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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. We solve for the equilibrium of a location game between the duopolists with an exogenously given price. When the two firms are constrained to locate at the same central spot, we show the nonexistence of pure strategy equilibria, conjecture the existence of mixed strategy equilibria, and show that any such possible equilibria will always yield positive expected profits.
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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.
This chapter discusses the issue of location for production activities. In general, the availability of resources, the location of population as a source of labor and as potential markets, soil, climate, and technical conditions rule out many locations for any specific economic activity. What remains is a set of feasible locations among which an economic choice is to be made. The main problems facing the location theorists can be listed as spatial demand and supply; spatial pricing and output; locational choice; spatial resource (land) use; and spatial equilibrium of production. The chapter discusses the analysis of spatial monopoly. It describes the spatial structure of three different price policies: mill, uniform, and (spatial) discriminatory pricing. The chapter compares these price policies in the context of two firms competing to attract customers, termed as “spatial duopoly.” The strategic interdependence between these firms may generate serious difficulties regarding the existence of a (noncooperative) price equilibrium.. The chapter also deals with the concept of spatial oligopoly in a homogeneous space. |It considers only the mill pricing and compares three solution concepts: Bertrand price equilibrium (competitive oligopoly), Losch price equilibrium (collusive oligopoly), and Cournot quantity equilibrium.
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.
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.
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 introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that are characterized by persistent excess volatility in returns to capital. We explore a quantitative case for theselearning equilibria. We use an evolutionary search algorithm to calibrate a version of the system under learning and show that this system can generate data that matches some features of the time-series data for U.S. stock returns and per-capita consumption. We argue that this finding provides support for the hypothesis that the observed excess volatility of asset returns can be explained by changes in investor expectations against a background of relatively small changes in fundamental factors.
The authors provide a comparison of three spatial price policies: uniform pricing, mill pricing, and spatial price discrimination. Profits, consumer surplus, and social surplus are compared in a duopoly model. Until recently, oligopoly analysis has been stalled because of nonexistence of equilibrium. Through the addition of product heterogeneity (using a logit specification), existence can be restored and price policies compared. In contrast to monopoly analysis, consumer surplus is highest under uniform pricing and lowest under mill pricing. Profit and social surplus follow the opposite ranking. Government regulation to encourage mill pricing may therefore benefit firms to the detriment of consumers. Copyright 1989 by Blackwell Publishing Ltd.
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.
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.
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
. 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...
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