Utility of Gambling When Events Are Valued: An Application of Inset Entropy∗
نویسنده
چکیده
The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights — a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, this becomes one of several standard utility representations, plus a weighted value function over events, plus an entropy term of the weights. In the finitely additive case, the latter is the Shannon entropy; in all other cases it is entropy of degree not 1. The primary mathematical tool is the theory of inset entropy.
منابع مشابه
SHAPLEY FUNCTION BASED INTERVAL-VALUED INTUITIONISTIC FUZZY VIKOR TECHNIQUE FOR CORRELATIVE MULTI-CRITERIA DECISION MAKING PROBLEMS
Interval-valued intuitionistic fuzzy set (IVIFS) has developed to cope with the uncertainty of imprecise human thinking. In the present communication, new entropy and similarity measures for IVIFSs based on exponential function are presented and compared with the existing measures. Numerical results reveal that the proposed information measures attain the higher association with the existing me...
متن کاملEntropy of a semigroup of maps from a set-valued view
In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...
متن کاملUtility of gambling I: entropy modified linear weighted utility
Behavioral axioms about preference orderings among gambles and their joint receipt lead to numerical representations consisting of a subjective utility term plus a term depending upon the events and the subjective weights. The results here are for uncertain alternatives, in much the same sense as Savage’s usage. Several open problems are described. Results for the risky case are in a second art...
متن کاملExtreme events and entropy: A multiple quantile utility model
This paper introduces a multiple quantile utility model of Cumulative Prospect Theory in an ambiguous setting. We show a representation theorem in which a prospect is valued by a composite value function. The composite value function is able to represent asymmetric attitude on extreme events and a rational prudence on ordinary events.
متن کاملRisk premiums and certainty equivalents of loss-averse newsvendors of bounded utility
Loss-averse behavior makes the newsvendors avoid the losses more than seeking the probable gains as the losses have more psychological impact on the newsvendor than the gains. In economics and decision theory, the classical newsvendor models treat losses and gains equally likely, by disregarding the expected utility when the newsvendor is loss-averse. Moreover, the use of unbounded utility to m...
متن کامل