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Statistical Physics and Economics
This systematic book covers in simple language the physical foundations of evolution equations, stochastic processes and generalized Master equations applied on complex economic systems, helping to understand the large variability of financial markets, trading and communications networks.
Mathematical Location and Land Use Theory
This second edition covers all main topics of spatial economics, plant location, and the theory of nested market areas. The book starts from the classical models of the space economy which are stated in terms of precise mathematical models. Especially, the book offers a lavish supply of computer graphics to make the results easily understandable. Extracts from reviews to the first edition: "This book is an excellent introduction to the theory of continuous location of economic activities in two-dimensional space based on differential equations and to their solution by vector calculus methods. As Puu states "good science is to be easily understood. This book is, indeed, a lucid and easily rea...
Combinatorial Optimization
This book offers an in-depth overview of polyhedral methods and efficient algorithms in combinatorial optimization.These methods form a broad, coherent and powerful kernel in combinatorial optimization, with strong links to discrete mathematics, mathematical programming and computer science. In eight parts, various areas are treated, each starting with an elementary introduction to the area, with short, elegant proofs of the principal results, and each evolving to the more advanced methods and results, with full proofs of some of the deepest theorems in the area. Over 4000 references to further research are given, and historical surveys on the basic subjects are presented.
Operations Research and Economic Theory
Martin Beckmann is going to celebrate his sixtieth birthday. This is almost unbelievable considering the vitality, ingenuity, and activity which he continues to show as he always did. It is an honor able and pleasant duty for the whole economics community to show hirn the respect, gratitude, and affection which he deserves. Thus, those' who have contributed to this festschrift may be thought of as a dele gation from a much larger community in which all of us are joined; the editors in particular feel deeply connected with and enriched by the personality and scientific work of Martin Beckmann. Martin Beckmann is one of those rare scholars who are not narrow minded specialists in one field; he has been active in many areas of economics and operations research which rapidly developed since World War 11, and he has contributed original and fruitful ideas in almost all of them. The variety of topics treated in this volume aims to re flect the impressive width of his scientific interests.
Traffic and Granular Flow ’99
"Are there common phenomena and laws in the dynamic behavior of granular materials, traffic, and socio-economic systems?" The answers given at the international workshop "Traffic and Granular Flow '99" are presented in this volume. From a physical standpoint, all these systems can be treated as (self)-driven many-particle systems with strong fluctuations, showing multistability, phase transitions, non-linear waves, etc. The great interest in these systems is due to several unexpected new discoveries and their practical relevance for solving some fundamental problems of today's societies. This includes intelligent measures for traffic flow optimization and methods from "econophysics" for stabilizing (stock) markets.
Dynamic Preferences, Choice Mechanisms, and Welfare
For most economic aspects of human behaviour, static deci sion models provide an insufficient description. More specifically, they ignore the fact that preferences may change over time and that at each point of time current preferences depend on aspects which are associated with the past or the future. The neglect of these phenomena may lead to results which have little in com mon with real life. Dynamic decision models were developed in order to cope with these complications. Spurred by the availability of new mathematical tools such as optimal control theory and dynamic programming, dynamic utility models mushroomed over the last two decades. Various frameworks were developed featuring dif...
Economic Evolution and Demographic Change
The articles collected in this volume have two features in common: they wantto integrate economics, demography and geography, and they want to overcome the stationary approach in modelling in favour of a dynamic one. The book is subdivided into three parts, where Part I is focussing on economic evolution, Part II on geographical development and Part III is related to demographic change. The present volume aims at providing a new look at this triangle in view of the classical background of discussions by introducing new research ideas focussing in nonlinear dynamics and stochastic modelling. Thus the main purpose of this book is to make a contribution to the interdisciplinary work needed to integrate the effortsbetween these three research fields and to serve as a research source in demonstrating the current state of art in dynamic modelling. The book isaddressed to social scientists in general, and those in particular with a background in economics, geographics and demographics. It should also be of interest to mathematicians, physicists, and systems analysts interested in model building and applications of nonlinear dynamics.
Stochastic Two-Stage Programming
Stochastic Programming offers models and methods for decision problems wheresome of the data are uncertain. These models have features and structural properties which are preferably exploited by SP methods within the solution process. This work contributes to the methodology for two-stagemodels. In these models the objective function is given as an integral, whose integrand depends on a random vector, on its probability measure and on a decision. The main results of this work have been derived with the intention to ease these difficulties: After investigating duality relations for convex optimization problems with supply/demand and prices being treated as parameters, a stability criterion is stated and proves subdifferentiability of the value function. This criterion is employed for proving the existence of bilinear functions, which minorize/majorize the integrand. Additionally, these minorants/majorants support the integrand on generalized barycenters of simplicial faces of specially shaped polytopes and amount to an approach which is denoted barycentric approximation scheme.
Axiomatic Utility Theory under Risk
The first attempts to develop a utility theory for choice situations under risk were undertaken by Cramer (1728) and Bernoulli (1738). Considering the famous St. Petersburg Paradox! - a lottery with an infinite expected monetary value -Bernoulli (1738, p. 209) observed that most people would not spend a significant amount of money to engage in that gamble. To account for this observation, Bernoulli (1738, pp. 199-201) proposed that the expected monetary value has to be replaced by the expected utility ("moral expectation") as the relevant criterion for decision making under risk. However, Bernoulli's 2 argument and particularly his choice of a logarithmic utility function seem to be rather a...
Bargaining in a Video Experiment
Bilateral bargaining situations are of great importance in reality. Traditional microeconomics, however, make cognitive and motivational assumptions of subjects` full rationality that are revealed as being unrealistic by a growing number of experimental investigations. The present book adds an important contribution to the understanding of principles of boundedly rational behavior by directly observing groups of subjects in a decision situation and videotaping their discussions. A very important result of the book is that the behavior of subjects is guided by aspirations regarding the final outcome. The levels of aspirations are influenced by prominence and different forms of the equity principle resulting in several fairness norms as to the allocation of the amount of money to be divided. Another important feature of the book stems from the analysis of break off discussions and enables a motivational explanation of the emergence of breakdowns in bargaining.
