buyer search costs and endogenous product design buyer search costs for price are changing in many markets through a model of buyer and seller behavior i consider the effects of changing search costs on prices both when product differentiation is fixed and when it is endogenously determined in equilibrium if firms cannot change product design lower buyer search costs for price lead to increased price competition however if product design is a decision variable lower search costs for price may also lead to higher product differentiation which decreases price competition in this case the overall effect of lower buyer search costs for price may even be higher prices lower social welfare and higher industry profits the result is especially interesting because recent technological changes such as internet shopping can affect the market structure through lowering buyer search costs

the strategic implications of scale in choice based conjoint analysis choice based conjoint cbc studies have begun to rely on simulators to forecast equilibrium prices for pricing strategic product positioning and patent copyright valuations whereas cbc research

chapter 4 competitive marketing strategies game theoretic models publisher summary this chapter reviews the key developments in the understanding of competitive marketing strategies product price advertising and distribution competition are all addressed while the emphasis is on models the chapter surveys the empirical literature as well there is a significant amount of empirical work to report but the ratio of theoretical to empirical work is nevertheless unpleasantly large much progress has been made in the last ten years or so in the study of competitive marketing strategies most of this chapter has been theoretical using simple models of firm and consumer behavior these models serve the function of demonstrating rigorously the existence of certain effects factors which need to be considered in analyzing real world competition

british bus deregulation competition and demand coordination abstract our framework formally explains some of the recent curious events surrounding deregulation of the british local bus industry the winner takes all nature of this market induces competitive providers to engage in predatory or preemptive behavior in scheduling and pricing unlike previous works we explicitly model consumers responses to firms schedule announcements we show that the market is unstable if demand is uncoordinated but stable otherwise our results highlight the important role played by demand coordinating mechanisms in local bus markets and our results suggest that pure strategy nash equilibria exist in models a la hotelling 1929 whenever demand is effectively coordinated

coalition building in a spatial economy abstract we analyze the possibility and consequences of coalition formation among suppliers of retail services we first provide a framework in which producers of substitutes have an incentive to cluster in marketplaces to attract consumers dispersed in space owing to spatial externalities the resulting spatial equilibrium can be welfare suboptimal we characterize regimes in which we find too little and those in which there is too much agglomeration of firms we analyze the role of coalitions of firms e g initiated by a land developer in this framework and show that such coalitions can overcome the suboptimality of the decentralized spatial allocation

boundedly rational nash equilibrium a probabilistic choice approach we propose an equilibrium for n person finite games based on bounded rationality using the legit model of discrete choice theory at equilibrium each player uses appropriate choice probabilities given those used by the others rationality is parameterized on a continuum from complete rationality to uniform random choice results on the existence of equilibrium and on convergence to nash as rationality becomes perfect are similar to results due to mckelvey and palfrey we identify conditions such that for a given rationality parameter range the path of choices over time when the players use fictitious play converges to equilibrium c 1997 academic press

information gatekeepers on the internet and the competitiveness of homogeneous product markets we examine the equilibrium interaction between a market for price information controlled by a gatekeeper and the homogenous product market it serves the gatekeeper charges fees to firms that advertise prices on its internet site and to consumers who access the list of advertised prices gatekeeper profits are maximized in an equilibrium where a the product market exhibits price dispersion b access fees are sufficiently low that all consumers subscribe c advertising fees exceed socially optimal levels thus inducing partial firm participation and d advertised prices are below unadvertised prices introducing the market for information has ambiguous social welfare effects

firm mobility and location equilibrium two types of location equilibria are compared the first one is that of a simultaneous price and location game the second is that of a two stage location then price game it is suggested that equilibrium locations are further apart under the second and profits are higher since firms internalize the harmful price competition effect of moving close to each other the paper introduces a nonpurchase option into the logit model of spatial competition and the sensitivity of the equilibrium is analyzed

long run competition in capacity short run competition in price and the cournot model in this article we investigate the nature of equilibrium in markets in which firms choose the scale of operation before they make pricing decisions we analyze a duopoly model in which firms choose their capacities before engaging in bertrand like price competition we demonstrate that the cournot outcome is unlikely to emerge in such markets and that the equilibrium tends to be more competitive than the cournot model would predict in addition our results indicate a tendency toward asymmetric firm sizes and price dispersion that results from the mixed strategies firms use in equilibrium

endogenous quality differentiation in congested markets firms selling a product with congestion externalities to a heterogeneous population of customers have an incentive to offer differentiated levels of quality in a price competitive market differentiation arises endogenously through the prices chosen by firms in equilibrium firms offer a range of prices which induce an efficiency improving range of quality levels and allow customers to self select their preferred price quality combinations additional results suggest that with many firms in the market the choice of prices dominates the choice of service capacities in determining congestion levels copyright 1991 by blackwell publishing ltd

price matching policy and the principle of minimum differentiation this paper shows that if duopolists are allowed to choose their product locations a price matching policy and their prices sequentially and independently both tacit collusion and minimum differentiation occur copyright 1995 by blackwell publishing ltd

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

an analysis of cost reduction innovation under capacity constrained inputs abstractthis article focuses on duopoly cost reduction innovation with the upstream input subjected to capacity constraints by two stage duopoly model some interesting conclusions are achieved f

costly search capacity constraints and bertrand equilibrium price dispersion this article analyzes the impact of transaction search costs and capacity constraints in an almost competitive market with homogeneous firms that compete on price we characterize conditions under which nash equilibria with price dispersion exist in equilibrium firms play pure strategies in prices and consumers adopt a symmetric mixed search strategy price dispersion is possible even though consumers all have the same search cost and valuation for the item and prices charged by all firms are common knowledge

existence and computation of mixed strategy nash equilibrium for 3 firms location problem location problems of firms on a closed interval were introduced by hotelling 3 and later investigated by eaton lipsey 2 firms sell a homogeneous product at a fixed price customers distributed along the interval buy one unit each from the firm nearest to them and firms aim to maximize the number of their customers it is well known that where the customers are evenly distributed along the interval and the number of firms is other than 3 the location problem has a pure strategy nash equilibrium see 2 the case of 3 firms is peculiar in that no pure strategy nash equilibrium exists for in any situation one of the extreme firms not located between the other two can increase its revenue by either moving towards or away from the other two firms the existence of mixed strategies is not obvious because the payoff functions are discontinuous whenever two or more firms are located at the same point in a recent paper dasgupta and maskin 1 investigate a class of games all derived from economic problems and all with some discontinuities in their payoff functions they demonstrate that the discontinuities in the payoff functions do not prevent the existence of mixed strategies nash equilibria in the games investigated in particular location problems of the type described earlier have such weak discontinuities and hence possess a mixed strategy nash equilibrium although their proof is constructive offering a method of approaching these equilibria as a limit of equilibria of finite games the equations involved very quickly become unmanageable in this note we compute a mixed strategy nash equilibrium for the 3 firms location problem let the customers be evenly distributed along 0 1 then a mixed strategy is a probability measure over 0 1 the symmetry of the problem suggests that the solution will be doubly symmetric in that all firms choose the same mixed strategy and that this strategy is symmetric around symmetric locations are given the same probabilities dasgupta and maskin confine their analysis to doubly symmetric solutions and prove that the strategies in any doubly symmetric equilibrium are atomless given the symmetric nature of the game and following the analysis of dasgupta and maskin we shall confine ourselves here to such doubly sym

a strategic analysis of flexible manufacturing systems abstract in this paper a game theoretic model is presented by which investment in flexible manufacturing systems fms is analyzed if the investment in this innovative production system is viable due to either revenue enhancements or cost reductions the result is a competition for the first move among similar firms in an oligopolistic industry as a result the schumpeterian hypothesis of investment in a technological innovation occuring within an industry by swarms appears to apply to fms diffusion empirical evidence supporting the results of the theoretical analysis is presented

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

hotelling s spatial competition as a model of sales abstract hotelling s spatial competition model is used to explain the existence of sales it is shown that 1 an equilibrium in randomized strategies exists when a pure strategy equilibrium fails to exist 2 with more dissimilarity among brands prices are chosen from a wider interval

product differentiation under congestion hotelling was right i introduction nobody goes there anymore it s too crowded attributed to yogi berra in the seminal hotelling 1929 model of spatial competition two firms compete to sell a product in stage 1 they locate along a unit line in stage 2 they set their prices consumers spread evenly along the line choose the best deal based on the posted price and linear transportation costs hotelling apparently solved for the stage 2 equilibrium in pure strategy prices and via backward induction showed that regardless of location either firm would increase its profits by moving closer to its competitor see figure 1 first line this gave rise to the principle of minimum differentiation the tendency of competing firms to make similar choices in geographical or product characteristic dimensions d aspremont gabszewicz and thisse 1979 critiqued this principle s validity within the hotelling model they showed that no pure strategy pricing equilibrium exists when the firms are sufficiently close together but not at the same location this is because for firms at close quarters the temptation is strong for one firm to cut its price just enough to steal the entire mass of customers located on the other side of its competitor in fact if locations are symmetric the hotelling pricing equilibrium exists only if firms locate in the outer quartiles thus hotelling s backward induction breaks down and there is no guarantee that firms located in the inner quartiles would want to move closer to each other see figure 1 second line at this point the literature diverges much of the literature follows d aspremont gabszewicz and thisse 1979 who introduce quadratic transportation costs and show that they provide greater tractability 1 with quadratic costs the differentiation result is reversed firms maximally differentiate in equilibrium 2 figure 1 omitted osborne and pitchik 1987 continue with hotelling s linear transportation costs despite the tractability challenges they characterize a mixed strategy pricing equilibrium when firms are located close to each other in the symmetric subgame perfect equilibrium with pure location choices that they compute both firms locate at the edges of the inner quartiles 0 24 of the distance from the midpoint see figure 1 third line thus substantial near efficient differentiation remains in equilibrium evidently firms incentives are to move farther apart over much of the region where hotelling s pricing equilibrium fails to exist this paper also retains linear transportation costs and adds one feature to the model negative network externalities specifically consumers are assumed to derive disutility in proportion to the number of customers of the firm they patronize this negative externality can be interpreted as congestion arising from firm capacity constraints queuing for parking customer service or to pay 3 in many cases the more crowded a store or restaurant the less attractive it is to patronize all else equal it can also be interpreted as a specific kind of snobbery which we term brand snobbery preferring the brand less consumed 4 we find that the greater are congestion costs relative to transportation costs the more of hotelling s line contains a hotelling like pure strategy pricing equilibrium the centered interval where the equilibrium does not exist for symmetrically located firms shrinks as congestion costs grow in importance and in the limit vanishes that is the hotelling pricing equilibrium can be supported at any location where the firms are located on opposite sides of the midpoint given sufficiently high congestion costs relative to transportation costs this result has implications for product differentiation in essence congestion costs extend the portion of the line over which hotelling logic applies that is over which firms can increase profits by moving closer to each other

competition of newspapers and the location of political parties in this paper we suggest a model for an analysis of how newspapers and political parties determine their ideological orientation and how both decisions depend on each other quite naturally dissemination of information plays an important role the model is set up as a two stage game because elements of horizontal as well as vertical product differentiation are present in this model location patterns in ideology space exhibit in general neither maximal nor minimal differentiation although we keep quite close to the downs model with information as the most important distinguishing feature furthermore the model shows by way of example that economic theory can be a useful tool to investigate issues which are central to communication science

balanced budget redistribution as the outcome of political competition this paper models balanced budget redistribution between socio economic groups as the outcome of electoral competition between two political parties equilibrium is unique in the present model and a sufficient condition for existence is given requiring that there be enough stochastic heterogeneity with respect to party preferences in the electorate the validity of hotelling s principle of minimum differentiation and of director s law are examined under alternative hypotheses concerning administrative costs of redistributions and voter s possibilities both of abstaining from voting and of becoming campaign activists for one of the parties the policy strategy of expected plurality maximization is contrasted with the strategy of maximizing the probability of gaining a plurality incomes are fixed and known so lump sum taxation is feasible however constraints on tax transfer differentiation between individuals are permitted in the analysis

spatial price and variety competition in an urban retail market abstract we develop a nested logit model of spatial competition in retail markets consumers choose stores on the basis of price variety and transport cost three games are considered a price game a variety game and a combined price and variety game the videocassette rental market in edmonton alberta is used for illustration centrally located stores set lower prices and higher varieties than stores on the market periphery prices in the price and price variety games are nearly identical despite large differences in varieties similarly equilibrium varieties in the price variety game are similar to varieties in the variety game

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

product and price competition in a two dimensional vertical differentiation model in this paper the one dimensional vertical differentiation model shaked and sutton shaked a j sutton 1982 relaxing price competition through product differentiation rev econom stud 49 3 13 moorthy moorthy k s 1988 product and price competition in a duopoly marketing sci 7spring 141 168 is extended to two dimensions and an analysis of product and price competition is presented a two stage game theoretic analysis in which two firms compete first on product positions and then on price is conducted closed form equilibrium solutions are obtained for each stage in which competitors are unrestricted in their choices of price or product positions a significant finding of this research is that unlike the one dimensional vertical differentiation model firms do not tend towards maximum differentiation although this solution is possible under certain conditions when the range of positioning options on each of the dimensions is equal maxmin product differentiation occurs that is in equilibrium the two firms tend to choose positions which will represent maximum differentiation on one dimension and minimum differentiation on the other dimension

bertrand equilibrium with capacity constraints and restricted mobility this paper considers price competition among firms when there are capacity constraints and buyers have limited ability to visit firms a natural method of allocating buyers among firms arises in the equilibrium of the buyers search game sufficient conditions are given under which the buyers equilibrium varies continuously with the prices charged by firms capacity constraints are used to guarantee that this ensures existence of mixed strategy equilibria for the pricing game played by sellers we show that natural pure strategy equilibria arise when the game is made large in appropriate ways since bertrand s criticism of cournot it has been known that models where sellers compete with prices may have undesirable properties when the commodities traded are homogenous in the simplest models with constant marginal costs price may be driven down to the competitive level even when there are only two firms more problematic if sellers are subject to capacity constraints nash in prices equilibrium may not exist at all these problems all arise because of a discontinuity in firms profit functions that arises when the prices of two or more firms are equal there have been many attempts to resolve this problem the simplest is to constrain sellers prices to be equal and to force them to compete in quantities this is the basis of most of the literature on monopolistic competi

discrete choice and variable returns to scale in previous studies of the probabilistic theory of qualitative choice e g marschak 1960 and mcfadden 1974 it has been assumed that an individual chooses among various alternatives with their utility levels independent of the number of individuals who choose each alternative there are however many examples in which the utility of a choice depends on the number of individuals who make the same choice for instance the utility of a given spatial choice may depend upon the number of others who choose neighboring locations neighborhood utility may decrease crowding or it may increase agglomerative economies with population size a second example is the automobile traveler s choice of routes the benefit of one route choice over another due to congestion depends on the number of drivers who choose the same route both of the examples suggested above deal with spatial choices of a particular kind but there are even examples from the more traditional macroeconomic theory one such example is of a product produced under variable returns to scale by a number of different sellers the price that each seller charges will depend upon the number of his customers if a buyer must choose to purchase from only one seller the price paid and thus utility will depend upon the total number of buyers choosing the same seller in all of the examples cited a reasonable model of choice is one that postulates uncertainty about the actual utility of each alternative the point of view is that a chooser s notional utility about each choice is a random variable in this case it is not certain which alternative will be chosen but the chosen alternative is the one with the greatest perceived utility it follows therefore that the probability that a given alternative is chosen is the probability that the utility perceived to be associated with it is larger than the utility perceived to be associated with any other alternative

taxes and agglomeration economies how are they related to nonprofit firm location author affiliation teresa d harrison department of economics drexel university 3141 chestnut street philadelphia pa 19104 usa tharrison drexel edu1 introductionnonprofits are an ever increasing component of the u s economy from 1997 2001 employment growth in the nonprofit sector averaged 2 5 outpacing both the business 1 8 and the government sectors 1 6 moore 2004 much of this growth stems from new nonprofits yet few studies have investigated possible determinants of nonprofit entry and location decisions most of these studies focus on demand side factors wolch and geiger 1983 downes and greenstein 1996 bielefeld murdoch and waddell 1997 for example downes and greenstein 1996 focus on demographic and religious characteristics of the surrounding community and its relation to private school location in this paper i use firm level data and focus on potentially important supply side variables tax rates and agglomeration economies most nonprofits are exempt from corporate sales and property taxes hansmann 1987 and gulley and santerre 1993 find evidence that higher corporate property and sales taxes are positively related to nonprofit market share however market share measures obfuscate the dynamics of the industry in terms of entry and exit rates if market share for nonprofits increases in response to higher tax rates this could be because new nonprofits are entering or because for profits are leaving the industry identifying these two cases is impossible with market share data using nonprofit tax return data i examine the relation between these tax exemptions and state county location decisions of new nonprofits to my knowledge this is the first paper to study these interactions at the individual firm level nonprofits also receive tax favored status due to the individual tax deduction on charitable contributions gentry and penrod 1998 employees of and donors to the nonprofits will be affected by the individual tax rates this in turn alters the costs to the nonprofit of location in a high or low tax area unlike previous studies i therefore investigate the relation between individual marginal tax rates and nonprofit location another potential supply side determinant of firm location decisions is the existing firm concentration in the area the potential economies of scale generated by proximity to other firms have been extensively examined in for profit industries 1 previous studies have generally found a positive relation between agglomeration and location carlton 1983 bartik 1985 woodward 1992 gius and frese 2002 rosenthal and strange 2003 to my knowledge bielefeld et al 2004 is the only study that examines nonprofit agglomeration finding evidence of agglomeration in dallas texas this warrants additional examination because nonprofit output is generally service driven and less mobile thus agglomeration implies greater direct competition making market saturation a larger issue in the nonprofit market using a nationwide dataset i examine how location and existing firm concentration are related and explore the potential presence of market saturation i also investigate possible differences between inter and intra industry agglomeration my results provide new insight into nonprofit firm behavior in most cases higher tax rates are associated with new firm location but the results for corporate and property taxes vary across the sample years i find that individual tax rates are an important consideration for nonprofits and are positively correlated to location my analysis also contributes to the literature by examining how the sensitivity to tax rates varies according to the sources of revenues for the institution firms that depend highly on individual donations are more likely to locate in high individual tax states while nonprofits with large mission related revenues are more sensitive to the property tax rate

cournot competition yields spatial agglomeration most theoretical models of spatial competition show a strong tendency toward spatial dispersion of firms yet common observations suggest that firms tend to agglomerate in this paper the authors show that competition between cournot type oligopolists that discriminate over space leads to spatial agglomeration one implication is that firms do not necessarily earn supernormal profits at the free entry equilibrium copyright 1991 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

the economics of product variety a survey demand for variety may arise from a taste for diversity in individual consumption and or from diversity in tastes even when each consumer chooses a single variant the full degree of variety potentially demanded will not in general be supplied because scale economies even to a small degree mean that the potential welfare or revenue gain from greater variety must be balanced against the lower unit production costs with fewer variants the economics of product variety consists essentially in analysing the effect of this balance in different situations and comparing the degree of product variety for different market structures with each other and with the optimum the survey commences with the work on market structures with single product firms generalized monopolistic competition tracing modern developments in both the chamberlinian and hotelling traditions the latter has been particularly fruitful due to the expansion of the original locational ideas into virtual spaces in product characteristics the emphasis in recent work on product variety has been on multiproduct firms in both monopolistic and oligopolistic structures including strategic market preemption although most work has been in a full information context there have been advances in product variety under imperfect information either by consumers to properties of the firms products or firms as to consumers demands

equilibrium vertical differentiation in a bertrand model with capacity precommitment both quality differentiation and capacity commitment have been shown to relax price competition however their joint influence on the outcome of price competition has not yet been assessed in this article we consider a three stage game in which firms choose quality then commit to capacity and finally compete in price when the cost of quality is negligible we show that firms do not differentiate their products in a subgame perfect equilibrium in other words capacity precommitment completely eliminates the incentive to differentiate by quality

the logit model of monopolistic competition brand diversity one of the important issues in the literature on monopolistic competition concerns whether the free entry equilibrium will provide sufficient variety of differentiated brands this paper examines variety issue using the logit choice model to capture brand differentiation the consumption value of each brand is drawn from the extreme value distribution and the consumer then purchases the brand with the highest value with the resulting demand structure the authors find that monopolistic competition results in two few firms and thus too few brands from the viewpoint of consumers this result supports the findings of other models with symmetrically differentiated brands copyright 1990 by blackwell publishing ltd

asymmetric capacity constraints and equilibrium price dispersion abstract price dispersion arises despite perfect information about prices in equilibrium the higher capacity firm adopts a high price high availability strategy the lower capacity firm adopts a low price low availability strategy and consumers are more likely to shop at the high price firm

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

spatial competition with price taking firms we consider a price taking equilibrium in the spatial setting a unique pricing equilibrium is shown to exist for any set of firm locations this equilibrium is then used to examine locational incentives in the two stage process in whiclh firms first choose locations anticipating the subsequent price taking outcome the result is spatial agglomeration if demand is inelastic and there are only two firms agglomeration does not occur if demand is too elastic or if there are more than two firms this paper presents a two stage model of spatial competition in which the prices in the second stage constitute a competitive equilibrium rather than being chosen by firms the analysis applies to an industry in which firms prices are regulated by an authority whose concern is to maximize social surplus as we show the prices the regulator would choose are those that would arise in the price taking equilibrium of course the full social optimum could be attained if the authority were also to regulate locations however apart from coarse restrictions such as zoning location regulation does not seem common in practice thus we model firms as deciding on the locations non cooperatively and anticipating correctly the subsequent price regulation for example when airlines were regulated they could choose the quality of their service such as departure times but price was controlled 2 the price taking equilibrium is also relevant even in the absence of regula tion when there are several suppliers at each location then the marginal cost curve associated with each point occupied by firms is simply interpreted as the supply curve the points occupied by suppliers can be thought of as market places or as shopping malls and the rents earned owing to increasing marginal costs can be extracted by the developer of the market place or mall the developer s location decision aims to maximize rents earned in choosing a location each developer takes into account how the ensuing price competition among suppliers both in the mall and across different malls affects the rents that can be extracted in this way locations are determined as a non cooperative equilibrium whereas prices are subsequently determined by walrasian competition we first assume that demand is completely inelastic and we prove the existence of a unique price equilibrium and that an allocation is optimal if and only if it can be supported by a price equilibrium the proofs do not require fixed point theorems and are a direct application of an intuitively appealing result of dubins and spanier 1961 we then extend our existence uniqueness and optimality results to allow for price sensitive demands different demand

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

marginal cost pricing when spot markets are complete the standard formulation of a spot market subject to uncertain excess demand uses a tatonnement process that restricts trade until the market clearing price is found here i present a model in which there is no restriction on trade during the process of the resolution of uncertainty about aggregate excess demand the idea is to enlarge the commodity space and define goods by the probability that they will sell in addition to other characteristics the probability of sale characteristic is the spot market analogue of the contingencies under which delivery will take place in the arrow debreu model a failure to distinguish goods by the probability of sale characteristic can lead to the rejection of the competitive paradigm even when everyone is a price taker and the allocation is efficient

equilibrium price dispersion under demand uncertainty the roles of costly capacity and market structure when capacity is costly and prices are set in advance firms facing uncertain demand will sell output at multiple prices and limit the quantity available at each price i show that the optimal price strategy of a monopolist and the unique pure strategy nash equilibria of oligopolists both exhibit intrafirm price dispersion moreover as the market becomes more competitive prices become more dispersed a pattern documented in the airline industry while generating similar predictions the model differs from the revenue management literature because it disregards market segmentation and fare restrictions that screen customers

location in the hotelling duopoly model with demand uncertainty abstract demand uncertainty is introduced into a hotelling environment with fixed prices by allowing random shocks to the desirability of the firm s product given these random shocks the choice of location affects the average level of demand as well as the riskness of demand reducing the distance to the other firm raises expected demand and payoff but also lowers the degree of differentiation between the firms thus raising demand uncertainty risk averse firms will locate away from the center and depending on degree of risk aversion markup and size of the market may locate on either side of the quartile points

perception and information in a competitive location model this paper considers a situation in which two competitors locate one facility each at the vertices of a tree their decisions are based on the capture of demands at the vertices of the tree as opposed to the usual models it is assumed that the true demands are unknown and that each competitor has its own perception of them the paper investigates a facility planner s advantage that results from knowledge concerning his competitor s perception stackelberg solutions are analyzed as well as possible advantages to the competitor who locates first

pricing and promotions in asymmetric duopolies this paper develops a modeling framework for making promotions decisions in contrast to some of the prior research the framework explicitly models promotions its central feature is the view of promotions competition as a multistage game in which regular prices are chosen first followed by the choice of promotion depths and frequencies it is used to illustrate the nature of competition between a national brand and private label in equilibrium the national brand promotes to ensure that the private label does not try to attract consumers away from the national brand moreover the private label does not promote this equilibrium is also contrasted with varian s framework used by other researchers in which mixed strategy equilibrium prices are interpreted as promotions

market research and innovation strategy in a duopoly we model a duopoly in which ex ante identical firms must decide where to direct their innovation efforts the firms face market uncertainty about consumers preferences for innovation on two product attributes and technology uncertainty about the success of their research and development r d investments firms can conduct costly market research before setting r d strategy we find that the value of market information to a firm depends on whether its rival is expected to obtain this information in equilibrium consequently one firm may forgo market research even though its rival conducts such research and learns the true state of demand we examine both vertical and horizontal demand structures with vertical preferences firms are a priori uncertain about which attribute all consumers will value more in this case a firm that conducts market research always attempts innovation on the attribute it discovers that consumers prefer and expends more on r d than a rival that has not conducted market research with horizontal preferences distinct segments exist each caring about innovation on only one attribute and firms are a priori uncertain how many consumers each segment contains in this case a firm that conducts market research may follow a niche strategy and attempt innovation to serve the smaller segment to avoid intense price competition for the larger segment a firm that conducts market research may therefore invest less in r d and earn lower postlaunch profits than a rival that has forgone such research

rational choice under an imperfect ability to choose we consider an individual who lacks the information processing capacity required for a direct comparison of all feasible allocations instead of finding at once a best allocation the individual myopically adjusts his current allocation toward higher utility the individual makes adjustment errors inversely proportional to his ability to choose we compare the stationary state of this process with the standard model we see how an imperfect ability to choose modifies both positive and normative predictions of the standard model and how the standard model can be obtained from our more general one as the special case corresponding to perfect ability jel d 11

mass media competition political competition and public policy if better informed voters receive favourable policies then mass media will affect policy because mass media provide most of the information people use in voting this paper models the incentives of the media to deliver news to different groups the increasing returns to scale technology and advertising financing of media firms induce them to provide more news to large groups such as taxpayers and dispersed consumer interests and groups that are valuable to advertisers this news bias alters the tradeoff in political competition and therefore introduces a bias in public policy the paper also discusses the effects of broadcast media replacing newspapers as the main information source about politics the model predicts that this change should raise spending on government programmes used by poor and rural voters

product differences and prices abstract under assumptions following hotelling s 1929 paper stability in competition the possibility of constructing an example in which equilibrium prices exist everywhere and the two merchants display tendencies to agglomerate is ruled out

product differentiation with consumer arbitrage abstract we determine the equilibrium to a game where two firms set delivered price schedules and consumers simultaneously declare where they want to take delivery of the product equilibrium pricing policies provide incentives for consumers not to demand their preferred varieties but rather to purchase more standard varieties this behavior may decrease market diversity the demanded varieties tend to agglomerate around the market center we also show that it is efficient for the cost of adapting the product to consumers to be shared through arbitrage but oligopoly gives rise to an inefficient level of personal arbitrage

where to locate in a circular city abstract we study the location choices by cournot oligopolists in a circular market where consumers are located uniformly along the circumference we analyze the subgame perfect nash equilibria spne of a two stage location quantity game we demonstrate that the equidistant location pattern is only one of the many equilibrium location patterns that arise in a circular market nonequidistant multiple or a continuum of location equilibria may also arise both spatial agglomeration and dispersion or a combination of agglomeration and dispersion may occur in equilibrium in the case of infinitely many location equilibria we establish the welfare equivalence of the equilibrium location patterns

does cournot competition yield spatial agglomeration abstract locations and quantities are chosen sequentially in spatial markets strikingly different location patterns emerge depending on the shape of the market in a circular city firms locate equidistant from each other in a linear city firms agglomerate at the center

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

the principle of minimum differentiation revisited return of the median voter we study a linear location model hotelling 1929 in which n with n 2 boundedly rational players follow noisy myopic best reply behavior we show through numerical and mathematical analysis that such players spend almost all the time clustered together near the center re establishing the principle of minimum differentiation that had been discredited by equilibrium analyses thus our analysis of the best response dynamics shows that when considering market dynamics as well as their policy and welfare implications it may be important to look beyond equilibrium analyses

perceptual position and competitive brand strategy in a two dimensional two brand market brand positioning and competitive reaction are important determinants of optimal brand strategy analyses of brand strategy have focused on optimal pricing and positioning issues using either empirical models of perceptions and preferences game theory to examine competition or both however the important issues of advertising and distribution strategy have not been fully addressed this paper analyzes competition and strategy between two brands that compete in a two dimensional market with advertising and distribution spending in addition to prices and product positions in particular for a unimodal taste distribution of ideal points we show how optimal competitive nash equilibrium marketing mix levels and profits depend on the positions of both brands brands can reposition to increase profit and under what conditions these strategies imply minimum versus maximum differentiation positioning equilibria and how the intensity of advertising and distribution competition affect equilibrium brand positions

equivalence results for optimal pass through optimal indexing to exchange rates and optimal choice of currency for export pricing firms sometimes write price lists or catalogs for their exports so they set prices for a period of time and do not adjust prices during that interval in response to changes in their environment the firm sets the price either in its own currency or the importer s currency this paper draws a simple link between the choice of currency and the pricing decision of a firm that changes prices in response to all shocks specifically if the latter firm s price has a lower variance in terms of its own currency than the importer s currency then the firm with a price list will set the price in its own currency and otherwise it will set price in the foreign currency this relationship is established by consideration of the firm with a price list as a special case of a firm that indexes its export price to the exchange rate jel f4 f1

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