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One of the most fascinating debates of our times is the discussion over the merits and capabilities of market economies. Very often, one sees strong endorsements to the idea that markets provide an efficient way of allocating resources. Some years ago, opposite views on this issue used to be very popular (at least in Europe) and were held by similarly qualified people. In my opinion, the contribution of economics to this question can not be dismissed on the grounds that economics still in its infancy and that this question is a'practical'one (whatever this means). Economics started with similar naive ideas, two hundred years ago. In particular it has taken a long time to realize that competition does not work in such a smooth way as many classical writers thought it did, and that many facts can not be explained by the theory of perfectly competitive markets. This issue is explored at depth in the Introduction to this Lectures. In this sense the contribution of the Theory of industrial Organization has been to make a convincing case for the view that monopoly and oligopoly can persist in the long run in a world populated by rational agents. Despite of the fact that we are far from having a satisfactory theory of how markets work, progress has been immense, and we certainly understand why current theories are still not completely satisfactory.

The history of many sciences is characterized by an almost continuous emer­ gence of new theories. From a normative point of view, the survival of a new theory should mainly be determined by its ability to explain a new body of facts which the existing theories are unable to explain. If in addition the new theory is able to explain all the results obtained by the existing theories and if it can point out why these theories fail to explain certain facts, it should become the dominant theory. Otherwise, it might coexist with other theories for some time. Hence, a new theory ought to be judged not only by confronting it with existing facts, but also by confronting it with existing theories. The idea that a theory should be able to account for the results ob­ tained by other theories, although implicitly adhered to by many scientists, has rarely been formalized. The statistics literature on parametric hypoth­ esis testing, though, might be seen as an instance of such a formalization.

The subject of the book is an approach to the modeling of and the reasoning under uncertainty. It develops the Dempster-Shafer Theory as a theory of the reliability of reasoning with uncertain arguments. A particular interest of this approach is that it yields a new synthesis and integration of logic and probability theory. The reader will benefit from a new view at uncertainty modeling which extends classical probability theory.

It is probably fair to say that there does not exist a unique and generally accepted not ion of justice. Even if one confines oneself to economic justice one can still get many answers to the question of how justice - henceforth we shall use the term'distributive justice'­ should be defined and characterized. This may be disappointing for the outside observer but one can also view this as achallenge, at least as long as one thinks that distributive justice is an issue economics should be concerned with. Many problems of distributive justice can be described as follows: There is a fixed collection of well-defined objects (usually commodi­ ties) which are quantitatively measurable and perfectly divisible. This collection is to be divided up among a certain number of individuals, the members of society, let's say. According to which principles or rules should this distribution be carried out? Should people be rewarded according to their ability or according to their needs? Should the distribution be such that nobody envies the bundle of any other member of society? Should the collection of entities be distributed in a way that yields the greatest benefi.

My interest in microsimulation started to develop when I was exposed to the works of Guy Orcutt and his associates on microsimulation of households in the USA, and those of Gunnar Eliasson and his associates on simulatio~ of Swedish firms. Their approaches promised the exciting possibility to represent an by simulating the behaviour of individual microeconomic entire economic system units on a computer. The construction of a large scale microsimulation model seemed to be a worthwhile adventure which could yield much more detailed results than existing models. It was also evident that microsimulation of firms is a relatively underdeveloped area, in spite of the large number of operational microsimulation models of households in the USA and Europe. Developing the computer implementation has been an integral part of the research. Translating initially vague ideas into mathematical formulae and subsequently into a structured computer language provides a testing ground for 10Bical consistency of ideas. When writing this book I have purposefully abstained from describing the computer program and dedicated solution algorithms. The reason is that the book is primarily directed towards readers interested in economics and therefore uses the language of economics and not that of computer science. The simulation model has been programmed for the personal computer in Turbo Pascal. Sophisticated memory management techniques have lifted constraints on the number of firms which can be simulated on the PC.

1. 1 Rational Expectations and Learning to Become Rational A characteristic feature of dynamic economic models is that, if future states of the economy are uncertain, the expectations of agents mat­ ter. Producers have to decide today which amount of a good they will produce not knowing what demand will be tomorrow. Consumers have to decide what they spend for consumption today not knowing what prices will prevail tomorrow. Adopting the neo-classical point of view that economic agents are'rational'in the sense that they behave in their own best interest given their expectations about future states of the ecomomy it is usually assumed that agents are Bayesian deci­ sion makers. But, as LUCAS points out, there remains an element of indeterminacy: Unfortunately, the general hypothesis that economic agents are Bayesian decision makers has, in many applications, lit­ tle empirical content: without some way of infering what an agent's subjective view of the future is, this hypothesis is of no help in understanding his behavior. Even psychotic behavior can be (and today, is) understood as'rational', given a sufficiently abnormal view of relevant probabili­ ties. To practice economics, we need some way (short of psychoanalysis, one hopes) of understanding which decision problem agents are solving. (LucAs (1977, p. 15)) 2 CHAPTER 1. INTRODUCTION 1. 1.

Jay Forrester's Economic Dynamics was published in 1971 and The Limits to Growth by Dennis Meadows and his associates appeared a year later. The publication of those two books gave rise to twenty years of intense research into the economics of exhaustible resources, research which everywhere has had a substantial impact both on public debate and on academic curricula. And now, just as that line of research is losing steam, economists are focussing on problems associated with the degradation of the natural environment, problems which call for models which, in their formal structure, are quite similar to those already developed in resource economics. This is therefore an appropriate moment for the appearance of a thorough exposition of the economics of exhaustible resources. For that is what Nguyen Manh Hung and Nguyen Van Quyen have provided. Their splendid new book covers equally well the older Hotelling-inspired theory of cake-eating and the economics of search and R&D designed to uncover new and cheaper sources of supply. It provides an entree to the whole subject of resource economics, as well as many new discoveries which will be of interest to experienced researchers.

We investigate a two-person game of litigation and settlement with incomplete information on one side. So far, various theoretical attempts have been made to answer the question of why some people choose not to resolve their disputes and instead go to court and incur litigation costs, even if bargaining leaves room for both parties to fare better when avoiding the conflict. We can distinguish between games which focus on strategic elements like games with incomplete information (see, for example, P'ng (1983), Samuelson (1982) and Schweizer (1989» and decision-theoretic models neglecting strategic elements (see, for example, Landes (1971) and Gould (1973». The single-person decision theory approach to litigation assumes litigants to have a subjective estimate of the likelihood that the plaintiff will win the action. Differing views on the probability of winning the court case help to explain the fraction of cases that actually go to trial. Among others, P'ng (1983) points out the shortcomings of the single-person decision theory approach which does not take into account, for example, the different fee systems in England and the U.S. and the differences in information conflicting parties may have. P'ng constructs a model of one-sided incomplete information where the settlement terms are given exogenously. Schweizer (1989), on the other hand, extends P'ng's model and allows for two-sided asymmetric information where the settlement terms are determined endogenously.

In auctions, bidders compete with one another in their attempt to 1 purchase the goods that are up for sale • But buyer competition may be reduced or disappear when a ring of colluding bidders is present. The purpose of the participants to a ring is to eliminate buyer competition and to realize a gain over vendors. When all participants are members of the ring, this is done by purchasing the item at the reserve price and splitting the spoils (the difference between the item market value and the reserve price) among the participants.'The term ring apparently derives from the fact that in a settlement sale following the auction, members of the collusive arrangement form a circle or ring to facilitate observation of their trading behavior by the ring leader'(Cassady jr. (1967)). If the coalition members knew other players'values, the problem faced by the ring might be easily solved: the player with the highest value should submit a serious bid and the other members, on the contrary, only phony bids. However, ring participants do not usually know the values of other members. Therefore, ring members have to find out some mechanism which selects the player who has to bid seriously and, eventually, esta­ blish side payments paid to each of the losers2.

The alternating double auction market institution is presented as a discrete time version of the open outcry market. The game in extensive form is analyzed in an almost perfect information setting, using the concept of subgame perfectness. By applying two new equilibrium selection criteria, a general existence result is obtained for'impatience equilibria'of the game. All such equilibria are shown to have unique properties concerning the traded quantities and prices. The most important results are that the equilibrium prices are independent of the number of traders and are always very close to - if not inside - the range of competitive prices. The latter can be evaluated as game theoretic support for the convergence of prices to the competitive price. The process of price formation is traced by applying the learning direction theory and introducing the'anchor price hypothesis'.

and should therefore constitute a part of every area of economic 3 theory. The spectrum covered by information economics today ranges from Stigler's search theory4 to industrial economics, including oligopoly theory, innovation, as well as research and develop­ 5 ment. However, the area information economics is most closely connected with is the theory of optimal contracts, mainly ana­ 6 lyzed in principal-agent models. Contract theory deals primar­ ily with the question of how optimal arrangements (contracts) for the purchase and sale of commodities and services between two or more agents should be structured. In these models, it is often assumed that the parties to the contract are informed differently or asymmetrically about relevant variables (e. g. the health of one party in the case of insurance contracts, or the effort in relation to employment contracts). As a result of this asymmetric in­ formation, phenomena such as moral hazard, adverse selection, signaling, and screening may arise. Frequently, results from con­ tract theory are referred to when making statements about the effects of asymmetric information on an economy. Models of this kind are often used to explain phenomena such as fixed wages or unemployment, among others. 7 However, such conclusions must be treated with caution for two reasons. In the first place, in these models, a contract (explicit or implicit) is determined by the solution of an optimization prob­ lem.

Considerable work has been done on chaotic dynamics in the field of economic growth and dynamic macroeconomic models during the last two decades. This book considers numerous new developments: introduction of infrastructure in growth models, heterogeneity of agents, hysteresis systems, overlapping models with'pay-as-you-go'systems, keynesian approaches with finance considerations, interactions between relaxation cycles and chaotic dynamics, methodological issues, long memory processes and fractals... A volume of contributions which shows the relevance and fruitfulness of non-linear analysis for the explanation of complex dynamics in economic systems.

Environmental Kuznets Curves - one of the most controversial issues of current environmental economics - suggest that economic growth may lead to environmental quality improvements. Why and under which circumstances this may be so, are the questions addressed in this book. The approach taken is formal, using techniques of static and dynamic optimisation. In addition, the main assumptions, arguments and conclusions are also presented in a non-formel way.

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 ferent restrictions on the way agents form preferences in an in­ tertemporal environment. Unfortunately, no systematic reappraisal of this literature ex­ ists. The survey provided in part I of this thesis attempts to fill in this gap. It introduces a comprehensive classification sys­ tem which allows for a coherent organization of all studies of intertemporal choice under certainty and complete information. 2 1. Introduction The latter implies that the individual knows in advance all fu­ ture preferences and choice possibilities. In this survey we show that all dynamic utility models can be viewed as special cases of the class of universal utility mod­ els. It is therefore desirable to investigate intertemporal decision making in terms of this least restrictive framework. Accordingly, all findings of part II of this thesis are derived for the class of universal utility models.

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 arbitrary since they are based entirely on intuitively 3 appealing examples. Not until two centuries later, did von Neumann and Morgenstern (1947) prove that if the preferences of the decision maker satisfy cer­ tain assumptions they can be represented by the expected value of a real-valued utility function defined on the set of consequences. Despite the identical mathematical form of expected utility, the theory of von Neumann and Morgenstern and Bernoulli's approach have, however, IFor comprehensive discussions of this paradox cf. Menger (1934), Samuelson (1960), (1977), Shapley (1977a), Aumann (1977), Jorland (1987), and Zabell (1987). 2Cramer (1728, p. 212), on the other hand, proposed that the utility of an amount of money is given by the square root of this amount.

This thesis was stimulated throughout the time of my participation in a research project on Dynamic Macroeconomics, supported by the German Research Foundation (DFG). The starting point was the central question of how to integrate price setting firms in a dynamic disequilibrium model. Almost all recent literature on imperfect competition in macroeconomics applies the objective demand approach by assuming that firms know the true demand curve they are faced with. While this approach can be ap­ plied in temporary monetary equilibrium models, it proves inadequate for formulating price adjustment in a dynamic disequilibrium model, where it has to be replaced by the concept of subjective demand. Based on this distinction, the thesis starts out with a comparison of the concepts of subjective and objective demand in an abstract framework and surveys the literature on general equilibrium theory with imperfect competition. The objective demand approach is criticized not only on the grounds of its strong rationality requirements and existence problems, but also by the observation that it cannot be applied successfully to characterize determinate rational expectations equilibria in intertemporal macroeco­ nomics. Finally, price setting firms using subjective demand functions are integrated in a dynamic disequilibrium model in order to study mo­ nopolistic and oligopolistic price adjustment.

1. Facts: A leisure term with an unbounded value function, when added to utility in the Lucas (1988)'mechanics of economic development', expands enormously the range of data covered by the theory. To explain this we have to ask two questions. First: why leisure would be so much desired? Perhaps because leisure is one's own time and such a leisure term means an unbounded value of individual freedom. But why leisure is economically productive, as implied by the results obtained in this study? Perhaps because cognitive innovations often occur during the time which in economics is registered as leisure? Then an unbounded leisure term would also make room for an unbounded creation of knowledge, as distinguished from the mere transmission of knowledge in education and training. In any case the leisure term seems to act as if it where the'hole'through which strong nonmaterial values affect economics. The ensuing'extended mechanics'is derived in Chapters 4-6 and proves to involve an extension of growth theory as well as a theory of the causal part of business cycles. Their empirical verification is given by showing (i) that the existence of the two Basic Growth Paths derived from this theory, defining its Growth Type 1 and Growth Type 2, respectively, is verified already by the statistics collected by Solow (1957) but ignored so far (see Chapter 5 of the present study); one of them, viz.

This book describes a series of laboratory experiments (with a total of 167 independent subjects) on forecasting behavior. In all experiments, the time series to be forecasted was generated by an abstract econometric model involving two or three artificial exogenous variables. This designprovides an optimal background for rational expectations and least-squares learning. As expected, these hypotheses do not explain observed forecasting behavior satisfactorily. Some phenomena related to this lack of rationality are studied: Concentration on changes rather than levels,underestimation of changes and overvaluation of volatile exogenous variables. Some learning behavior is observed. Finally, some aspects of individual forecasts such as prominence of'round'number, dispersion, etc.,are studied.

International commodity markets have traditionally attracted the attention of economists, econometricians, and policy makers especially in and following politically tumultuous times. For instance, the primary commodity price boom of 1973/74 and the subsequent period of highly volatile world market prices initiated increased research on commodity markets which quickly focused on possible price stabilization schemes, particularly on buffer stocks. Simultaneously, the issue clearly advanced in priority on the political agenda, such that the United Nations Conference on Trade and Development (UNCTAD) proposed an'Integrated Program for Commodities'(IPC) intended to stabilize the world market prices of ten so-called'core commodities'l (UNCTAD (1974, 1976a), Behrman (1979)). Many developing nations welcomed the IPC almost enthusiastically, but it did not receive more than lukewarm support by major industrialized countries, apparently due to the experience with some thirty international commodity agreements past World War II2. Critical evaluations have, among others, been presented by McNicol (1978), Gordon-Ashworth (1984), and Macbean & Nguyen (1987). The most detailed of these studies is Gordon-Ashworth's, who concludes that'on balance... the performance of international commodity agreements has been too unreliable and their distributive effects too uneven to secure the development goals that have been set'(1984, p. 284)3. Consequently, the IPC turned out to be quite controversial a topic on the UNCTAD's 1976 meeting in Nairobi and has not been able to gain any impetus since. lThese were cocoa, coffee, copper, cotton, jute, rubber, sisal, sugar, tea, and tin.

In the first part of this book bargaining experiments with different economic and ethical frames are investigated. The distributive principles and norms the subjects apply and their justifications for these principles are evaluated. The bargaining processes and the resulting agreements are analyzed. In the second part different bargaining theories are presented and the corresponding solutions are axiomatically characterized. A bargaining concept with goals that depend on economic and ethical features of the bargaining situation is introduced. Observations from the experimental data lead to the ideas for the axiomatic characterization of a bargaining solution with goals.

The structure of a Silverman game can be explained very quickly: Each of two players independently selects a number out of a prede­ termined set, not necessarily the same one for both of them. The higher number wins unless it is at least k times as high as the other one; if this is the case the lower number wins. The game ends in a draw if both numbers are equal. k is a constant greater than 1. The simplicity of the rules stimulates the curiosity of the the­ orist. Admittedly, Silverman games do not seem to have a direct applied significance, but nevertheless much can be learnt from their study. This book succeeds to give an almost complete overview over the structure of optimal strategies and it reveals a surprising wealth of interesting detail. A field like game theory does not only need research on broad questions and fundamental issues, but also specialized work on re­ stricted topics. Even if not many readers are interested in the subject matter, those who are will appreciate this monograph.

This report portrays the results of experimental research on dynamic duopoly markets with demand inertia. Two methods of experimentation are studied: game-playing experiments where subjects interact spontaneously via computer terminals, and computer tournaments between strategies designed by subjects. The principal aim of this study is the understanding of boundedly rational decision making in the dynamic duopoly situation. 1. 1 Motivation The experiments examine a multistage duopoly game where prices in each period are the only decision variables. Sales depend on current prices and also on past sales (demand inertia). Applying the game-theoretic concept of subgame perfect equilibrium, the game is solved by backward induction. The result is a uniquely determined system of decision rules. However, we can hardly expect that human beings behave according to the equilibrium strategy of this game. It is unlikely that subjects are able to compute the equilibrium. And even if a subject is able to compute it, he might not make use of this knowledge. Only if he expects the others to behave according to the equilibrium, it is optimal for him to play the equilibrium strategy. We have evidence from several earlier experimental studies on oligopoly markets that, even in less complex oligopoly situations where the equilibrium solutions are very easy to compute, human behavior often is different from what is prescribed by normative theory.! Normative theory is based on the concept of ideal rationality. However, human capabilities impose cognitive limits on rationality.

This monograph is a treatise on adjustment processes. We consider price adjustment processes in exchange economies and strategy adjustment processes in noncooperative games. In the most simple version of an exchange economy, i.e. a pure exchange economy, there exist markets on which prices are determined by the demand and supply created by a finite number of consumers willing to exchange their initial endowments in order to maximize their utilities. An equilibrium situation is attained if, for some price vector, demand equals supply in all markets. Starting from a situation not being an equi­ librium an adjustment process reaches an equilibrium via adaptations of prices. The advantage of the adjustment processes we will present in this monograph is that they exist and converge under far weaker assumptions than existing processes. The second subject concerns the problem of finding Nash equilibria in noncooperative games. A Nash equilibrium is a situation from which no player can improve his position by unilaterally changing his strategy. We present a new algorithm for finding such equilibria. The sequence of stra­ tegy vectors generated by the algorithm can be interpreted as the path followed by a strategy adjustment process.

As large physical capital stock projects need long periods to be built, a time-to-build specification is incorporated in factor demand models. Time-to-build and adjustment costs dynamics are identified since by the first moving average dynamics, whereas by the latter autoregressive dynamics are induced. Empirical evidence for time-to-build is obtained from data from the Dutch construction industry and by the estimation result from the manufacturing industry of six OECD countries.

Inventory changes constitute in all countries a small fraction of the Gross National Product but also a major source or an indicator of cyclical fluctuations. In this volume both possible ways of propagation are investigated by examining in the first part what macroeconomists have learned and still have to learn about inventories in the light of statistical definitions and problems. In the second part, the role of monetary shocks in propagating business cycles is considered through liquidity effects and in relation to inventory adjustment. A possible linkage between inventory and labor market is shown. Finally, new evidence and theoretical insights are provided on the linear-quadratic inventory model and its ability to discriminate econometrically among competing firm behavior.

Result 1.10 Simple equity standards were superior to more complex ones, even though the latter might be economically more relevant. Result 1.11 Equity based on quantity (input) and return (output) was most successful and received a hit rate of almost i within a range of 10%, i.e., within a distance of ±5% of the predicted share. Result 1.12 A substantial share of observations is consistent with egalitarian considerations. 1.7 Summary The study investigates the predictive power of equity theory and strategic concepts within ultimatum bargaining with advance produc­ tion. This is different from many other experimental studies on non­ cooperative bargaining games, since usually the ressource to be dis­ tributed between the subjects is given by the experimenter. Here, the'pie'is produced via joint production effort. This scenario is more general than bargaining without production, and we think it is more natural as well. The description of the raw data showed that the production choices are considerably dispersed, but nevertheless systematically biased to­ ward the respective player's efficient production level. The distribu­ tions of demanded return shares and demanded surplus shares partly replicated findings of other studies; namely, a low percentage of high demands and a considerable proportion of equal surplus splits. But, they also indicate that'advance production'compared to'no pro­ duction'should be considered an important treatment in studies on ultimatum bargaining.

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.

This manuscript is about the joint dynamics of stock returns and trading volume. It grew out of my attempt to construct an intertemporal asset pricing model with rational agents which can. explain the relation between volume, volatility and persistence of stock return documented in empirical literature. Most part of the manuscript is taken from my thesis. I wish to express my deep appreciation to Peter Kugler and Benedikt Poetscher, my advisors of the thesis, for their invaluable guidance and support. I wish to thank Gerhard Orosel and Gerhard Sorger for their encouraging and helpful discussions. Finally, my thanks go to George Tauchen who has been generous in giving me the benefit of his numerical and computational experience, in providing me with programs and in his encouragement. Contents 1 Introduction 1 7 2 Efficient Stock Markets Equilibrium Models of Asset Pricing 8 2. 1 2. 1. 1 The Martigale Model of Stock Prices 8 2. 1. 2 Lucas'Consumption Based Asset Pricing Model 9 2. 2 Econometric Tests of the Efficient Market Hypothesis 13 2. 2. 1 Autocorrelation Based Tests 14 16 2. 2. 2 Volatility Tests Time-Varying Expected Returns 25 2. 2. 3 3 The Informational Role of Volume 29 3. 1 Standard Grossman-Stiglitz Model 31 3. 2 The No-Trad Result of the BEO Model 34 A Model with Nontradable Asset 37 3. 3 4 Volume and Volatility of Stock Returns 43 4. 1 Empirical and Numerical Results 45 4.

For some seven decades, econometrics has been almost exclusiveley dealing with constructing and applying econometric equation systems, which constitute constraints in econometric optimization models. The second major component, the scalarvalued objective function, has only in recent years attracted more attention and some progress has been made. This book is devoted to theories, models and methods for constructing scalarvalued objective functions for econometric optimization models, to their applications, and to some related topics like historical issues about pioneering contributions by Ragnar Frisch and Jan Tinbergen.

Go to, let us go down, and there confound their language, that they may not understand one another's speech. So the LORD scattered them abroad from thence upon the face of all the earth: and they left off to built the city. (Genesis 11.7-8) 1.1 Static Focal Points 1.1.1 Coordination In real life, people quite often face situations in which they prefer to act in the same way, but they are not particular about the concrete way of acting. Some examples are given below: Credit cards: Buyers want to possess the credit cards potential sellers do accept. Also, sellers wish to have contracted the credit card company the credit cards of which potential customers usually carry along. For both, basically, it is all the same which credit card this is. What matters is that both choices coincide. Communication, information transmission: The transmission of in­ formation requires that the signals used have the same meaning to both the sender and the receiver. But it is inessential which signal has a certain mean­ ing. In verbal communication, this basically means that the people involved use the same (natural) language, though even then some ambiguities remain. Things are a bit more difficult for non-verbal communication, for example data transmission between computers-both sides have to use the same or compatible protocols. Again, what matters is the protocols to be the same for both sides.

I started to deal with genetic algorithms in 1993 when I was working on a project on learning and rational behavior in economic systems. Initially I carried out simulations in an overlapping generations model but soon got dissatisfied with the complete lack of theoretical foundation for the observed behavior. Thus, I started to work on a mathematical representation of the behavior of a simple genetic algorithm in the special setup of an interacting population of economic agents and step by step arrived at the results collected here. However, I believe that much more can and has to be done in this field. I would like to thank Gustav Feichtinger who not only supervised my doctoral thesis but always supported and encouraged me throughout the last few years. Special thanks are also due to K. Hornik, A. Mehlmann and M. Kopel who contributed largely to the work. During the preparation of the monograph I also benefited from helpful comments of A. Geyer-Schulz, G. Rote, G. Tragler and A. Rahman. Special thanks to W. A. Muller from Springer-Verlag for his support. Financial support from the Austrian Science Foundation under contract number P9112-S0Z is gratefully acknowledged.

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.

The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.), and supported by Nihon Keizai Shimbun Inc.. A lot of economic problems can be formulated as constrained optimiza­ tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the­ ories. Although our special emphasis was laid upon'nonlinearity'and'con­ vexity'in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark­ able rapid growth of this discipline during the last decade. The conference was designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who were seeking for effective mathematical weapons for their researches. Thirty invited talks (six of them were plenary talks) given at the conf- ence were roughly classified under the following six headings : 1) Nonlinear Dynamical Systems and Business Fluctuations,. 2) Fixed Point Theory, 3) Convex Analysis and Optimization, 4) Eigenvalue of Positive Operators, 5) Stochastic Analysis and Financial Market, 6) General Equilibrium Analysis.

Most real-life problems involve making decisions to optimally achieve a number of criteria while satisfying some hard or soft constraints. In this book several methods for solving such problems are presented by the leading experts in the area. The book also contains a number of very interesting application papers which demonstrate theoretical modelling, analysing and solution of real-life problems.

This is a book on general equilibrium in which firms are allowed to exhibit increasing returns to scale (more precisely, in which the convexity of production sets is not assumed). As such, it provides a full fledged general equilibrium model and analyzes the chief questions concerning existence and optimality. Increasing returns is a topic which many economists find it to be simultaneously very imponant, very difficult and very discouraging. It is very important because it refers to a well established technological phenomenon which is essentially incompatible with the functioning of competitive markets. It is very difficult because the standard concepts and tools for the analysis fail (in particular, the supply mappings are not well defined). It is very discouraging because the available models do not seem to solve the basic questions: Normative models where nonconvex firms follow marginal pricing do not achieve efficient outcomes, and positive models cannot incorporate monopolistic competition as a way of defming the behavior of those firms with increasing returns to scale. I would like to think that this monograph will contribute to show that'the increasing returns question'is neither too difficult nor too discouraging. Concerning the difficulty, it will be shown that the analysis can be carried out with essentially the same tools as those applicable to the standard competitive model. As for the relevance of the results available, let me point out the following.

As Ken Wallis has pOinted out. all macroeconomic forecasters and policy analysts use economic models. That is. they have a way of going from assumptions about macroeconomic policy and the international environment. to a prediction of the likely future state of the economy. Some people do this in their heads. Increasingly though. forecasting and policy analysis is based on a formal. explicit model. represented by a set of mathematical equations and solved by computer. This provides a framework for handling. in a consistent and systematic manner. the ever-increasing amounts of relevant information. Macroeconometric modelling though. is an inexact science. A manageable model must focus only on the major driving forces in a complex economy made up of millions of households and fIrms. International economic agencies such as the IMF and OECD. and most treasuries and central banks in western countries. use macroeconometric models in their forecasting and policy analysis. Models are also used for teaching and research in universities. as well as for commercial forecasting in the private sector.

Over more than two centuries the developmentofeconomic theory has created a wide array of different concepts, theories, and insights. My recent books, Capital and Knowledge (Zhang, 1999) and A TheoryofInternational Trade (Zhang, 2000) show how separate economic theories such as the Marxian economics, the Keynesian economics, the general equilibrium theory, the neoclassical growth theory, and the neoclassical trade theory can be examined within a single theoretical framework. This book isto further expand the frameworkproposed in the previous studies. This book is a part of my economic theory with endogenous population, capital, knowledge, preferences, sexual division of labor and consumption, institutions, economic structures and exchange values over time and space (Zhang, 1996a). As an extension of the Capital and Knowledge, which is focused on the dynamics of national economies, this book is to construct a theory of urban economies. We are concerned with dynamic relations between division of labor, division ofconsumption and determination of prices structure over space. We examine dynamic interdependence between capital accumulation, knowledge creation and utilization, economicgrowth, price structuresand urban pattern formation under free competition. The theory is constructed on the basisofa few concepts within a compact framework. The comparative advantage of our theory is that in providing rich insights into complex of spatial economies it uses only a few concepts and simplified functional forms and accepts a few assumptions about behavior of consumers, producers, and institutionalstructures.

A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog­ raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so­ phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.

1. 1 Integrating results The empirical study of macroeconomic time series is interesting. It is also difficult and not immediately rewarding. Many statistical and economic issues are involved. The main problems is that these issues are so interrelated that it does not seem sensible to address them one at a time. As soon as one sets about the making of a model of macroeconomic time series one has to choose which problems one will try to tackle oneself and which problems one will leave unresolved or to be solved by others. From a theoretic point of view it can be fruitful to concentrate oneself on only one problem. If one follows this strategy in empirical application one runs a serious risk of making a seemingly interesting model, that is just a corollary of some important mistake in the handling of other problems. Two well known examples of statistical artifacts are the finding of Kuznets'pseudo-waves'of about 20 years in economic activity (Sargent (1979, p. 248)) and the'spurious regression'of macroeconomic time series described in Granger and Newbold (1986, §6. 4). The easiest way to get away with possible mistakes is to admit they may be there in the first place, but that time constraints and unfamiliarity with the solution do not allow the researcher to do something about them. This can be a viable argument.

Think of the following situation: A project yielding a gross profit of 100 is offered to two firms. The project can only be conducted by a cooperation of the two firms. No firm is able to conduct the project alone. In order to receive the project the firms have to agree on the allocation of the gross profit. Each of both firms has an alternative project it conducts in case the joint project is not realized. The profitability of an allocation of the joint gross profit for a firm depends on the gross profit from its alternative project. The gross profit from an alternative project can be either 0 (low alternative value) or O

As a new type of technique, simplicial methods have yielded extremely important contributions toward solutions of a system of nonlinear equations. Theoretical investigations and numerical tests have shown that the performance of simplicial methods depends critically on the triangulations underlying them. This monograph describes some recent developments in triangulations and simplicial methods. It includes the D1-triangulation and its applications to simplicial methods. As a result, efficiency of simplicial methods has been improved significantly. Thus more effective simplicial methods have been developed.

Economic theory of the last fifty years has been dominated by the paradigm of General Equilibrium Theory, based on the scientific work of Walras-Pareto-Cassel-Wald-Hicks-Arrow-De­ breu-McKenzie. Some of its grounding assumptions are: all prices are fully flexible; an auctioneer appropriately manipulates all prices according to the law of supply and demand; every con­ sumer has only one budget constraint; all agents are perfectly informed; no actions are taken by agents before a vector of prices has been found such that all markets clear. Indeed, when all markets clear every agent can implement her/his chosen (opti­ mal) action and nobody is urged to change his/her decisions. Under these assumptions it is generally said that in a (one pe­ riod, competitive) general equilibrium model there is no place for money. The present monograph takes general equilibrium as the ba­ sis on which to build the model presented. But its first aim is to completely dispense with the Walrasian auctioneer by giving firms the task of choosing their output price~ period after period.

Planning in a general sense is concerned with the design of communication and decision making mechanisms in organizations where information and choice are decentralized. Non-cooperative planning theory as it is developed in this book treats the incentive aspects hereof. It stresses how strategic behavior and opportunism may impede planning, and how this can be coped with via the organization of communication and decision making, the design of information and control systems, and the development of incentive schemes. In particular, the book contains a thorough investigation of incentive provision in information production.

For several decades, scholars have developed methods for solving optimization problems which emerge in economics, econometrics, operations research, and other disciplines. A considerable effort has been made to construct equations from which constraints can be derived, but surprisingly little has been done to construct the other part of optimization models: the scalar-valued objective function, the constrained maximum or minimum of which gives the optimal solution. The given volume is intended to attract attention to the problem, to present the major achievements in the field and to stimulate further research and teaching.

This book is on applications of game theory. The title of this book is not'Game Theory and its Applications'because it does not construct a general theory for considered games. The book contains a lot of examples of applica­ tion of game theory together with the background of those games considered and a list of unsolved problems. Also we consider only the game where the optimal strategies of the players are found in closed form. This book is an attempt to carryon the approach developed in nice books'Search Games'by Gal and'Geometric Games and their Applications'by Ruckle. The first chapter of this book supplies the required definitions and theorems from game theory. The second chapter deals with discrete search games where both players act simultaneously: the games of protection of a channel from infiltration of a submarine, the submarine versus helicopter game, the matrix search games and others. The third chapter considers the game where the players allocate their contin­ uousefforts. In these games players face up an alternative either not to come into contest if the cost of efforts seems too high, or come into it. In the last case the player have to decide how much resources they can afford to spend. The allocation models of search, antiballistic protection and marketing are investigated.