Utility Theory

Utility-Based Learning from Data provides a pedagogical, self-contained discussion of probability estimation methods via a coherent approach from the viewpoint of a decision maker who acts in an uncertain environment.

Cooperative game theory is a branch of (micro-)economics that studies the behavior of self-interested agents in strategic settings where binding agreements among agents are possible. Our aim in this book is to present a survey of work on the computational aspects of cooperative game theory. We begin by formally defining transferable utility games in characteristic function form, and introducing key solution concepts such as the core and the Shapley value. We then discuss two major issues that arise when considering such games from a computational perspective: identifying compact representations for games, and the closely related problem of efficiently computing solution concepts for games. We survey several formalisms for cooperative games that have been proposed in the literature, including, for example, cooperative games defined on networks, as well as general compact representation schemes such as MC-nets and skill games. As a detailed case study, we consider weighted voting games: a widely-used and practically important class of cooperative games that inherently have a natural compact representation. We investigate the complexity of solution concepts for such games, and generalizations of them.

This is an excerpt from the 4-volume dictionary of economics, a reference book which aims to define the subject of economics today. 1300 subject entries in the complete work cover the broad themes of economic theory. This extract concentrates on utility and probability.

This book is devoted to the study of a class of optimal control problems arising in mathematical economics, related to the Robinson–Solow–Srinivasan (RSS) model. It will be useful for researches interested in the turnpike theory, infinite horizon optimal control and their applications, and mathematical economists.

This textbook offers a comprehensive analysis of medical decision making under uncertainty by combining Test Information Theory with Expected Utility Theory. The book shows how the parameters of Bayes’ theorem can be combined with a value function of health states to arrive at informed test and treatment decisions. The authors distinguish between risk-neutral, risk-averse and prudent decision makers and demonstrate the effects of risk preferences on physicians’ decisions. They analyze individual tests, multiple tests and endogenous tests where the test outcome is chosen by the decision maker. Moreover, the topic is examined in the context of health economics by introducing a trade-off between enjoying health and consuming other goods, so that the extent of treatment and thus the potential improvement in the patient’s health becomes endogenous. Finally, non-expected utility models of choice under risk and uncertainty (i.e. ambiguity) are presented. While these models can explain observed test and treatment decisions, they are not suitable for normative analyses aimed at providing guidance on medical decision making.