Subjective Expected Utility with Topological Constraints

35 Pages Posted: 27 Apr 2018

See all articles by Marcus Pivato

Marcus Pivato

THEMA, CY Cergy Paris Université

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 technological constraints on the acts an agent can perform and on the events she can observe. To model this, we assume that the set S of possible states of the world and the set X of possible outcomes each have a topological structure. The only feasible acts are continuous functions from S to X, and the only observable events are regular open subsets of S. We axiomatically characterize Subjective Expected Utility (SEU) representations of conditional preferences over acts, involving a continuous utility function on X (unique up to positive affine transformations), and a unique Borel probability measure on S, along with an auxiliary apparatus called a "liminal structure", which describes the agent’s imperfect perception of events. We also give other SEU representations, which use residual probability charges or compactifications of the state space.

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

JEL Classification: D81

Suggested Citation

Pivato, Marcus and Vergopoulos, Vassili, Subjective Expected Utility with Topological Constraints (April 8, 2018). Available at SSRN: https://ssrn.com/abstract=3157647 or http://dx.doi.org/10.2139/ssrn.3157647

Marcus Pivato (Contact Author)

THEMA, CY Cergy Paris Université ( email )

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

HOME PAGE: http://https://sites.google.com/site/marcuspivato/

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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