Utility Theory

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.

This work, now in a thoroughly revised second edition, presents the economic foundations of financial markets theory from a mathematically rigorous standpoint and offers a self-contained critical discussion based on empirical results. It is the only textbook on the subject to include more than two hundred exercises, with detailed solutions to selected exercises.

This work, now in a thoroughly revised second edition, presents the economic foundations of financial markets theory from a mathematically rigorous standpoint and offers a self-contained critical discussion based on empirical results. It is the only textbook on the subject to include more than two hundred exercises, with detailed solutions to selected exercises.

This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book concludes with a problem section. Hints, answers and solutions are included.