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Theory and simulations in spatial economics [electronic resource] /
Abstract
Chapter 2 deals with a linear city model ̉la Hotelling where the two firms share linear transport costs with their customers. Mill pricing and uniform delivery pricing are special limiting cases. We characterize the conditions for the existence of a pure strategy equilibrium in the two-stage location-price game. These enable us to identify the causes for non-existence in the two limiting cases. Chapter 3 provides simulations as well as theoretical analysis of potential spatial separation of heterogeneous agents operating on a two-dimensional grid space that represents a city. Heterogeneity refers to a characteristic which is also a determinant of individual valuation of land. We study spatial separation with respect to the distinguishing characteristic and investigate the details of emerging spatial patterns. Simulations suggest that the process of interaction with little trade friction goes through stages which resemble its end-state with high trade friction. Chapter 4 simulations, in addition to some theory, are used to investigate certain aspects of a city formation process. The model assumes two types of economic agents, workers and employers, operating on a two-dimensional grid. The agents have simple preferences, positive for the opposite type and negative for the own type in the own location. In addition, they have positive or negative preference for agglomeration in the own location. The model helps build intuition about a potentially important factor for agglomeration formation, namely, the disparity between entrepreneurial and technical skills in localities. We also determine the minimum level of positive preference for agglomeration that leads to agglomeration formation. System requirements: PC, World Wide Web browser and PDF reader. Available electronically via Internet. Title from electronic submission form. Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 2000. Vita. Abstract. Includes bibliographical references.
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Ex ante homogeneous products may, after the purchase of one of them, be ex post differentiated by switching costs including
learning costs, transaction costs, or “artificial” costs imposed by firms, such as repeat-purchase discounts. The nonco-operative
equilibrium in an oligopoly with switching costs may be the same as the collusive outcome in an otherwise identical market
without switching costs. However, the prospect of future collusive profits leads to vigorous competition for market share
in the early stages of a market's development. The model thus explains the emphasis placed on market share as a goal of corporate
strategy.
The Prisoner's Dilemma has long been considered the paradigm for studying the emergence of cooperation among selfish individuals. Because of its importance, it has been studied through computer experiments as well as in the laboratory and by analytical means. However, there are important differences between the way a system composed of many interacting elements is simulated by a digital machine and the manner in which it behaves when studied in real experiments. In some instances, these disparities can be marked enough so as to cast doubt on the implications of cellular automata-type simulations for the study of cooperation in social systems. In particular, if such a simulation imposes space-time granularity, then its ability to describe the real world may be compromised. Indeed, we show that the results of digital simulations regarding territoriality and cooperation differ greatly when time is discrete as opposed to continuous.
This important study shows that an understanding of product differentiation is crucial to understanding how modern market economies function and that differentiated markets can be analyzed using discrete choice models of consumer behavior.
Product differentiation - in quality, packaging, design, color, and style - has an important impact on consumer choice. It also provides a rich source of data that has been largely unexplored because there has been no generally accepted way to model the information available. This important study shows that an understanding of product differentiation is crucial to understanding how modern market economies function and that differentiated markets can be analyzed using discrete choice models of consumer behavior. It provides a valuable synthesis of existing, often highly technical work in both differentiated markets and discrete choice models and extends this work to establish a coherent theoretical underpinning for research in imperfect competition.The discrete choice approach provides an ideal framework for describing the demands for differentiated products and can be used for studying most product differentiation models in the literature. By introducing extra dimensions of product heterogeneity, the framework also provides richer models of firm location. Discrete Choice Theory of Product Differentiation introduces students and researchers to the field, starting at the beginning and moving through to frontier research. The first four chapters detail the consumer-theoretic foundations underlying choice probability systems (including an overview of the main models used in the psychological theory of choice), while the next four chapters apply the probabilistic choice approach to oligopoly models of product differentiation, product selection, and location choice. The final chapter suggests various extensions of the models presented as well topics for further research.
How do social structures and group behaviors arise from the interaction of individuals? Growing Artificial Societies approaches this question with cutting-edge computer simulation techniques. Fundamental collective behaviors such as group formation, cultural transmission, combat, and trade are seen to "emerge" from the interaction of individual agents following a few simple rules.
In their program, named Sugarscape, Epstein and Axtell begin the development of a "bottom up" social science that is capturing the attention of researchers and commentators alike.
The study is part of the 2050 Project, a joint venture of the Santa Fe Institute, the World Resources Institute, and the Brookings Institution. The project is an international effort to identify conditions for a sustainable global system in the next century and to design policies to help achieve such a system.
Copublished with the Brookings Institution
Bradford Books imprint
The authors show how a common approach that emphasizes the three-way interaction among increasing returns, transportation costs, and the movement of productive factors can be applied to a wide range of issues in urban, regional, and international economics.
Since 1990 there has been a renaissance of theoretical and empirical work on the spatial aspects of the economy—that is, where economic activity occurs and why. Using new tools—in particular, modeling techniques developed to analyze industrial organization, international trade, and economic growth—this "new economic geography" has emerged as one of the most exciting areas of contemporary economics.
The authors show how seemingly disparate models reflect a few basic themes, and in so doing they develop a common "grammar" for discussing a variety of issues. They show how a common approach that emphasizes the three-way interaction among increasing returns, transportation costs, and the movement of productive factors can be applied to a wide range of issues in urban, regional, and international economics. This book is the first to provide a sound and unified explanation of the existence of large economic agglomerations at various spatial scales.
A History of Economic Theory offers a comprehensive account of the builders and building blocks of modern mainstream economics. Jurg Niehans shows how the analytical tools used by economists have evolved from the eighteenth century to the present. Niehans first surveys the development of classical economics from the scholastic and mercantilist traditions to Marx. He then follows the progress of marginalist economics from Thunen to Fischer. In the book's final section, he describes economic theory in the model-building era from Pigou and Keynes to Rational Expectations. Building his story around the economists themselves, Niehans presents a pantheon of economic theory. It includes the famous from Smith and Riccardo to Samuelson and Friedman, as well as detailed discussions of lesser-known figures who have nevertheless made classic contributions. For each theorist Niehans offers a biographical sketch followed by a description, interpretation, and critical assessment of his work. With the current revival of interest in the history of economics, economists will find A History of Economic Theory not only a rich source of information but also a challenging analysis of the dynamics of scientific progress.
This book presents the basic theory of urban land use and city size in a unified framework. The residential location behaviour of households is analyzed in a microeconomic framework, and the equilibrium and optimal patterns of residental land use are examined. In addition, the corresponding equilibrium and optimal city sizes are studied in a variety of contexts. The present book is an outgrowth of a series of lectures given at the University of Pennsylvania over the past several years. Throughout the text, mathematical analyses are accompanied by intuitive explanations and diagrams. My central purpose is to develop the existing theory of urban land use and city size in a manner that is accessible to students. To do so, I have attempted to unify the main results of the theory in terms of the bid rent function approach. The origin of this approach is quite old. Indeed, von Thunen (1826) created his original model of agricultural land use using this approach. But, surprisingly, the approach is closely related to the duality approach of modern microeconomics. Consequently, by employing it, one can develop modern land use theory in a manner that is not only more intuitive but also more rigorous than traditional methods. -from Author
Of the Division of LabourOf the Principle which Gives Occasion to the Division of LabourOf the Natural and Market Price of CommoditiesNote
We show how the spatial duopoly proposed by Launhardt in 1885, where firms have access to different transportation technologies, allows one to model in a simple and elegant way the two major types of product differentiation, i.e. horizontal and vertical. We consider the cases where firms are located near the market end points or near the market center. Launhardt's analysis of price determination is then extended by allowing firms to choose strategically their transportation rates. Subgame perfect Nash equilibria involve minimum (maximum) vertical product differentiation when horizontal product differentiation is large (small) enough.
It is well known that Hotelling's model of spatial competition has no location-price equilibrium in pure strategies. The present paper studies that model where the linear space is replaced by a one-dimensional bounded space without a boundary, i.e. a circle. It is shown that the modified model does have a subgame perfect equilibrium in pure strategies and that the ‘equal distance’ location pattern is an equilibrium.
This paper contains a description of a general class of city formation models. Individual economic agents have preferences for locations that depend upon the population distribution. A location's attractiveness depends upon some combination of its population and its average distance to other agents. Economic variables enter indirectly. Taking this broad perspective leads to a deeper understanding of how cities form as well as of the sensitivity to initial conditions of their locations and sizes. In addition, this class of models supports scenarios where cities emerge: without any assumptions that agents wish to live near or with one another, agents cluster into cities.
Economic theorists traditionally banish discussions of information to footnotes. Serious consideration of costs of communication, imperfect knowledge, and the like would, it is believed, complicate without informing. This paper, which analyzes competitive markets in which the characteristics of the commodities exchanged are not fully known to at least one of the parties to the transaction, suggests that this comforting myth is false. Some of the most important conclusions of economic theory are not robust to considerations of imperfect information.
This paper deals with the evolution of conventions in a finite population of boundedly rational players. We apply methods from the theory of automata networks to analyze the effects of different interaction structures. It is shown that the size of the reference group for each player has an important impact on the evolutionary stability of a particular convention, and that the interaction structure crucially determines the distribution of conventions in the population.
Advancing the state of the art of simulation in the social sciences requires appreciating the unique value of simulation as a third way of doing science, in contrast to both induction and deduction. Simulation can be an effective tool for discovering surprising consequences of simple assumptions. This essay offers advice for doing simulation research, focusing on the programming of a simulation model, analyzing the results sharing the results, and replicating other people's simulations. Finally, suggestions are offered for building of a community of social scientists who do simulation.
A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.
"I have spent my whole professional life as an international economist thinking and writing about economic geography, without being aware of it," begins Paul Krugman in the readable and anecdotal style that has become a hallmark of his writings. Krugman observes that his own shortcomings in ignoring economic geography have been shared by many professional economists, primarily because of the lack of explanatory models. In Geography and Trade he provides a stimulating synthesis of ideas in the literature and describes new models for implementing a study of economic geography that could change the nature of the field. Economic theory usually assumes away distance. Krugman argues that it is time to put it back - that the location of production in space is a key issue both within and between nations.
How do social structures and group behaviors arise from the interaction of individuals? Growing Artificial Societies approaches this question with cutting-edge computer simulation techniques. Fundamental collective behaviors such as group formation, cultural transmission, combat, and trade are seen to "emerge" from the interaction of individual agents following a few simple rules. In their program, named Sugarscape, Epstein and Axtell begin the development of a "bottom up" social science that is capturing the attention of researchers and commentators alike. The study is part of the 2050 Project, a joint venture of the Santa Fe Institute, the World Resources Institute, and the Brookings Institution. The project is an international effort to identify conditions for a sustainable global system in the next century and to design policies to help achieve such a system.
This paper introduces the concept of incentive based asynchronous updating in which the order of updating is determined by incentives. Previously, asynchronous updating has been shown to yield greater stability than synchronous updating for a variety of dynamical systems. However, in those models the order of updating is random. When incentives determine the ordering, the dynamics and end states change. For a conformity model on a two dimensional cellular automata, incentive based asynchronous updating yields greater linear disparity. For the game of life, it results in much greater sensitivity to initial conditions. Citation Copyright 1997 by Kluwer Academic Publishers.
How does social order emerge among autonomous but interdependent agents? The expectation of future interaction may explain cooperation based on rational foresight, but the "shadow of the future" offers little leverage on the problem of social order in "everyday life" -- the habits of association that generate unthinking compliance with social norms. Everyday cooperation emerges not from the shadow of the future but from the lessons of the past. Rule-based evolutionary models are a promising way to formalize this process. These models may provide new insights into emergent social order -- not only prudent reciprocity, but also expressive and ritual self-sacrifice for the welfare of close cultural relatives.
Space allows firms to implement a large variety of price policies, depending on the way transportation costs are passed on to customers. Somewhat surprisingly, the bulk of the work on spatial price theory has been focused on the study of mill pricing (see Gabszewicz and Thisse, 1986, for a recent survey). It is probable that the main reason for this emphasis lies in the close connection between spatial competition with mill prices and the model of product differentiation à la Hotelling-Lancaster (see, for example, Eaton and Lipsey, 1989, for further details).
We study a population of agents, each of whom can be an Altruist or an Egoist. Altruism is a strictly dominated strategy. Agents choose their actions by imitating others who earn high payoffs. Interactions between agents are local, so that each agent affects (and is affected by) only his neighbors. Altruists can survive in such a world if they are grouped together, so that the benefits of altruism are enjoyed primarily by other Altruists, who then earn relatively high payoffs and are imitated. Altruists continue to survive in the presence of mutations that continually introduce Egoists into the population.
A Hotelling-type model of spatial competition is considered, in which two firms compete in uniform delivered prices. First, it is shown that there exists no uniform delivered price–location equilibrium when the product sold by the firms is perfectly homogeneous andwhen consumers buy from the firm quoting the lower delivered price. Second, when the product is heterogeneous and when preferences are identically, independently Weibull-distributed with standard deviation μ, we prove that there exists a single uniform delivered price–location equilibrium iff μ≧1/8 times the transportation rate times the size of the market. In equilibrium, firms are located at the center of the market and charge the same uniform delivered price, which equals their average transportation cost, plus a mark-up of 2μ. Finally, we discuss how our result extends to the case of n firms and proceed to a comparison of equilibria under uniform mill and delivered pricing.
This paper discusses the dynamic implications of learning in a large population coordination game, focusing on the structure of the matching process that describes how players meet. As in M. Kandori, G. Mailath, and R. Rob (1992), experimentation and myopia create 'evolutionary' forces that lead players to coordinate on the risk dominant equilibrium. To describe play with finite time horizons, it is necessary to consider the rates at which the dynamic systems converge. In large populations with uniform matching, play is determined largely by historical factors. When players interact with small sets of neighbors, evolutionary forces may determine the outcome. Copyright 1993 by The Econometric Society.
A partly analytical, partly computational approach is used to study mixed strategy equilibria of Hotelling's model of sp atial competition in which each of two firms chooses a location in a line segment and a price. There is a unique (up to symmetry) subgame perfect equilibrium in which the locations choices are pure. In it, t he locations are close to the quartiles of the market, and the suppor t of the equilibrium mixed-price strategy of each firm is the union o f two short intervals. There is also a subgame perfect equilibrium in which the firms randomize over locations. Copyright 1987 by The Econometric Society.
The purpose of this note is to show that the so-called Principle of Minimum Differentiation, as based on Hotelling's 1929 paper "Stability in Competition," is invalid.
[eng] Transportation costs and monopoly location in presence of regional disparities. . This article aims at analysing the impact of the level of transportation costs on the location choice of a monopolist. We consider two asymmetric regions. The heterogeneity of space lies in both regional incomes and population sizes: the first region is endowed with wide income spreads allocated among few consumers whereas the second one is highly populated however not as wealthy. Among the results, we show that a low transportation costs induces the firm to exploit size effects through locating in the most populated region. Moreover, a small transport cost decrease may induce a net welfare loss, thus allowing for regional development policies which do not rely on inter-regional transportation infrastructures. cost decrease may induce a net welfare loss, thus allowing for regional development policies which do not rely on inter-regional transportation infrastructures. [fre] Cet article d�veloppe une statique comparative de l'impact de diff�rents sc�narios d'investissement (projet d'infrastructure conduisant � une baisse mod�r�e ou � une forte baisse du co�t de transport inter-r�gional) sur le choix de localisation d'une entreprise en situation de monopole, au sein d'un espace int�gr� compos� de deux r�gions aux populations et revenus h�t�rog�nes. La premi�re r�gion, faiblement peupl�e, pr�sente de fortes disparit�s de revenus, tandis que la seconde, plus homog�ne en termes de revenu, repr�sente un march� potentiel plus �tendu. On montre que l'h�t�rog�n�it� des revenus constitue la force dominante du mod�le lorsque le sc�nario d'investissement privil�gi� par les politiques publiques conduit � des gains substantiels du point de vue du co�t de transport entre les deux r�gions. L'effet de richesse, lorsqu'il est associ� � une forte disparit� des revenus, n'incite pas l'entreprise � exploiter son pouvoir de march� au d�triment de la r�gion l
In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. In contrast with the principal-agent models that are extended within, here the presence of ties in the agents' best-response correspondences yields discontinuous payoff functions for the agencies. These discontinuities are dealt with via efficient tie-breaking rules. The main results of this paper are a proof of existence of (mixed-strategies) Nash equilibria in the case of profit-maximizing agencies, and of socially efficient allocations when the firms are risk minimizers. It is also shown that in the particular case of the entropic risk measure, there exists an efficient "fix-mix" tie-breaking rule, in which case firms share the whole market over given proportions.
Examines how Hotelling's result is modified by the relaxation of some of his assumptions relative to: 1) number of firms, 2) shape of the demand curve, and 3) type of space. First pure locational models are considered. Then models with price determination are discussed. Shows that, in many cases, the 'Principle of Minimum Differentiation' as based on the Hotelling paper does not hold.- from Author
We study the location equilibrium in Hotelling's model of spatial competition. As d'Aspremontet al.have shown, with quadratic consumer transportation cost the two sellers will seek to move as far away from each other as possible. We show that the location game possesses an infinity of mixed strategy Nash equilibria. In these equilibria coordination failure invalidates the principle of “maximum differentiation” and firms may even locate at the same point.Journal of Economic LiteratureClassification Numbers: C72, D43, L11.
. I describe some of the issues involved in pricing information goods such as computer software, databases, electronic journals and so on. In particular I discuss the incentives to engage in differential pricing and examine some of the forms such differential pricing may take. This paper was presented at the Research Libraries Group Symposium on "Scholarship in the New Information Environment" held at Harvard Law School, May 2-3, 1995 and will be published in the conference proceedings. Keywords. Pricing, price discrimination, information goods. Address. Department of Economics, University of Michigan, Ann Arbor, MI 48109-1220. E-mail: Hal.Varian@umich.edu Pricing Information Goods Hal R. Varian Digital materials typically have the property that it is very costly to produce the first copy and very cheap to produce subsequent copies. It is often said, for example, that the "first copy costs" are more than 70% of the cost of an academic journal. Cost structures of this form pose spe...
Stability in Competition
- Harold Hotelling
Hotelling, Harold, (1929). "Stability in Competition", Economic
Journal, Vol. 39, 41-57.
Hotelling's Duopoly with Uniform Delivered Pricing
- Amoz Kats
- Jacques-François Thisse
Kats, Amoz, and Jacques-François Thisse, (1991). "Hotelling's
Duopoly with Uniform Delivered Pricing", Working Paper, Department
of Economics, Virginia Polytechnic Institute and State University, April
1991.