Activity analysis is extended into consumption theory. It is assumed that goods possess, or give rise to, multiple characteristics in fixed proportions and that it is these characteristics, not goods themselves, on which the consumer’s preferences are exercised.

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A New Approach to Consumer Theory

The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Digraphs Theory Algorithms And Applications

Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In this survey, we present an overview of the many brands of deterministic dynamical systems motivated by evolutionary game theory, including ordinary differential equations (and, in particular, the replicator equation), differential inclusions (the best response dynamics), difference equations (as, for instance, fictitious play) and reaction-diffusion systems. A recurrent theme (the so-called `folk theorem of evolutionary game theory') is the close connection of the dynamical approach with the Nash equilibrium, but we show that a static, equilibrium-based viewpoint is, on principle, unable to always account for the long-term behaviour of players adjusting their behaviour to maximise their payoff.

https://www.ams.org/bull/2003-40-04/S0273-0979-03-00988-1/S0273-0979-03-00988-1.pdf

Evolutionary Game Dynamics

This is a review of the Health Utilities Index (HUI®) multi-attribute health-status classification systems, and single- and multi-attribute utility scoring systems. HUI refers to both HUI Mark 2 (HUI2) and HUI Mark 3 (HUI3) instruments. The classification systems provide compact but comprehensive frameworks within which to describe health status. The multi-attribute utility functions provide all the information required to calculate single-summary scores of health-related quality of life (HRQL) for each health state defined by the classification systems. The use of HUI in clinical studies for a wide variety of conditions in a large number of countries is illustrated. HUI provides comprehensive, reliable, responsive and valid measures of health status and HRQL for subjects in clinical studies. Utility scores of overall HRQL for patients are also used in cost-utility and cost-effectiveness analyses. Population norm data are available from numerous large general population surveys. The widespread use of HUI facilitates the interpretation of results and permits comparisons of disease and treatment outcomes, and comparisons of long-term sequelae at the local, national and international levels.

/pdf/the-health-utilities-index-hui-concepts-measurement-4xxo4rb56w.pdf

The Health Utilities Index (HUI®): concepts, measurement properties and applications

Recent work on the fundamental processes of regulation in biology (Ashby, 1956) has shown the importance of a certain quantitative relation called the law of requisite variety. After this relation had been found, we appreciated that it was related to a theorem in a world far removed from the biological—that of Shannon on the quantity of noise or error that could be removed through a correction-channel (Shannon and Weaver, 1949; theorem 10). In this paper I propose to show the relationship between the two theorems, and to indicate something of their implications for regulation, in the cybernetic sense, when the system to be regulated is extremely complex.

http://pespmc1.vub.ac.be/Books/AshbyReqVar.pdf

C. A. B. Smith

Papers

Theory of Games and Economic Behaviour. By John Von Neumann and Oskar Morgenstern. Pp. xviii, 625. 66s. 6d. 1944. (Princeton U.P.; Humphrey Milford)