Subjective expected utility representations for Savage preferences on topological spaces

Marcus Pivato and Vassili Vergopoulos

MPRA Paper from University Library of Munich, Germany

Abstract: In many decisions under uncertainty, there are technological constraints on both the acts an agent can perform and 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. In this environment, we axiomatically characterize a Subjective Expected Utility (SEU) representation of preferences over acts, 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. With additional topological hypotheses, we obtain a unique Borel probability measure on S, along with an auxiliary apparatus called a liminal structure, which describes the agent’s informational constraints. We also obtain SEU representations involving subjective state spaces, such as the Stone-Čech compactification of S and the Stone space of B.

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: 2017-03-08
New Economics Papers: this item is included in nep-mic and nep-upt
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