expanding demand through price advertisement abstract retail stores frequently advertise prices when consumer search is costly advertising low prices expands the number of consumers who visit and buy we show that this demand enhancement may offset a retailer s loss in margins from the low price making advertisement desirable we further show that a multi product monopolist may choose to advertise low prices only for select products even when advertised and non advertised products are substitutes for duopolist retailers at a common location an equilibrium exists in which for some range of advertising costs one store advertises and the other free rides on its competitor

preferences for environmental quality under uncertainty abstract although the expected effects of environmental policies and interventions are rarely known with certainty stated preference surveys rarely elicit preferences over uncertain environmental outcomes this article presents empirical results challenging the view that ignoring such uncertainty during preference elicitation is of no consequence so long as people only care about final environmental states we show that measured preferences for final environmental states water quality in this case depend on whether people choose between final states or between lotteries over final states in contrast to the typical finding for monetary lotteries we find significant under weighting of low probability events related to water quality

equilibrium in hotelling s model of spatial competition we study hotelling s two stage model of spatial competition in which two firms first simultaneously choose locations in the unit interval then simultaneously choose prices under hotelling s assumptions uniform distribution of consumers travel cost proportional to distance inelastic demand of one unit by each consumer the price setting subgames possess equilibria in pure strategies for only a limited set of location pairs because of this problem pointed out independently by vickrey 1964 and d aspremont et al 1979 hotelling s claim that there is an equilibrium of the two stage game in which the firms locate close to each other is incorrect a result of dasgupta and maskin 1986 guarantees that each price setting subgame has an equilibrium in mixed strategies we first study these mixed strategy equilibria we are unable to provide a complete characterization of them although we show that for a subset of location pairs all equilibria are of a certain type we reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations at each of a large number of location pairs we have computed approximate solutions to the system of equations next we use our analytical results and computations to study the equilibrium location choices of the firms there is a unique up to symmetry subgame perfect equilibrium in which the location choices of the firms are pure in it the firms locate 0 27 from the ends of the market at this equilibrium the support of the subgame equilibrium price strategy is the union of two short intervals most of the probability weight is in the upper interval so that this strategy is reminiscent of occasional sales by the firms we also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations in fact in the class of strategy pairs in which the firms use the same mixed strategy over locations and this strategy is symmetric about 0 5 there is a single equilibrium in this equilibrium most of the probability weight of the common strategy is between 0 2 and 0 4 and between 0 6 and 0 8 there is a wide range of pure nash as opposed to subgame perfect equilibrium location pairs the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close

individual risk attitudes measurement determinants and behavioral consequences this paper studies risk attitudes using a large representative survey and a complementary experiment conducted with a representative subject pool in subjects homes using a question asking people about their willingness to take risks in general we find that gender age height and parental background have an economically significant impact on willingness to take risks the experiment confirms the behavioral validity of this measure using paid lottery choices turning to other questions about risk attitudes in specific contexts we find similar results on the determinants of risk attitudes and also shed light on the deeper question of stability of risk attitudes across contexts we conduct a horse race of the ability of different measures to explain risky behaviors such as holdings stocks occupational choice and smoking the question about risk taking in general generates the best all round predictor of risky behavior

the boundaries of loss aversion abstract in this article the authors propose some psychological principles to describe the boundaries of loss aversion a key idea is that exchange goods that are given up as intended do not exhibit loss aversion for example the authors propose that money given up in purchases is not generally subject to loss aversion the results of several experiments provide preliminary support for the hypotheses the authors find that consistent with prospect theory loss aversion provides a complete account of risk aversion for risks with equal probability to win or lose the authors propose boundaries for this result and suggest further tests of the model

large market asymptotics for differentiated product demand estimators with economic models of supply io economists often estimate demand for differentiated products using data sets with a small number of large markets by modeling demand as depending on a small number of product characteristics one might hope to obtain increasingly precise estimates of demand parameters as the number of products in a single market grows large in this paper i address the question of consistency and asymptotic distributions of iv estimates of demand in a small number of markets as the number of products increases in some commonly used demand models under conditions on economic primitives i show that under the common assumption of a bertrand nash equilibrium in prices product characteristics lose their identifying power as price instruments in the limit in many of these models giving inconsistent estimates in these cases i find that consistent estimates can still be obtained for many of the cases i consider but care must be taken in modeling demand and choosing instruments for cases where consistent estimates can be obtained i provide sufficient conditions for consistency and asymptotic normality of estimates of parameters and counterfactual outcomes a monte carlo study confirms that the asymptotic results provide an accurate description

technical note existence and uniqueness of price equilibria in defender this note provides a formal proof that for the defender model with uniformly distributed tastes the nash price equilibria exist and for a given set of positions that they are unique we also show that the profit function is well behaved continuous and quasi concave and that the maximum occurs on the concave portion of the curve

social networks and new product choice to successfully market new products in a social network it is essential to identify influential individuals whose product recommendations influence the consumption choices of their peers in this study we use spatial econometric methods to determine how individuals revise their preferences for product attributes when exposed to product recommendations from peers and how different individuals who vary in their degree of network connectedness exert influence on the product choices of others we find evidence that consumers look to others for guidance from peers in their preference for subjective taste specific parameters but tend not to respond to peer price choices our spatial methods allow us to empirically determine the influence exerted by individual members on the consumption choices of other members of the social network we find that connected members of the social network are not always the most influential in revising the consumption choices of others our estimates reveal that network proximity explains only 8 8 of influence

efficiency and surplus bounds in cournot competition we derive bounds on the ratios of deadweight loss and consumer surplus to producer surplus under cournot competition to do so we introduce a parameterization of the degree of curvature of market demand using the parallel concepts of concavity and convexity the more concave is demand the larger the share of producer surplus in overall surplus the smaller is consumer surplus relative to producer surplus and the lower the ratio of deadweight loss to producer surplus deadweight loss over total potential surplus is at rst increasing with demand concavity then eventually

the principle of minimum differentiation holds under sufficient heterogeneity the so called principle of minimum differentiation stated by hotelling has been challenged by many authors this paper restores the principle by showing that n firms locate at the center of the market and charge prices higher than the marginal cost of production when heterogeneity in consumers tastes is large enough

a definition of more systematic risk with some welfare implications producers are subject to similar production risks and so their outputs are likely correlated using the entire data set rather than summary statistics we study an ordinal definition of systematic risk for risk neutral producers in perfect competition we trace the effects of an increase in systematic risk through to impacts on welfare measures and production decisions expected welfare falls under more systematic risk but either of expected producer surplus or expected consumer surplus may rise our definition of systematic risk also has relevance for the incentive to incur r d expenditures the benefits of diversity and the gains from risksharing

market segmentation strategies of multiproduct firms we analyze a multiproduct duopoly and ask whether firms should offer general purpose products or tailor their offerings to fit specific consumer needs offering a targeted product has two effects utility increases for some consumers due to increased fit whereas utility decreases for others due to increased misfit previous work has not considered these two effects jointly and has therefore not been able to capture the tradeoff inherent in market segmentation we show that in addition to the degree of fit and misfit the intensity of competition and the fixed cost of offering an additional product determine firms market segmentation strategies extending product lines to target more narrowly defined consumer segments has been a favorite strategy of brand managers for years popular buzzwords like one on one marketing and niche marketing underline its importance in practice in this context we ask to what extent market segmentation is justified from a profitability point of view consider a competitive environment in which each firm can either offer a general purpose product or segment the market by offering products that are tailored to consumers needs while a consumer ceteris paribus prefers a product that is targeted at her own segment she would rather buy a general purpose product than a product that is targeted at another segment segmenting the market therefore has two effects first if a consumer s preferred product is offered she is better off because she is able to buy a product that exactly fits her needs we call this positive aspect of market segmentation fit second if the consumer s preferred product is not offered she is worse off because she ends up with a product that does not satisfy her needs at all this negative aspect of market segmentation is denoted as misfit

testing models with multiple equilibria by quantile methods this paper proposes a method for testing complementarities between explanatory and dependent variables in a large class of economic models the proposed test is based on the monotone comparative statics mcs property of equilibria our main result is that mcs produces testable implications on the small and large quantiles of the dependent variable despite the presence of multiple equilibria the key features of our approach are that i we work with a nonparametric structural model of a continuous dependent variable in which the unobservable is allowed to be correlated with the explanatory variable in a reasonably general way ii we do not require the structural function to be known or estimable iii we remain fairly agnostic on how an equilibrium is selected we illustrate the usefulness of our result for policy evaluation within berry levinsohn and pakes s 1999 model

additional information for comments on alternative models of demand for automobiles by charlotte wojcik abstract in a recent paper in this journal econ lett 68 2000 113 wojcik argues that the nested logit is likely to be superior to demand specifications we and others have used in recent empirical work we review the relevant models and their uses consider her application and find that her conclusions are incorrect

on the analysis of asymmetric first price auctions we provide a new set of tools for studying asymmetric rst price auctions connecting their equilibria to the concavity of the underlying type distributions and showing how one can use surplus expressions related to symmetric auctions to bound equilibrium behavior in asymmetric auctions we apply these tools to studying procurement auctions in which as is common in practice one seller is given an advantage re ecting for example better reliability or quality we show conditions under which for any given rst price handicap auction there is a second price auction with bonuses that outperforms it with most of our results involving ex post dominance

risk aversion and incentive effects new data without order effects holt and laury 2002 used a menu of ordered lottery choices to make inferences about risk aversion under various payment conditions the main results of that paper were a subjects are risk averse even for relatively small payments of less than 5 b risk aversion increases sharply with large increases in the scale of cash payoffs and c there is no significant effect from increasing the scale of hypothetical payment with a few exceptions noted in the paper all treatments began with a low payment choice followed by a choice with hypothetical payments that had been scaled up by 20 50 or 90 followed by a real cash decision with the same high payment scale 20 50 or 90 followed by a single final low 1 real payment choice those in the 90 treatment could earn amounts ranging from 9 00 to 346 50 in this task as glenn w harrison et al 2004 correctly note this design confounds order and treatment effects since the high real payment choice was always completed after the low real and high hypothetical payment tasks in a new experiment reported below we first seek to replicate harrison et al s finding that the order effect participating in a low payment choice before making a high payment choice magnifies the scale effect in a second treatment each subject completes the menu of lottery choices under just one payment condition 1 or 20 real or hypothetical thereby eliminating any order effects i new data

valuation using multiple price list formats we examine the properties of a popular method for elicitation of valuations from experimental subjects the multiple price list format the main advantages of this format are that it is relatively transparent to subjects and provides simple incentives for truthful revelation the main disadvantages are that it only elicits interval responses and could be susceptible to framing effects we consider extensions to address and evaluate these concerns in the context of eliciting willingness to pay for products we find that the multiple price list can elicit relatively precise valuations for products and that those valuations are robust to possible framing effects it therefore offers an attractive procedure for eliciting valuations for goods all data instructions and statistical results are stored in the exlab digital library at http exlab bus ucf edu

a location model with preference for variety we propose a new location model where consumers are allowed to make multiple purchases i e one unit from each firm this model may fit many markets e g newspapers credit cards better than existing models a common feature of these markets is that some consumers are loyal to one brand while others consume more than one product our model yields predictions consistent with this observation if firms are allowed to choose their locations on the interval then spatial differentiation may not be maximal and in some cases it may even be minimal thus under certain conditions we restore hotelling s principle of minimum differentiation

asymmetric equilibria in spatial competition abstract the main purpose of this paper is to study the impact of consumer concentration around the market center on the equilibrium locations of location price games in the case of symmetric triangular density it is shown that no symmetric equilibrium exists however we demonstrate the existence of asymmetric equilibria in pure strategies these equilibria are also characterized our secondary purpose is to study the sequential entry of two firms when the location space is not restricted to the market space this leads us to uncover a substantial first mover advantage which has been neglected in the literature

equilibrium with product differentiation tive consumer formulations is used to examine the properties of single and multiple price equilibria conditions under which decreases in the intensity of consumer preferences reduce price are given it is shown that with certain types of demand curves entry can eliminate price cost markups even given product differentiation if competition is localized it is demonstrated that entry does not affect the markup finally the effect of spurious product differentiation on price is examined

note competitive price and positioning strategies brand positioning and brand pricing are important strategic decisions for marketing managers such decisions are interrelated and depend upon competitive brand positions and prices however any unilateral decisions may encourage repositioning and price adjustment by competitors thus leading to either new market equilibria or a price positioning war this paper examines such price and positioning decisions in a competitive environment by extending the defender consumer model to more complex equilibria we assume that the brands are already in the market and that positions are sticky in the sense that brands cannot leapfrog one another among the insights for such incumbent brands are if prices are symmetric and held constant firms seek to reposition toward the center of the market but price advantages by central firms can mediate that central tendency such that an equilibrium exists with positive profits if brand positions are held constant the nash equilibria for prices exist and are unique and category profits the sum of brand profits are maximized for maximum brand differentiation for two and three brand markets the subgame perfect nash equilibrium where positioning decisions are made with foresight on the price equilibria causes firms to unilaterally seek maximum brand differentiation but for four or more brands greater foresight and or cooperation appears necessary to reach the point of maximum brand differentiation these results apply where the defender consumer model is an exact description of consumer response and where the competitive reaction assumptions hold in any empirical situation such forces might be softened resulting in differentiated but not maximally differentiated brands

the effects of banning advertising in junk food markets we develop a structural model to analyze the eects of banning advertising on market equilibria and welfare in junk food markets we consider the impact on demand and prices and show how to quantify welfare eects when advertising might lead consumers to take decisions that are inconsistent with their underlying preferences we use transaction level data on the potato chips market and nd that banning advertising leads to a direct reduction in demand but also toughens price competition leading to lower prices and increased demand welfare increases as consumers benet from no longer making distorted

learning by doing organizational forgetting and industry dynamics learning by doing and organizational forgetting have been shown to be important in a variety of industrial settings this paper provides a general model of dynamic competition that accounts for these economic fundamentals and shows how they shape industry structure and dynamics previously obtained results regarding the dominance properties of flrms pricing behavior no longer hold in this more general setting we show that forgetting does not simply negate learning rather learning and forgetting are distinct economic forces in particular a model with learning and forgetting can give rise to aggressive pricing behavior market dominance and multiple equilibria whereas a model with learning alone cannot

adaptive learning models of consumer behavior abstract in a model of dynamic duopoly optimal price policies are characterized assuming consumers learn adaptively about the relative quality of the two products a contrast is made between belief based and reinforcement learning under reinforcement learning consumers can become locked into the habit of purchasing inferior goods such lock in permits the existence of multiple history dependent asymmetric steady states in which one firm dominates in contrast belief based learning rules must lead asymptotically to correct beliefs about the relative quality of the two brands and so in this case there is a unique steady state

wildfires in poland the impact of risk preferences and loss aversion on environmental choices abstract this paper examines how risk preferences and loss aversion affect individual choices regarding environmental risks specifically forest wildfires in poland we also examine how the same individuals make choices in the context of financial risks estimating risk loss aversion and weighting probability parameters allows us to directly test whether prospect theory or expected utility theory is the better underlying behavioural model in both domains we find that in a sample consisting of a general population of poles the majority of respondents demonstrate behaviour consistent with prospect theory in both environmental and financial domains this finding has significant implications for future non market valuation studies additionally in this study we find evidence for similar risk preferences across those two domains

differentiating the consumer benefits from labeling of gm food products although recurrent evidence is found that consumers have different willingness to pay for gm and non gm products there is disagreement in the scientific community about the size of consumer benefits from gm labeling in this article we use a theoretical model based on a standard constant elasticity of substitution ces to explain the importance of the quality effect it is shown that failing to consider the quality effect may yield an overestimation of benefits from gm labeling voluntary or mandatory

risk perceptions risk preference and acceptance of risky food consumers risk preferences are often overlooked in studies of consumer demand for risky food we find that risk preferences elicited through context less lottery choices are significantly related to consumers stated preferences for genetically modified gm food these results suggest risk preferences elicited in the laboratory are not artificial in the sense that they appear to be related to the same risk preferences that govern other individual decisions such as food choice consistent with theoretical expectations risk perceptions and risk preferences were found to be significant determinants of acceptance of gm food which has important implications for explaining consumer behavior

personalized pricing and advertising an asymmetric equilibrium analysis we study personalized price competition with costly advertising among n quality cost differentiated firms strategies involve mixing over both prices and whether to advertise in equilibrium only the top two firms advertise earning bertrand like profits welfare losses initially rise then fall with the ad cost with losses due to excessive advertising and sales by the wrong firm when firms are symmetric the symmetric equilibrium yields perverse comparative statics and is unstable our key results apply when demand is elastic when ad costs are heterogeneous and with noise in consumer tastes

exclusive dealing as a barrier to entry evidence from automobiles exclusive dealing contracts between manufacturers and retailers force new entrants to set up their own costly dealer networks to enter the market we ask whether such contracts may act as an entry barrier and provide an empirical analysis of the european car market we first estimate a demand model with product and spatial differentiation and quantify consumers valuations for dealer proximity and dealer exclusivity we then perform policy counterfactuals to assess the profit incentives and possible entry deterring effects of exclusive dealing we find that there are no unilateral incentives to maintain exclusive dealing but there is a collective incentive for the industry as a whole furthermore a ban on exclusive dealing would raise the smaller entrants market share but more importantly consumers would gain not so much because of increased price competition but rather because of the increased spatial availability which compensates for the demand inefficiency from a loss of dealer exclusivity

consumer heterogeneity and strategic quality decisions though recent studies show that quality differentiation is an equilibrium outcome products of similar qualities frequently are observed in the marketplace this inconsistency may be explained by incorporating consumer heterogeneity along unobservable attributes into a model of competition in this paper consumers not only take into account the quality and price of a product but also their heterogeneous tastes along other attributes which are unobservable to firms we investigate the effect of heterogeneity along the unobservable attributes on both quality and price equilibrium in a two stage game framework we show that when consumers are sufficiently heterogeneous along the unobservable attributes the firms offer products of identical qualities in equilibrium under low levels of heterogeneity along the unobservable attributes however our results are consistent with past research which argues for quality differentiation

risk aversion and incentive effects comment charles a holt and susan k laury 2002 develop an experimental design to determine the risk attitude of an individual they use their observations to argue that increased incentives appear to change risk attitudes leading to greater risk aversion popular utility functions that do not allow for such effects are therefore misspecified building on this finding they estimate a flexible utility function that characterizes their aggregate data well but that does not assume constant absolute or relative risk aversion the basic holt and laury 2002 hl design should become an important tool for the interpretation and design of experiments in which risk attitudes could play a role however their most important result showing the effect of scaling up the stakes of the lottery choice task is confounded by a possible order effect an order effect occurs when prior experience with one task affects behavior in a subsequent task the primary methodological contribution of experiments in economics is to enhance control ideally such control makes the explanatory variables of interest in this case scale orthogonal to other explanatory variables such as order allowing clearer inferences about behavior than one could get from field econometric data we argue that not controlling for order effects results in a misspecification of utility functions that is as important as that of scale the subjects in the hl design were given sequences of three or four tasks as shown in table 1 task 1 involved choices over lotteries with a baseline level of prizes which we will refer to as the 1 scale task 2 involved hypothetical choices over prizes with a scaled up level of prizes either 20 50 or 90 task 3 repeated task 2 but with choices that involved real payoffs task 4 was a return to the baseline task with real 1 prizes in some sessions subjects were not given task 2 or task 3 what could one infer from the comparison of measured risk attitudes in the 1 and 20 tasks in hl unfortunately any observed difference could be due either to the scale of the prizes involved or the task order or some combination of both thus the effect of scale is intrinsically confounded with the possible effect of task order this is a logical flaw in their design which

spatial price discrimination with heterogeneous products product heterogeneity is introduced into the context of spatial price discrimination many of the strong properties of the standard homogeneous goods case which are attained as a limit case here are shown to be no longer valid in particular the social optimum is no longer sustainable as a market equilibrium unless products are either identical or else very different

near optimality of second price mechanisms in a class of asymmetric auctions consider a setting with n sellers having i i d costs with log concave density f from cumulative f and a buyer who puts a premiumi on procuring from seller i we show how for any given 1 n a sim ple second price bonus auction can be chosen which comes surprisingly close to giving the auctioneer the same surplus as an optimal mecha nism the bonuses depend only on the magnitude and monotonicity of the slope of virtual costs given f we show that these in turn depend only on fairly coarse information about f we explore how this result generalizes to asymmetrically distributed costs abstract

time to change what to sow risk preferences and technology adoption decisions of cotton farmers in china this paper examines the role of individual risk attitudes in the decision to adopt a new form of agricultural biotechnology in china i conducted a survey and a field experiment to elicit the risk preferences of chinese farmers who faced the decision of whether to adopt genetically modified bt cotton a decade ago in my analysis i expand the measurement of risk preferences beyond expected utility theory to incorporate prospect theory i find that farmers who are more risk averse or more loss averse adopt bt cotton later farmers who overweight small probabilities adopt bt cotton earlier

developments in non expected utility theory the hunt for a descriptive theory of choice under risk this article reviews recent developments in the economic theory of individual decision making under risk since the 1950s it has been known that individual choices violate the standard model of expected utility in predictable ways considerable research effort has now been devoted to the project of developing a superior descriptive model following an overview of non expected utility theories which distinguishes between conventional and non conventional approaches the paper seeks to assess these alternative models in terms of empirical success using laboratory and field data and theoretical usefulness the closing sections reflect on some new directions emerging in this literature

a framework for mapping and comparing behavioural theories in models of social ecological systems formal models are commonly used in natural resource management nrm to study human environment interactions and inform policy making in the majority of applications human behaviour is represented by the rational actor model despite growing empirical evidence of its shortcomings in nrm contexts while the importance of accounting for the complexity of human behaviour is increasingly recognized its integration into formal models remains a major challenge the challenges are multiple i there exist many theories scattered across the social sciences ii most theories cover only a certain aspect of decision making iii they vary in their degree of formalization iv causal mechanisms are often not specified we provide a framework mohub modelling human behavior to facilitate a broader inclusion of theories on human decision making in formal nrm models it serves as a tool and common language to describe compare and communicate alternative theories in doing so we not only enhance understanding of commonalities and differences between theories but take a first step towards tackling the challenges mentioned above this approach may enable modellers to find and formalize relevant theories and be more explicit and inclusive about theories of human decision making in the analysis of social ecological systems

comparative advertising disclosing horizontal match information improved consumer information about horizontal aspects of products of similar quality leads to better consumer matching but also to higher prices so consumer surplus can go up or down while profits rise with enough quality asymmetry though the higher quality and hence larger firm s price falls with more information so both effects benefit consumers this occurs when comparative advertising is used against a large firm by a small one comparative advertising as it imparts more information therefore helps consumers although it also improves the profitability of the small firm overall welfare goes down because of the large loss to the attacked firm

rationalizability learning and equilibrium in games with strategic complementarities we study a rich class of noncooperative games that includes models of oligopoly competition macroeconomic coordination failures arms races bank runs technology adoption and diffusion r d competition pretrial bargaining coordination in teams and many others for all these games the sets of pure strategy nash equilibria correlated equilibria and rationalizable strategies have identical bounds also for a class of models of dynamic adaptive choice behavior that encompasses both best response dynamics and bayesian learning the players choices lie eventually within the same bounds these bounds are shown to vary monotonically with certain exogenous parameters we study the class of noncooperative supermodular games introduced by topkis 1979 and further analyzed by vives 1985 1989 who also pointed out the importance of these games in industrial economics supermodular games are games in which each player s strategy set is partially ordered the marginal returns to increasing one s strategy rise with increases in the competitors strategies so that the game exhibits strategic complementarity 2 and if a player s strategies are multidimensional marginal returns to any one com ponent of the player s strategy rise with increases in the other components this class turns out to encompass many of the most important economic applications of noncooperative game theory in macroeconomics diamond s 1982 search model and bryant s 1983 1984 rational expectations models can be represented as supermodular games in each of these models more activity by some members of the economy raises the returns to increased levels of activity by others in oligopoly theory some models of bertrand oligopoly with differentiated products qualify as supermodu lar games in these games when a firm s competitors raise their prices the marginal profitability of the firm s own price increase rises a similar structure is present in games of new technology adoption such as those of dybvig and spatt 1983 farrell and saloner 1986 and katz and shapiro 1986 when more users hook into a communication system or more manufacturers adopt an interface standard the marginal return to others of doing the same often rises similarly in some specifications of the bank runs model introduced by diamond and dybvig 1983 when more depositors withdraw their funds from a bank it is more worthwhile for other depositors to do the same in the warrant exercise

aggregation and imperfect competition on the existence of equilibrium we present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products the central result provides general conditions under which there exists a pure strategy price equilibrium for any number of firms producing any set of products this includes products with multi dimen sional attributes in addition to the proof of existence we provide conditions for uniqueness our analysis covers location models the characteristics approach and probabilistic choice together in a unified framework to prove existence we employ aggregation theorems due to prekopa 1971 and borell 1975 our companion paper caplin and nalebuff 1991 introduces these theorems and develops the application to super majority voting rules we present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products the central result is that there exists a pure strategy price equilibrium for any number of firms producing any set of products in addition to the proof of existence we provide conditions for uniqueness our model both unites diverse strands of the earlier literature and opens up uncharted areas for future analysis in particular we expand the traditional one dimensional framework to allow for multi dimen sional product differentiation our approach involves twin restrictions on consumer preferences one on individuals preferences the other on the distribution of preferences across society these are generalizations of the restrictions supporting 64 majority rule presented in caplin and nalebuff 1988 to prove existence we apply a new technique of aggregation this technique is valuable in a variety of other problems in the companion paper we use the aggregation result to generalize our earlier work on 64 majority rule and to characterize the relationship between the distribution of human capital and the distribution of income caplin and nalebuff 1991 there are additional applications in statistics and in search theory we begin with a brief review of the early literature on imperfect competition describing in more detail the existence problem and previous solutions section 3 presents our twin assumptions and shows that they cover many standard cases in section 4 we introduce the aggregation theorem and use it in the analysis of demand functions the proof of existence of equilibrium is in section

two stage perfect equilibrium in hotelling s model hotelling i 929 suggests that his spatial competition model can be used to describe a wide range of differentiation problems he points to the selection of product variety within an industry as a potential application most of the subsequent work in his tradition has taken the equivalence of the two problems for granted in this note we look more closely at this equivalence we distinguish between two types of differentiated products according to the variety of preferences assumed with respect to those products building on this distinction we recognize that the demand faced by a firm locating on hotelling s line is analogous to the demand faced by a firm selecting a horizontally differentiated product it should be emphasized thus that the equivalence between the geographical and the product selection problem is by no means general and relies on specific assumptions about consumers preferences next we formulate a small model close to hotelling s one in which firms select a horizontally differentiated product within this model it will be shown that a pure strategy price equilibrium exists for every pair of products this statement is to be contrasted with the results of d aspremont et al i979 who have shown that in the original hotelling s setting an equilibrium fails to exist when firms are too close together 1 in addition we will examine the product selection problem faced by firms in a two stage game in the first stage each firm selects a product in the second stage the firm defines a price for its product we will seek the existence of a perfect equilibrium in this game a perfect equilibrium in this context can be viewed as a nash equilibrium in a game in which firms select a product aware of the non cooperative price equilibrium that will occur for each of their choices it will be shown that contrary to hotelling s principle the two firms will maximise their differentiation i e firms will locate at opposite ends of the market

monopolistic competition in the spirit of chamberlin special results the idea of large group monopolistic competition was first introduced by chamberlin in i 933 although a large literature has developed on this topic since that time it can be argued that few of the models which have been formulated really capture monopolistic competition in chamberlin s sense in a companion paper to this one hart i 983 a model was presented which it was claimed did satisfy the desiderata of large group monopolistic competition specifically the model had the property that i there were many firms producing differentiated commodities 2 each firm was negligible in the sense that it could ignore its impact on and hence reactions from other firms 3 free entry led to zero profit of operating firms but 4 each firm faced a downward sloping demand curve and hence equilibrium price exceeded marginal cost the model of hart i983 was quite general and only such issues as the existence and limiting properties of equilibrium were considered the purpose of the present paper is to analyse a special case of this model in greater detail and to consider in this context the old question of whether too few or too many brands are produced under monopolistic competition before embarking on the analysis however let me briefly indicate why i believe that there is a need for a new model of monopolistic competition further discussion of this may be found in hart i983 in the last few years a sizeable literature has developed on imperfect competition and product differentiation see for example dixit and stiglitz i977 lancaster i979 salop i979 and spence i976 in much of this literature see for example spence i976 markets of fixed finite size are considered where the entry of firms is limited by the existence of set up costs under these conditions only a finite number of firms can operate and hence firms will not be negligible in the sense of 2 in addition due to the integer problem operating firms will generally make strictly positive profits i e 3 is violated models of

competition of firms discriminatory pricing and location1 two costlessly mobile firms are to be located in a market region a subset of the plane the firms compete by setting locations and delivered price schedules to study this competitive stiuation an appropriate extensive form game is defined along with an appropri ate noncooperative solution concept existence and general properties of the equilibrium are demonstrated among the results are each firm increases its profit by locating so as to decrease total cost to both firms of serving the market firms will never locate coinciden tally if they have identical production costs and transport cost rates or if these are different and the firms are located in a circular market region having a uniform demand distribution this paper studies competition between two profit maximizing firms in space who are costlessly mobile and may discriminate in price we will allow the firms to set locations and delivered price schedules and we will be concerned with the existence and properties of equilibria in location and price starting with hotelling 9 the spatial competition literature has focused on location on bounded linear markets by two or more firms hotelling assumed identical firms that produced a single good with constant cost of production and considered consumers to be uniformly distributed and to have inelastic demand he also assumed that the consumers pay transport cost and purchase the good from the cheapest source hotelling claimed that a nash equilibrium in locations for the two firm market existed and yielded back to back locations at the center of the market many authors most recently d aspremont gabszewicz and thisse 2 have noted that an equilbrium in prices and location does not exist for hotelling s model however if the firms employ identical exogeneously specified prices hotelling s conclusions hold subsequent work by smithies 14 hartwick and hartwick 7 and eaton 3 claimed to show that a nash equi librium in f o b prices and locations can exist in markets with a uniform distribu tion of consumers each of whom have identical elastic demand functions for the two and three firm problems the work of d aspremont et al casts doubt on these conclusions without the adoption of restrictive conditions our work contrasts with these works and related research which has dealt with linear markets with uniform distributions of customers and with identical firms our work will involve markets that are subsets of the plane having nonuniform distributions of customers our firms will be allowed to be different that is have differences in production and transport costs however the fundamental difference in our approach is that our firms will set discriminatory prices and not price f o b in many ways our work will represent the discriminatory pricing

bertrand equilibrium in a differentiated duopoly this paper studies the stability of price competition in a horizontally differentiated duopoly the firms demand is derived from a distribution of consumer preferences this description of the consumer sector is applicable to a large class of differentiated commodity markets including spatial competition models the author shows that there is a pure price setting equilibrium when consumer tastes are sufficiently dispersed further conditions on the dispersedness of preferences guarantee uniqueness of the equilibrium in addition the author examines the relation between consumer preferences and the competitiveness and efficiency of the equilibrium outcome copyright 1992 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association