopylov, I., 2010. Simple axioms for countably additive subjective probability. Journal of Mathematical Economics 46, 867–876. Lipman, B. L., 1999. Decision theory without logical omniscience: toward an axiomatic framework for bounded rationality. Rev. Econom. Stud. 66 (2), 339–361. Mukerji, S., 1997. Understanding the nonadditive probability decision model. Econom. Theory 9 (1), 23–46. Pivato, M., Vergopoulos, V., 2018a. Subjective expected utility with topological constraints. Pivato, M., Vergopoulos, V., 2018b. Contingent plans on topological spaces. Pivato, M., Vergopoulos, V., 2018c. Measure and integration on Boolean algebras of regular open subsets in a topological space. (preprint) Available at http://arxiv.org/abs/1703.02571. Savage, L. J., 1954. The foundations of statistics. John Wiley & Sons, Inc., New York; Chapman & Hill, Ltd., London. Stinchcombe, M. B., 1997. Countably additive subjective probabilities. Rev. Econom. Stud. 64 (1), 125– 146. Wakker, P., 1988. The algebraic versus the topological approach to additive representations. J. Math. Psych. 32 (4), 421–435. Willard, S., 2004. General topology. Dover Publications, Inc., Mineola, NY. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/85757 
Available Versions of this Item

Subjective expected utility representations for Savage preferences on topological spaces. (deposited 09 Mar 2017 09:06)
 Subjective expected utility with imperfect perception. (deposited 11 Apr 2018 13:34) [Currently Displayed]