Subjective Expected Utility with Imperfect Perception

48 Pages Posted: 26 Apr 2018

See all articles by Marcus Pivato

Marcus Pivato

THEMA, Université de Cergy-Pontoise

Vassili Vergopoulos

‡Paris School of Economics, and University Paris 1 Panthéon-Sorbonne.

Date Written: April 8, 2018

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.

Keywords: subjective expected utility, imperfect perception, technological feasibility, topological space, continuous utility, regular open set, Borel measure

JEL Classification: D81

Suggested Citation

Pivato, Marcus and Vergopoulos, Vassili, Subjective Expected Utility with Imperfect Perception (April 8, 2018). Available at SSRN: https://ssrn.com/abstract=3157729 or http://dx.doi.org/10.2139/ssrn.3157729

Marcus Pivato (Contact Author)

THEMA, Université de Cergy-Pontoise ( email )

33 Boulevard du Port
Cergy-Pontoise Cedex, Cedex 95011
France

Vassili Vergopoulos

‡Paris School of Economics, and University Paris 1 Panthéon-Sorbonne. ( email )

48 Boulevard Jourdan
Paris, 75014 75014
France

HOME PAGE: http://https://www.parisschoolofeconomics.eu/en/vergopoulos-vassili/

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