increasing dominance with no efficiency effect abstract i uncover a new force towards increasing dominance the property whereby in dynamic games the leader tends to increase his or her lead in expected terms the new effect results from the strategic choice of covariance in races i assume that players must choose not the amount of resources to spend but how to allocate those resources i show that in equilibrium the laggard chooses a less promising path in effect trading off lower expected value for lower correlation with respect to the leader this results in increasing dominance and holds true even if no joint payoff or efficiency effect is present journal of economic literature classification numbers c7 l1

investment and market dominance we analyze a model of oligopolistic competition with ongoing investment special cases include incremental investment patent races learning by doing and network externalities we investigate circumstances under which a firm with low costs or high quality will extend its initial lead through investments to this end we derive a new comparative statics result for general games with strategic substitutes which applies to our investment game finally we highlight plausible countervailing effects that arise when investments of leaders are less effective than those of laggards or in dynamic games when firms are sufficiently patient

tipping and concentration in markets with indirect network effects this paper develops a framework for measuring tipping the increase in a firm s market share dominance caused by indirect network effects our measure compares the expected concentration in a market to the hypothetical expected concentration that would arise in the absence of indirect network effects in practice this measure requires a model that can predict the counterfactual market concentration under different parameter values capturing the strength of indirect network effects we build such a model for the case of dynamic standards competition in a market characterized by the classic hardware software paradigm to demonstrate its applicability we calibrate it using demand estimates and other data from the 32 64 bit generation of video game consoles a canonical example of standards competition with indirect network effects in our example we find that indirect network effects can lead to a strong economically significant increase in market concentration we also find important roles for beliefs on both the demand side as consumers tend to pick the product they expect to win the standards war and on the supply side as firms engage in penetration pricing to invest in growing their networks

choosing price or quantity the role of delegation and network externalities we consider a differentiated duopoly and endogenise the firm choice of the strategy variable price or quantity to play on the product market in the presence of network externalities we model this choice by assuming both competition between entrepreneurial owner managed firms and competition between managerial firms in which market decisions are delegated from owners to revenue concerned managers while network externalities are shown not to alter the symmetric equilibrium quantity choice arising in the no delegation case sufficiently strong network effects allow us to eliminate the multiplicity of equilibria under delegation and lead to a unique equilibrium in which both firms choose price

mobile termination network externalities and consumer expectations we re examine the literature on mobile termination in the presence of network externalities externalities arise when firms discriminate between on and o net calls or when subscription demand is elastic this literature predicts that profit decreases and consumer surplus increases when termination charges increase this is puzzling since in reality regulators are pushing termination rates down while being opposed to do so by network operators this puzzle is resolved when consumers expectations are assumed passive but required to be fulfilled in equilibrium as defined by katz and shapiro aer 1985 instead of being responsive to non equilibrium prices as assumed until now

pricing a network good to deter entry of a network good we show that the installed user base of a network good can serve a preemptive function similar to that of an investment in capacity if the entrant s good is incompatible with the incumbent s good and there are network externalities in demand consequently the threat of entry can lead the incumbent to set low prices we identify some factors that should be considered in thinking about the welfare eiects of entry deterrence in this and similar models i introduction both sides in us v microsoft seem to agree that microsoft s pricing of windows does not correspond to short run pro t maximization by a monopolist schmalensee s direct testimony argues that microsoft s low prices are due at least in part to its concern that higher prices would encourage other rms to develop competing operating systems while this idea may seem intuitive it has been seen as controversial by some commentators e g hall and hall 1999 because neither side has proposed a formal model where such limit pricing would make sense in response this paper develops a highly simpli ed model of complete information limit pricing based on the idea that the installed base of a network good can ll a preemptive role similar to that of investment in physical capacity to model the role of the incumbent s installed base we assume that there are overlapping generations of consumers each of whom lives for two periods and purchases only when young we also assume there are only two types of consumers and we further assume that the distribution of values is such that the incumbent s steady state pro t is highest when it

effects of the minimum wage on the employment status of youths an update the large decline in the relative value of the minimum wage during the 1980s makes that period a valuable one for identifying the impact of variation in the minimum wage on youth employment this study produces the robust finding that when the experience of the 1980s is included a 10 percent increase in the minimum wage is estimated to reduce teen employment by less than 1 percent the lower end of the range of previous estimates because this small employment effect is offset by a labor force withdrawal effect the study finds no discernible effect on measured unemployment the study also finds no apparent effect of the minimum wage on the employment of young adults aged 20 24

hedonic price indexes for spreadsheets and an empirical test for network externalities in this article i first estimate hedonic price equations for computer spreadsheet programs and then use the analysis to empirically test whether network externalities exist in this industry the study shows that consumers are willing to pay a significant premium for spreadsheets that are compatible with the lotus platform and for spreadsheets that offer links to external databases and a similar premium for spreadsheets that offer local area network externalities finally the quality adjusted real price of computer spreadsheets declined by approximately 15 per year from 1986 to 1991

platform competition in two sided markets many if not most markets with network externalities are two sided to succeed platforms in industries such as software portals and media payment systems and the internet must get both sides of the market on board accordingly platforms devote much attention to their business model that is to how they court each side while making money overall this paper builds a model of platform competition with two sided markets it unveils the determinants of price allocation and end user surplus for different governance structures profit maximizing platforms and not for profit joint undertakings and compares the outcomes with those under an integrated monopolist and a ramsey planner jel l5 l82 l86 l96

the economics of predation what drives pricing when there is learning by doing predatory pricing a deliberate strategy of pricing aggressively in order to eliminate competitors is one of the more contentious areas of antitrust policy and its existence and efficacy are widely debated the purpose of this paper is to formally characterize predatory pricing in a modern industry dynamics framework that endogenizes competitive advantage and industry structure our framework encompasses important phenomena such as learning by doing network effects switching costs dynamic demand and certain types of adjustment costs due to its prominent role in legal cases involving alleged predation we examine learning by doing in more detail we first show that predation like behavior arises routinely in our learning by doing model equilibria involving predation like behavior typically coexist with equilibria involving much less aggressive pricing to disentangle predatory pricing from mere competition for efficiency on a learning curve we next decompose the equilibrium pricing condition and develop alternative characterizations of a firm s predatory pricing incentives we finally measure the impact of these incentives on industry structure conduct and performance we show that forcing a firm to ignore the predatory incentives in setting its price can have a large impact and that this impact stems from eliminating equilibria with predation like behavior along with the predation like behavior however a fair amount of competition for the market is eliminated

market share dynamics in a duopoly model with word of mouth communication abstract we analyze dynamic price competition in a homogeneous goods duopoly where consumers exchange information via word of mouth communication a fraction of consumers who do not learn any new information remain locked in at their previous supplier in each period we analyze markov perfect equilibria in which firms use mixed pricing strategies market share dynamics are driven by the endogenous price dispersion depending on the parameters we obtain different classes of dynamics when firms are impatient there is a tendency towards equal market shares when firms are patient there are extended intervals of market dominance interrupted by sudden changes in the leadership position

business to business bargaining in two sided markets abstract bargaining regularly takes place on the business to business side of two sided markets however little is known about the consequences of these negotiations in this paper we allow the platform or a policy maker to choose between a standard design offering posted prices to both sides or a design with bargaining offering a posted price to consumers and negotiating with at least some firms we find that the platform pursues negotiations when it has a strong bargaining position and does so by targeting firms with the largest network effects while this behavior may appear exploitive we show that profits and welfare often align across platform designs this alignment stems from how bargaining incentivizes the platform greater platform bargaining power allows the platform to extract more of the network surpluses since it can convert more of the firm surplus into profits and this incentivizes the platform to draw in greater participation generating greater welfare these results suggest that platform and policy maker preferences often align in this setting

dynamic competition with network externalities why history matters we consider dynamic competition among platforms in a market with network exter nalities a platform that dominated the market in the previous period becomes focal in the current period in that agents play the equilibrium in which they adopt the focal platform whenever such equilibrium exists yet when faced with higher quality competition can a low quality platform remain focal in the finite horizon case the unique equilibrium is efficient for patient platforms with an infinite time horizon however there are multiple equilibria where either the lowor high quality platform dominates if qualities are stochastic the platform with a better average quality wins with a higher probability even when its realized quality is lower and this probability increases as platforms become more patient hence social welfare may decline as platforms become more forward looking

a model of the evolution of duopoly does the asymmetry between firms tend to increase or decrease this paper is an attempt to identify some of the factors that affect the evolution of market structure in a model of dynamic competition between two firms the stochastic evolution of the state of competition depends on the respective effort rates of the firms the question is whether the current leader works harder than the laggard does the gap between firms tend to increase or decrease we show that several effects are at work the state tends to evolve in the direction where joint payoffs are greater since joint payoffs are related to joint product market profits less joint effort costs there are two classes of effect the joint profit effect and various joint cost effects the latter result in part from the pattern of profits and in part from endpoint effects that give relief from efforts asymptotic expansions illuminate these influences moreover we show by numerical simulation that there is another kind of joint cost effect the pattern of joint effort costs can influence the pattern of evolution of market structure and the evolution of the pattern of market structure can influence the pattern of efforts in a mutually self reinforcing manner in particular there may be equilibria in which this last effect means that the laggard works harder than the leader even though all the other effects work in favour of the leader

competition and increasing returns to scale a model of bank size this study examines the causal effects of bank size on banks survival asset quality and leverage two forces drive these effects increasing returns to scale derived from banks expertise and competition the first enables bigger banks to survive competition better have higher asset quality and be more leveraged it drives banks into a race for expansion this race toughens competition between banks which edges out small banks and may worsen all banks asset quality consequently the banking industry will be dominated by a small number of highly leveraged banks in this study financial intermediation arises endogenously and co exists with direct finance

standardization in decentralized economies this paper presents a dynamic model inspired by evolutionary game theory of how standards and norms emerge in decentralized economies it shows that standardization outcomes depend on adopters attitudes to problems caused by incompatibility if individuals display aversion to incompatibility standardization never fails to happen eventually but societies sometimes end up picking inferior standards in this case official action can be useful to quickly achieve sensible standardization on the other hand when individuals display tolerance or neutrality to incompatibility there is neither path dependency nor a lock in problem and regulation seems a poor alternative to laissez faire

the minimum wage and the employment of youth evidence from the nlsy using panel data on individuals from the national longitudinal survey of youth we find that employed individuals who were affected by the increases in the federal minimum wage in 1979 and 1980 were about 3 percent less likely to be employed a year later even after accounting for the fact that workers employed at the minimum wage may differ from their peers in unobserved ways

the learning curve market dominance and predatory pricing sufficient conditions for id and iid are given in the case of two step learning in which a firm reaches the bottom of its learning curve after just two sales however examples are also constructed for the two step learning case in which neither id nor iid holds it is also shown that in equilibrium iid implies that learning is privately disadvantageous although it is socially advantageous finally introducing avoidable fixed costs and possible exit into the model yields a new theory of predatory pricing based on the learning curve hypothesis

intraconnectivity and interconnectivity when value creation may reduce profits this paper analyses firms decisions to provide connectivity to their customers we distinguish between intraconnectivity the ability of one firm s customers to connect to each other and interconnectivity the ability of one firm s customers to connect with another firm s customers the profitability implications of allowing connectivity are not a straightforward consequence of the consumer value of connectivity because connectivity affects not only the customer value but also the intensity of competition by creating or changing network externality we find that if sales are driven by brand switching rather than by category expansion a firm may find it optimal not to provide intraconnectivity even if providing it is not costly and may find it optimal to provide interconnectivity even at a cost exceeding the consumer value of connectivity on the other hand if category expansion is possible providing intraconnectivity may be profitable in this case either the equilibrium intraconnectivity provision may be asymmetric or both firms may find it individually optimal to provide intraconnectivity under certain conditions in the latter case the firms choice of intraconnectivity is a prisoner s dilemma game

avoiding market dominance product compatibility in markets with network effects as is well recognized market dominance is a typical outcome in markets with network effects a firm with a larger installed base offers a more attractive product which induces more consumers to buy its product which produces a yet bigger installed base advantage such a setting is investigated here but with the main difference that firms have the option of making their products compatible when firms have similar installed bases they make their products compatible in order to expand the market nevertheless random forces could result in one firm having a bigger installed base in which case the larger firm may make its product incompatible we find that strategic pricing tends to prevent the installed base differential from expanding to the point that incompatibility occurs this pricing dynamic is able to neutralize increasing returns and avoid the emergence of market dominance

bandwagon effects and long run technology choice abstract we introduce a class of bandwagon games which generalizes the notion of network externalities when there are more than two competing technologies and various degrees of partial compatibilities among them we then apply the stochastic evolutionary approach to this class of games we determine the conditions under which a globally pairwise risk dominant technology is the long run equilibrium lre we also show the conditions under which one technology takes over another technology by directly switching consumers from the latter to the former also called direct domination parametric examples illustrate the properties of the technology which is the lre journal of economic literature classification numbers c72 c73

network effects aftermarkets and the coase conjecture a dynamic markovian approach this paper investigates the expansion of the network of a monopolist firm that produces a durable good and is also involved in the corresponding aftermarket we characterize the markov perfect equilibrium of the continuous time dynamic game played by the monopolist and the forward looking consumers under the assumption that consumers benefit from the subsequent expansion of the network the paper contributes to the theoretical discussion on the validity of the coase conjecture analyzing whether coase s prediction that the monopolist serves the market in a twinkling of an eye remains valid in our setup we conclude that the equilibrium network development may actually be gradual contradicting coase s conjecture we find that a necessary condition for such a result is the existence of aftermarket network effects that accrue at least partly to the monopolist firm

network competition ii price discrimination our companion article developed a clear conceptual framework of negotiated or regulated interconnection agreements between rival operators and studied competition between interconnected networks under the assumption of nondiscriminatory pricing this article relaxes this assumption and allows networks to charge different prices for calls terminating on the subscriber s network and those terminating on a rivals network this creates a price differential between services that are identical for the consumer and generates network externalities despite network interconnection we show that in both the mature and entry phases of the industry the nature of competition is substantially affected by such price discrimination

bertrand supertraps we study oligopoly price competition between multiproduct firms firms whose products interact in the profit function specifically we focus on the impact of intrafirm product interactions on the level of equilibrium profits this impact may be decomposed in two different ways a a direct effect keeping the competitors actions fixed plus a strategic effect i e through the competitors actions or alternatively b a competitive advantage effect change in firmi only plus an imitation effect change in all other firms we derive conditions such that a the strategic effect more than outweighs the direct effect and conditions such that b the imitation effect more than outweighs the competitive advantage effect bertrand supertraps for example an increase in the degree of economies of scope would increase profits if prices were fixed or if the change were limited to firmi s cost function however if all firms increase the degree of economies of scope then all firms receive lower profits a variety of other applications is considered including learning curves core competencies demand synergies systems competition compatibility bundling network effects switching costs durable goods long term contracts

information management and pricing in platform markets we study platform markets in which the information about users preferences is dispersed first we show how the dispersion of information introduces idiosyncratic uncertainty about participation decisions and how the latter shapes the elasticity of the demands and the equilibrium prices we then study the effects on profits consumer surplus and welfare of platform design blogs forums conferences advertising campaigns post launch disclosures and other information management policies affecting the agents ability to predict participation decisions on the other side of the market

technology adoption hysteresis and absence of lock in we introduce a simple model of technology adoption with overlapping generations of players technologies generate network effects and players are both backward and forward looking we use results from the supermodular games literature to guarantee equilibrium existence and uniqueness in line with the empirical literature the equilibrium adoption path exhibits hysteresis and technologies cannot lock in we characterize the expected time of adoption which can be seen as a measure of technology dominance

the choice of titling system in land abstract this paper analyzes the choice of the socially optimal titling system assuming rational individual choices about recording assurance and registration decisions it focuses on the enforcement of property rights to land under private titling and the two existing public titling systems recording and registration when the reduction in the expected costs of forfeiture balances the higher cost of initial registration a registration system is more efficient than a recording system implications for title assurance land improvements and transactions are also considered

the impact of the minimum wage if workers can adjust effort abstract in traditional models a binding minimum wage creates a excess supply of low skilled workers for minimum wage jobs employment falls and some jobs are reallocated from high to low rent workers this disequilibrium cannot persist competition to secure the property rights to now scarce jobs undoes most of the effects of the minimum wage workers who attach the highest value to the jobs are willing to work harder to keep them marginal workers are squeezed out of the market as high rent workers ratchet up effort level this process erodes the rent conferred by the minimum wage but also increases the value of marginal product which reduces the size of the employment effect the minimum wage confers more money income on low skilled workers and creates some distortion in the optimum combination of wage rate and effort level under plausible conditions the minimum wage has little effect on rent employment output and profits

competition between networks a study of the market for yellow pages this paper estimates the importance of network effects in the market for yellow pages i estimate three simultaneous equations consumer demand for usage of a directory advertiser demand for advertising and a publisher s first order condition derived from profit maximizing behaviour estimation shows that advertisers value consumer usage and that consumers value advertising implying a network effect i find that internalizing network effects would significantly increase surplus as an application i consider whether the market benefits from monopoly which takes advantage of network effects or oligopoly which reduces market power i find that a more competitive market is preferable copyright 2004 wiley blackwell

bertrand competition under network externalities abstract two firms engage in price competition to attract buyers located on a network the value of the good of either firm to any buyer depends on the number of neighbors on the network who adopt the same good when the size of externalities increases linearly with the number of adoptions we identify the set of pricing strategies that are consistent with an equilibrium in which one of the firms monopolizes the market the set includes marginal cost mc pricing as well as bipartition pricing which offers discounts to some buyers and charges markups to others we show that mc pricing fails to be an equilibrium under non linear externalities in a general network but identify conditions for an equilibrium with bipartition pricing to be robust against perturbations in the externalities from linearity the analysis is applied to platform competition in a two sided market under local and approximately linear externalities

we re number 1 price wars for market share leadership i examine the dynamics of oligopolies when firms derive subjective value from market leadership in equilibrium prices alternate in tandem between high levels and occasional price wars which take place when market leadership is at stake the stationary distribution of market shares is typically multimodal that is much of the time there is a stable market leader even though shareholders do not value market leadership per se a corporate culture that values market leadership may increase shareholder value the online appendix is available at https doi org 10 1287 mnsc 2017 2725 this paper was accepted by bruno cassiman business strategy

minimum wage laws are they overrated l minimum has been fixed in nominal terms at about 55 percent of the current average wage rising wages in the rest of the economy gradually erode the real minimum wage and eventually the process is repeated sometimes the increase in the nominal minimum is accompanied by a permanent reduction in those businesses exempted from the law proposals for a lower minimum wage for young workers or to index the minimum wage to the average wage have been debated but not adopted the minimum wage was last increased to 3 35 in 1981 since then average hourly wages have risen by 25 percent eliminating any momentum for a lower minimum wage for youth but reviving proposals for another increase in the nominal minimum economists are fascinated by the minimum wage because we have strong theoretical predictions about the direction of the effect of the minimum wage on employment and fairly widely accepted methods to estimate the size of that impact it probably didn t hurt that the earliest and later estimates lined up well with the predictions but that is not the only reason for our fascination with the topic depending on whether we include those who say they earn less than the minimum wage minimum wage workers account for 6 to 12 percent of those employed gilroy 1981 p 157 and less than 5 percent of wage and salary income the minimum wage gives economists a relatively rare opportunity to study the impact of an exogenous increase in the price of labor and thus a chance to refine our thinking

the marginal price effects of antitrust rules against price discrimination abstract the two central pricing rules contained in most antitrust laws are prohibitions of below cost pricing and prohibitions of discriminatory pricing this article shows that the rule against discriminatory pricing may actually induce firms to charge exclusionary below cost prices even in the complete absence of any predatory intent on the part of firms

snowball a dynamic oligopoly model with indirect network effects abstract allowing for innovation dynamics in the software market this paper studies the conditions under which standardization in the hardware market arises and persists over time in the model software firms repeatedly invest in quality upgrades compete in the product market and make exit as well as entry decisions the results show that in general excess inertia does not occur a platform becomes the standard in a market only if it is better than the competing platforms furthermore low overall rates of innovation always lead to variety conversely the higher the speed of innovation the more likely standardization is

welfare analysis of regulating mobile termination rates in the u k we develop a calibrated simulation model of the u k mobile telephony market and use it to analyze the effects of reducing mobile termination rates mtr s as recommended by the european commission we find that reducing mtr s is likely to increase both consumer surplus and networks profits depending on the strength of call externalities i e benefits to the recipient of a call social welfare may increase by as much as 1 billion to 4 6 billion per year we also use the model to estimate the welfare effects of the 2010 merger between orange and t mobile and find that the merger led to a substantial reduction in consumer surplus

preemptive patenting and the persistence of monopoly this article takes a different tack and inquires whether institutions such as the patent system create opportunities for firms with monopoly power to maintain their monopoly power the results apply to other situations such as brand identification spatial location and capacity expansion which share the characteristic that early or preemptive actions may lower the returns to potential competitors

dynamic price competition with network effects i consider a dynamic model of competition between two proprietary networks consumers die and are replaced with a constant hazard rate and firms compete for new consumers to join their network by offering network entry prices i derive a series of results pertaining to a existence and uniqueness of symmetric equilibria b monotonicity of the pricing function e g larger networks set higher prices c network size dynamics increasing dominance vs reversion to the mean and d firm value how it varies with network effects finally i apply my general framework to the study of termination charges in wireless telecommunications i consider various forms of regulation and examine their impact on firm profits and market share dynamics

aftermarket power and foremarket competition i revisit the issue of aftermarkets by developing an infinite period model with overlapping consumers if the aftermarket is characterized by constant returns to scale then social surplus and consumer surplus are invariant with respect to aftermarket power under increasing returns to scale however greater aftermarket power leads to greater concentration in the foremarket higher barriers to entry higher social surplus and possibly higher consumer surplus

the elusive effects of minimum wages the main theme of david card and alan krueger s book myth and measurement the new economics of the minimum wage is that the data do not support the view that minimum wages reduce employment the most important chapter considers data for the fast food industry where it is suggested that recent minimum wage increases may actually have increased employment contrary to the standard theorem that labor demand curves slope down a more reasonable view of the evidence in this book and in many other studies going back to 1915 is that the employment effects of minimum wages are small and difficult to detect in the noisy data available

network effects and environmental externalities do clean technologies suffer from excess inertia abstract we study the diffusion of a clean substitute to a dirty durable in a dynamic model consumer utility of both durables increases in their respective market shares due to network effects first we characterize the optimal dirty good tax the tax should achieve a long run optimal division of the market between the two goods along the transition path to this steady state the optimal tax depends on the current and future market shares of the clean durable thus even if the marginal environmental damage from an additional dirty durable is constant the optimal tax should not be constant second we study whether excess inertia can occur if the emission tax is not optimally set we then find that a constant tax that only accounts for the environmental damage caused by the dirty good may lead to excess inertia excess inertia could happen even if the clean technology is proprietary and the technology owner has incentives to sponsor the initial market diffusion of the technology

network competition and entry deterrence we develop a model of logit demand that extends to a multi firm industry the traditional duopoly framework of network competition firstly we show that incumbents establish inefficiently the reciprocal access charge below cost when they compete in prices but they behave efficiently if they compete in utilities secondly we study how incumbents determine the industry wide access charge under the threat of entry we show that incumbents may accommodate all possible entrants only a group of them or may completely deter entry when entry deterrence is the preferred option incumbents distort the access charge upwards

theory and evidence on the political economy of the minimum wage this paper examines how closely the minimum wage has been set to the most popularly stated goals of minimun wage policy i first estimate these goals the minimum wage rate at which the relevant labor demand is unitary elastic maximizing the total earnings of minimum wage workers about 5 35 and the level that would lift a typical minimum wage worker s family out of poverty about 5 17 i can reject that the actual minimum wage policy has been driven by desire to achieve these goals and find that a simple interest group model best explains the historical path of the minimum wage rate

network competition i overview and nondiscriminatory pricing we develop a model of unregulated competition between interconnected networks and analyze the mature and transition phases of the industry in this deregulated environ ment networks pay negotiated or regulated access charges to each other and com pete in prices for customers we show that a competitive equilibrium may fail to exist for large access charges or for large network substitutability and that freely negotiated access charges may prevent effective competition in the mature phase of the industry and erect barriers to entry in the transition toward competition last we examine the meaning and impact of policies such as the efficient component pricing rule

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

how do switching costs affect market concentration and prices in network industries i investigate the effects of switching costs on the market outcome in network industries using a dynamic duopoly model of price competition in the presence of an outside option i find that the role of switching costs depends on network effects and the outside option without a viable outside option high switching costs can neutralize the tendency towards high market concentration associated with network effects but with a viable outside option switching costs increase market concentration furthermore switching costs lower prices if network effects are modest and there exists a viable outside option but generally raise prices otherwise

market structure and the competitive effects of switching costs abstract we revisit the effects of switching costs on dynamic competition we consider stationary markovian strategies with market shares being the state variable and characterize a relatively simple markov perfect pricing equilibrium at which there is switching by some consumers at all times for the case of low switching costs and infinitely lived consumers we show that switching costs are pro competitive in the long run steady state while the overall effect in the short run transient state depends on market structure in particular switching costs are anti competitive in relatively concentrated markets and pro competitive otherwise