# Subjective expected utility with topological constraints

*Marcus Pivato* () and
*Vassili Vergopoulos*

MPRA Paper from University Library of Munich, Germany

**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 (search for similar items in EconPapers)

**JEL-codes:** D81 (search for similar items in EconPapers)

**Date:** 2018-04-08

**New Economics Papers:** this item is included in nep-mic and nep-upt

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**Persistent link:** https://EconPapers.repec.org/RePEc:pra:mprapa:85749

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