Subjective Expected Utility with Topological Constraints
35 Pages Posted: 27 Apr 2018
Date Written: April 8, 2018
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: Suggested Citation