State‑Dependent Utility and Stochastic Probability Weights

[g charles]

Dear All:

Please find attached an attempt at extending Machina's (1982) preference functional, and some proposed applications. All comments are welcome.

Best wishes,

G

Short title: State‑Dependent Utility and Stochastic Probability Weights

Abstract:

This paper extends Machina’s local expected utility model to an infinite‑dimensional setting using abstract Wiener space. The framework separates two forces often conflated in behavioral models: local utility curvature and stochastic subjective probability weights. Because these weights arise from Wiener integrals, they need not be nonnegative or additive without normalization—linking state‑dependent utility, nonlinear beliefs, and probability weighting within a single structure. The model nests SEU, RDU, and CPT as special cases, while allowing utility and decision weights to vary with the underlying state. This state dependence implies that stochastic choice and even transitivity failures can arise probabilistically, not just deterministically.

Bottom line: Many departures from expected utility can be understood as fluctuations in state‑dependent weights rather than wholesale violations of rationality.

[g charles]

Typo on slide #20 corrected in the attached. Some terms were hitherto undefined!