This article addresses the value of information that affects the ambiguity faced by a decision maker. Our analysis is applied to the case of a farmer whose production can be damaged by a pest attack with unknown probability, this damage being reduced if the farmer decides to use a pesticide. Early warning systems have precisely been implemented in many countries to help farmers avoid inappropriate decisions in terms of pesticide use. We investigate, both theoretically and experimentally, how farmers value these (...) systems. We propose a two-state self-insurance model in which an α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-MaxMin Expected Utility farmer may use pesticides that reduce the loss in the accident state while incurring a cost in both states. Her decision to self-insure or not depends on risk and ambiguity attitudes. We compile and compare the value of two types of information leading to a reduction of ambiguity and analyze their properties with respect to ambiguity attitude. Both types of information are valued positively if the farmer is ambiguity averse. We conduct a framed field experiment in which farmers and agricultural students have to decide whether or not to apply pesticides depending on risk, ambiguity and the associated monetary gains resulting from pesticide cost. The experimental findings support the theory. The average value of information among all participants is between €0.9/ha and €3.3/ha depending on the information gain. (shrink)

This note completes the main result of Zimper, by showing that additional conditions are needed in order the law of iterated expectations to hold true for Choquet decision makers. Due to the comonotonic additivity of Choquet expectations, the equation E[f, ν] = E[E[f, ν], ν], is valid only when the act f is comonotonic with its dynamic form, that we name “conditional certainty equivalent act”.

This paper studies decisions under ambiguity when attention is paid to extreme outcomes. In a purely subjective framework, we propose an axiomatic characterization of affine capacities, which are Choquet capacities consisting in an affine transformation of a subjective probability. Our main axiom restricts the well-known Savage’s Sure-Thing Principle to a change in a common intermediate outcome. The representation result is then an affine combination of the expected utility of the valued act and its maximal and minimal utilities.