walrasian equilibria as limits of noncooperative equilibria part i mixed strategies abstract we examine the connection between walrasian equilibria of a limit economy with infinitesimal firms and the noncooperative cournot equilibria of approximating finite economies with significant firms following earlier work of novshek and sonnenschein we allow for set up cost and permit a minimal form of mixed strategies we depart from them by requiring that the aggregate production set exhibits some degree however small of decreasing returns contrasting with their results it is shown that a regular walrasian equilibrium of a limit economy can always be approximated by a sequence of noncooperative equilibria for the tail of the approximating finite economies thus there is a surprising qualitative discontinuity when one passes from the novshek sonnenschein case of aggregate constant returns to scale of the decreasing returns case of this paper

dynamic price competition with fixed capacities in this paper we study price competition for an oligopoly in a dynamic setting where each of the sellers has a fixed number of units available for sale over a fixed number of periods demand is stochastic and depending on how it evolves sellers may change their prices at any time this reflects the fact that firms constantly and almost costlessly change their prices reacting to updates in their estimates of market demand competitor prices or inventory levels in a setting with demand uncertainty we show that there is a unique subgame perfect equilibrium for a duopoly in which all states sellers engage in bertrand competition and the seller with the lower equilibrium reservation value sells a unit at a price equal to the competitor s equilibrium reservation value this structure therefore extends the marginal value concept of bid price control used in many revenue management implementations to a competitive model we give a closed form solution to the equilibrium price paths for a duopoly and extend all the results to an n firm oligopoly we then study extensions to multiple customer types uncertain valuations and differentiated products this paper was accepted by martin lariviere operations management

optimal penal codes in price setting supergames with capacity constraints this paper constructs optimal pure strategy penal codes for a broad class of symmetric bertrand supergames with capacity constraints the results should simplify the analysis of bertrand supergames because the punishments comprising the penal codes constructed below have a very simple form and the associated payoffs are often easy to calculate it is also shown that for a commonly employed subclass of the games considered the admission of mixed strategies does not allow severer punishments the analysis draws heavily on the pathbreaking work of abreu 1984 he demonstrated that in the search for optimal penal codes attention can be restricted to simple penal codes simple penal codes are characterized by a vector of outcome paths one for each player the ith outcome path is interpreted as the punishment to be imposed on the ith player if he deviates from the equilibrium path or from any punishment path section 2 explains the basic framework of analysis the class of bertrand games studied is very general no particular rationing rule is imposed some mild restrictions are placed on the firms sales functions instead the commonly used models of levitan and shubik 1972 and beckman 1965 are special cases of the games analysed below it is assumed throughout that there is a price firms can be induced to charge if the punishment for charging a different price gives the offending firm a payoff equal to its security level for the supergame thus either there must exist a static nash equilibrium in pure strategies or else the discount factor must not be too close to zero in section 3 optimal penal codes are constructed and it is established that the punishments comprising them always drive punished firms to their security levels the arguments employed make clear that optimal penal codes are not generally unique this issue is addressed in section 4 where it is also shown that the levitan shubik rationing rule exhibits more types of optimal penal codes than do other rules in particular if the levitan shubik rule is employed then punishments that are analogous to abreu s 1986 symmetric two phase punishments for cournot games can be used to construct optimal penal codes in bertrand games this property does not hold generally however

black agricultural economists in the labor market theoretical and empirical issues the american economic association aea and the american agricultural economics association aaea have had a long tradition of monitoring the labor market characteristics for economists and agricultural economists evaluations of labor market conditions for economists are represented by the works of breneman and kleinman clague and levine tolles jones and clague and tolles and melichar labor market characteristics for agricultural economists have been evaluated by helmberger melichar schotzko lee broder and ziemer and strauss and tarr it is somewhat surprising however given the emphasis on resource allocation efficiency and equity among economists that no comprehensive research has been conducted on the labor market characteristics of black economists and agricultural economists despite the failure of economists to apply their analytical tools to the issues of participation by blacks in the economists labor market it is significant that the aea demonstrated awareness of the problem and issues in this area in 1969 when it sponsored a session entitled increasing the supply of black economists at its annual meeting at this session boulding argued cogently that the cultureboundness of economists was an obvious factor associated with the profession s neglect of problems of particular interest to disadvantaged racial and cultural groups concurrently chandler addressed the status of blacks in the economics profession and presented an affirmative action plan for the profession

neoclassical and marxian conceptions of production incorporating information deficiencies into the neoclassical paradigm has introduced some broad similarities with the marxian analysis of the labor process both approaches predict the existence of a variety of contractual regimes and that workers with equal productivities can be adjudged unequal in the market place and while the marxian approach sees unemployment as inevitable the new neoclassical models also allow for equilibrium unemployment these similarities and areas of divergence in the assessment of productive efficiency and welfare are explored a crucial difference arises from the individualism of the neoclassical model as opposed to the class approach in the marxian model copyright 1988 by oxford university press

behavioral demand effects when buyers anticipate inventory shortages abstract firms often worry about how buyers will react when there is an inventory shortage but the anticipation of facing a shortage may also impact buyer behavior in this paper we use a combination of theoretical modeling computational methods and laboratory experiments to understand buyers search behavior in markets where there is potential for either a costly or costless inventory shortage when inventory shortages are costly to buyers we find their equilibrium purchasing strategy generates a newsvendor problem among the firms in turn experimental data suggests buyer behavior can be explained by prospect theory better than by standard assumptions of fully rational expected utility maximizing agents indicating that potential inventory shortages generate loss aversion among buyers and there is systematic mis identification of the probability with which they will be able to procure an item using computational methods we find firms are able to extract more surplus from behavioral buyers via higher prices than would be predicted by the standard model on the other hand when inventory shortages are not costly to buyers the effect of behavioral biases on the part of buyers is not relevant but in this case there can be a benefit to reducing inventory via a reduction in price competition

fiscal versus traditional market variables in canadian migration this paper evaluates the hypothesis that the influence of traditional market variables on migration in canada has diminished over time this is attributed to a crowding out process whereby growth of social security type programs has cushioned the effects of say unemployment and thus motivation to migrate for jobs and fiscal policies have exerted unintended effects implications are that market forces that would work naturally to induce migration from low to high income regions and thus equalize earned incomes have been short circuited and that traditional tools of manpower policy for influencing migration such as job creation skill enhancement or wages are less effective currently than they might have been in the past

bertrand equilibria with entry limit results abstract we study the limiting behaviour of bertrand equilibria where firms must supply the whole of the demand coming to them for two different cases first when entry is exogenous and second when it is free the limit equilibrium set is characterised for both cases for a large class of cost functions

asymmetric price adjustments a supply side approach using a model of dynamic price competition we provide an explanation from the supply side for the well established observation that output prices react faster in response to input cost increases than to decreases when costs decline the opportunity of profitable storing in anticipation of higher future costs allows competitive firms to coordinate on prices above current marginal costs the initial price response is only partial and profitable storing relaxes competition conversely when costs rise storing is not beneficial in anticipation of lower future costs and firms immediately adjust their prices to current marginal costs which entails the standard bertrand outcome our results shed new light on the empirical evidence about asymmetric pricing and can stimulate further empirical investigation on this puzzle

price setting supergames with capacity constraints this paper examines the role of industry capacity in enforcing collusion in the context of repeated games for a fixed capacity per firm it is shown that changes in the number of firms have a non monotone effect on the best enforceable cartel price this is due to the fact that while an additional firm lowers the share that each of the other firms enjoys at the collusive price it also increases the losses to each firm should the cartel fail

plant closings and exit behaviour in declining industries the plant closing and exit strategies of firms operating in a declining industry are examined a dynamic game theoretic model is utilized the perfectness criterion is used to restrict the set of nash equilibria there are two key equilibrium results first when firms have the same number of plants high cost plants close before lower cost plants second a larger firm i e a firm operating more plants begins closing plants before a smaller firm as long as cost differences are not large copyright 1988 by the london school of economics and political science

general equilibrium theory with imperfect competition abstract this survey is organized as follows i introduction ii the main issues iii negishi s model iv objective demand in the cournot nash framework v objective demand in the bertrand nash framework vi the assumption of quasi concavity of the profit functions vii compromises between the conjectural and the objective approach viii insights into the notion of perfect competition ix conclusion

industrial organization and public policy competition policy has been dominated by politics industrial organization can expect to exert an influence only insofar as it commands superior knowledge that is true with respect to the long run since economies of scale are limited to the short run competition is feasible in the long run therefore a trade off approach seeking to identify optimal market structures is misleading competition policy should instead be directed at prohibiting protective strategies of incumbents to deter entry competition being a process of creative destruction political viability of a competitive order requires competition policy to be supplemented by a social welfare policy

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

bertrand the cournot paradigm and the theory of perfect competition in this paper we extend to a general equilibrium context bertrand s classic critique of cournot we present a game theoretic model of a pure exchange monetary economy in which buyers as well as sellers announce both quantities and prices when buyers act strategically the edgeworth nonexistence problem is circumvented under weak conditions a pure strategy nash equilibrium exists for this game we make precise the bertrand idea that when agents in a finite economy are permitted to compete by price the resulting allocations will be competitive specifically the nash equilibria for our game yield allocations that are competitive allocations for the underlying exchange economy provided that there are at least two buyers and two sellers actively trading in every market under this characterization of strategic behaviour then two is enough for competition our objective is to provide a general equilibrium game theoretic formulation of the idea of bertrand price competition bertrand s classic critique of cournot can be paraphrased as follows when agents regard price rather than quantity as the strategic variable no price above the competitive equilibrium price can be sustained as a noncooperative equilibrium this idea is made precise in our game theoretic model of a pure exchange economy in which buyers as well as sellers act strategically our treatment of buyers behaviour is novel while sellers announce price and quantity vectors buyers specify sums of money and menus of alternative nonmonetary commodity bundles a buyer s action is a commitment to purchase any one of the specified commodity bundles in exchange for the sum of money our first result is that under weak conditions a nash equilibrium in pure strategies exists the paper thus also points to a way of resolving the classical edgeworth nonexistence problem second all nash equilibria yield allocations that are competitive for the underlying economy provided that in every market at least two buyers and two sellers are actively trading under this characterization of strategic

how do competitive pressures affect incentives to innovate when there is a market for inventions competition and intellectual property ip protections are complements in stimulating innovation when ip is appropriable a market for inventions forms and competitive pressures increase incentives to innovate competition among producers the demand side of the market for inventions and competition among inventors the supply side of the market for inventions create incentives to innovate when ip is not fully appropriable markets for inventions are limited and competitive pressures can decrease incentives to innovate firms vertically integrate r d and production and share technology to appropriate the returns to ip this implies that antitrust policy and ip protections are complements

portfolio manager behavior and global financial crises abstract i develop a two market agent based model to study how global portfolio managers affect global financial crises and stability first i create an agent based model where fund managers make their allocation decisions between two markets and a risk free asset based on the mean variance framework simulation results reveal that global managers do not create global financial crises second i extend the base model by incorporating insights from behavioral finance where risk is instead determined by fund manager losses simulation results reveal that slight global manager losses can trigger a widening of both markets risk premium accelerating the decline in asset prices worldwide statistical analysis reveals that global managers are a stabilizing force in smaller numbers however they become destabilizing in larger numbers the ability to reduce risk by diversifying across markets results in excessive risk taking if global managers exist in larger numbers systematic over leverage may result such that a deleveraging process can lead to the spreading of financial crises

price quantity strategic market games this paper is yet another in a rapidly growing series e g 2 11 on strategic approaches to economic equilibrium our aim here is to make precise the remark implicitly due to bertrand 1 or 10 ch 4 5 that if the agents in an economy use price setting strategies then the strategic nash equilibria will in fact be walrasian and this without any assumption of a large number of small agents however in our models not only prices but also quantities are set by the agents thus it might actually be more appropriate to call them bertrand cournot types of models we begin with a standard walras exchange economy with a finite number of traders and commodities this is recast as a game in strategic form in essentially two different ways there is a trading post for each commodity to which traders send contingent statements about how much they wish to buy and sell and at what prices in model 1 the trading point is determined by the intersection of the aggregate supply and demand curves in model 2 trade takes place so as to meet as many contingent statements as possible each buyer whose orders are filled pays the price he quoted using a fiat money which can be borrowed costlessly and limitlessly but after trade is over there is a settlement of accounts and a penalty is levied on those who are bankrupt no attempt is made to model the penalty in any detail it is simply described in the form of a disutility but this in turn may be imagined to stem from confiscation of assets see remark 5 or the necessity of procuring highly priced loans etc call a noncooperative equilibrium active if it turns out that no trader is isolated i e trapped as the sole buyer or seller at some trading post then our results may be described as follows in model 1 the active2 n e of the game coincide with the c e of the market furthermore there is a subset of tight active n e which also coincide with the c e and each n e in this subset is strong

understanding rent dissipation on the use of game theory in industrial organization game theory has had a deep impact on the theory of industrial organization in a similar but less controversial way as the rational expectations revolution in macroeconomics the reason it has been embraced by a majority of researchers in the field is that it imposes some discipline on theoretical thinking it forces economists to clearly specify the strategic variables their timing and the information structure faced by firms as is often the case in economics the researcher learns as much from constructing the model the extensive form as from

tail expectation and imperfect competition in limit order book markets abstract perfect competition in liquidity provision in limit order markets is characterized by a tail expectation condition glosten 1994 in this paper we model imperfect competition in schedules by infinitely many liquidity suppliers quoting on a limit order book we show that there are zero rent mixed strategy equilibria featuring finite numbers of active liquidity suppliers none of the equilibria satisfies the competitive outcome not even on average considering a sequence of equilibria with the number of active liquidity suppliers becoming large we show that the aggregate stochastic marginal price schedule converges to the deterministic competitive marginal price schedule

stability in large bayesian games with heterogeneous players bayesian nash equilibria that fail to be hindsight or alternatively ex post stable do not provide reliable predictions of outcomes of games in many applications we characterize a family of large bayesian games with many players in which all equilibria are asymptotically hindsight stable and discuss the consequences of this robustness property in contrast to earlier literature we establish hindsight stability in a class of games in which players are not anonymous and type spaces and action spaces can be infinite

oscillations in the rodriguez model of entry and price dynamics abstract this paper is concerned with improving the existence of limit cycles in rodriguez s industry evolution model approximate expression period and stability conditions of the permanent oscillations near the equilibrium are explicitly found by applying the bifurcation method of iooss and joseph

the existence of equilibrium in discontinuous economic games ii applications in part i of this study we established two existence theorems for mixed strategy equilibrium in games with discontinuous payoff functions see theorems 4 4 and 5 5 in dasgupta and maskin 1986 hereafter d m 1986 in this second part we use the second of these two theorems to prove the existence of mixed strategy equilibrium in some wellknown discontinuous economic games that fail to have pure strategy equilibria the models we analyse are the bertrand edgeworth example of price setting duopolists with capacity constraints see section 2 2 price competition among firms producing differentiated products hotelling 1929 and d aspremont gabszewicz and thisse 1979 see section 2 3 spatial competition eaton and lipsey 1975 and shaked 1975 see section 3 and models of market dependent information rothschild and stiglitz 1976 and wilson 1977 section 4 the paper concludes section 5 with a classification of these models

bertrand edgeworth equilibrium large markets with non manipulable residual demand abstract in a model of price competition among capacity constrained firms with non manipulable residual demand we demonstrate that if the number of firms is large then the unique equilibrium yields the competitive price the result goes through even when firms produce to order

walrasian and marshallian stability abstract it is well known that there is no direct relation between stability of the walrasian t tonnement process and stability of the marshallian quantity adjustment process it is shown that if short run walrasian t tonnement with a given number of firms is distinguished there is under the assumption of no joint production local stability of the short run walrasian adjustment process if and only if there is local stability of the long run marshallian adjustment process with exit and entry of firms according to profit levels

the efficiency of monopolistically competitive equilibria in large economies commodity differentiation with gross substitutes abstract a general model of commodity differentiation is developed using two different approaches to the theory of demand it is shown that a local version of bertrand s argument holds under reasonable conditions if all commodities are sustitutes and sunk costs are small there is never too little commodity differentiation relative to the optimum under the same conditions monopolistically competitive equilibria are approximately perfectly competitive if the optimal collection of commodities is sufficiently rich

general equilibrium with free entry a synthetic approach to the theory of perfect competition the purpose of this essay is to explain a new theory of perfect competition that synthesizes the arrow debreu mckenzie and marshallian theories and summarizes the recent work of a large number of researchers the synthetic theory provides a logically precise general equilibrium framework that can be used both for positive analysis as well as to form a basis for the classical theorems of welfare economics in these aspects it follows the adm theory however as in the marshallian theory there is free entry in the form of an unbounded pool of firms which have access to the existing technology also as in the marshallian theory the average cost curves available to each firm are u shaped in contrast to both the marshallian and the adm theories we do not take price taking as a hypothesis we use the term perfect competition to describe a situation in which firms are arbitrarily small relative to the markets in which they are involved the firms in our model correctly perceive the effect of the amount that they place on the market on prices and they act to maximize profit with this in mind perfectly competitive equilibria are defined as the limit points of equilibria as firms become small relative to the market and following cournot we observe that as firms become small their ability to influence price disappears a new condition is identified which is important for the viability of competitive markets loosely speaking this condition requires that prices provide the proper entry signals for firms if one thinks of each firm as associated with the use of an unpriced and nondivisible resource sometimes referred to as entrepreneurship then in equilibrium the returns to that factor must fall with entry and rise with exit not only the stability theorems of the synthetic theory but also the existence theorem reject the application of the competitive model to a regime in which entry drives up and exit reduces the profit of similar firms

labor market segmentation to what paradigm does it belong the dictionary defines a paradigm as a model or pattern in grammar an example of a conjugation or declension showing a word in all its inflectional forms a paradigm is thus a practical example which perfectly illustrates an abstract principle its hallmark in this dictionary definition is the complete correspondence between the abstract and the applied between theory and praxis the term was adapted to the discussion of scientific theory by thomas kuhn and its current vogue in economics is attributable directly to his book as kuhn used the term paradigm retains its double meaning of theory and of praxis but the relationship between the two becomes ambiguous scientists believe kuhn seems to argue that their inquiry is based upon a theory of how the world operates and how the investigation of its operation ought to proceed but normal science is in fact largely a set of practices in which members of a given scientific community customarily engage students seeking to follow their professors in careers in which the latter will judge them and ultimately determine their fate are not encouraged to andertake projects which depart radically from those which their professors conceive for them when suggestions for such projects trise either from students or competing nembers of the community they are as often reated by sarcasm and ridicule as the subect of seasoned discourse and debate in this rocess what students acquire is less an abtract understanding of what they are doing han a set of habits or instincts about what constitutes a legitimate mode of inquiry or a plausible explanation the disjuncture between theory and practice which arises in this way creates the potential for a scientific revolution to ask in this context about the paradigm to which notions of labor market segmentation belong is thus to ask a question about the relationship between that mode of research and the theory and practice of normal economics i never considered myself a revolutionary indeed quite the contrary but as an exponent of labor market segmentation in the community of normal economics i can assure you that labor market segmentation does not fit the paradigm the sentiments and reactions which kuhn tells us greet the abnormal and aparadigmatic in a discipline that is fury disdain resentment sarcasm and condescension have definitely greeted labor market segmentation this is a matter of fact an observation about praxis the question is then what aspect of the conceptual structure of the discipline accounts for this practical result in most discussions labor market segmentation is contrasted with human capital theory but this does not account for the hostile reception it has received it fails first because the treatment accorded market segmentation by the profession is not that different from the treatment accorded human capital when it first appeared gary becker describes his personal experience on this score in the introduction to his book of essays the economic approach to human behavior and the disdain and antagonism which he attributes to his colleagues are at least as great as anything experienced by the proponents of segmentation but perhaps more fundamentally the two views are not as we shall see shortly necessarily in conflict professor of economics mitsui professor for probems of contemporary technology massachusetts intitute of technology

rationing rules and bertrand edgeworth equilibria in large markets abstract in a market with concave downward sloping demand and symmetric firms which compete in prices with constant marginal costs and capacity limits it is shown that the supports of the symmetric mixed strategy nash equilibria converge to the unique competitive price provided that unsatisfied demand is allocated according to the surplus maximizing rationing rule

a theory of dynamic oligopoly ii price competition kinked demand curves and edgeworth cycles we provide game theoretic foundations for the classic kinked demand curve equilibrium and edgeworth cycle we analyze a model in which firms take turns choosing prices the model is intended to capture the idea of reactions based on short run commitment in a markov perfect equilibrium mpe a firm s move in any period depends only on the other firm s current price there are multiple mpe s consisting of both kinked demand curve equilibria and edgeworth cycles in any mpe profit is bounded away from the bertrand equilibrium level we show that a kinked demand curve at the monopoly price is the unique symmetric renegotiation proof equilibrium when there is little discounting we then endogenize the timing by allowing firms to move at any time subject to short run commitments we find that firms end up alternating thus vindicating the ad hoc timing assumption of our simpler model we also discuss how the model can be enriched to provide explanations for excess capacity and market sharing keiiwords tacit collusion markov perfect equilibrium kinked demand curve edgeworth cycle excess capacity market sharing endogenous timing

conspicuous consumption dynamics abstract we formalize veblen s idea of conspicuous consumption as two alternative forms of interdependent preferences dubbed envy and pride agents adjust consumption patterns gradually in the direction of increasing utility from an arbitrary initial state the distribution of consumption among agents with identical preferences converges to a unique equilibrium distribution when pride is stronger the equilibrium distribution has a right skewed density when envy is stronger the equilibrium is concentrated at a single point and the adjustment dynamics involve a shock wave that can be interpreted as a growing moving homogeneous middle class

bertrand edgeworth duopoly with proportional residual demand a complete characterization is given for the prices charged by bertrand edgeworth duopolists with capacity constraints in general for the game in which firms strategy spaces consist of price offers nash equilibrium involves nondegenerate mixed strategi es equilibria never extend below the highest competitive price with tw o firms the bertrand edgeworth model displays a bias for the highest of several market clearing prices moreover these strategies never stop short of the lowest monopoly price if firms are of unequal siz e the larger firm assigns positive probability to a monopoly price possibly even to several monopoly prices copyright 1993 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

large scale service marketplaces the role of the moderating firm recently large scale web based service marketplaces where many small service providers compete among themselves in catering to customers with diverse needs have emerged customers who frequent these marketplaces seek quick resolutions and thus are usually willing to trade prices with waiting times the main goal of this paper is to discuss the role of the moderating firm in facilitating information gathering operational efficiency and communication among agents in service marketplaces surprisingly we show that operational efficiency may be detrimental to the overall efficiency of the marketplace furthermore we establish that to reap the expected gains of operational efficiency the moderating firm may need to complement the operational efficiency by enabling communication among its agents the study emphasizes the scale of such marketplaces and the impact it has on the outcomes this paper was accepted by yossi aviv operations management

price competition in a capacity constrained duopoly abstract this paper characterizes the set of nash equilibria in a model of price setting duopoly in which each firm has limited capacity and demand is continuous and decreasing in general there is a unique equilibrium so that comparative static exercises are meaningful the properties of the equilibrium conform with a number of stylized facts the equilibrium prices are lower the smaller is demand relative to capacity when demand is in an intermediate range the firms use mixed strategies they randomly hold sales if capacities are chosen simultaneously before prices the set of equilibrium capacities coincides with the set of cournot quantities

determining the appropriate depth and breadth of a firm s product portfolio abstract some firms have broad product lines others have lean product lines to determine the appropriate number of entries in a specific firm s product line the author develops a model that balances the benefits of increased revenue from a broad product line against production and engineering costs two innovations were central in the development of the model 1 redefining how products are scored on various product attributes so that attribute scores vary normally across the population of products and 2 redefining how the number of entries in a product portfolio is calculated in order to discount the significance of entries that are highly similar to existing products the author also introduces the notion of a centroid time to more easily adjust sales and total development costs for product life cycle and investment life cycle effects these redefinitions enable a firm s profit to be modeled as a simple function of its effective number of product entries the effective number of competitors entrie

a two stage bertrand edgeworth game abstract in our investigation we are expanding a bertrand edgeworth duopoly into a two stage game in which during the first stage the firms can select their rationing rule we will show that under certain conditions the efficient rationing rule is an equilibrium action of the first stage

perfectly competitive markets as the limits of cournot markets a perfectly competitive partial equilibrium market for a single homogeneous good with a bounded continuum of infinitesimal firms is considered cost functions are essentially unrestricted and are allowed to vary smoothly across firms a sequence net of cournot markets each with a finite number of firms which converge smoothly to the perfectly competitive limit in terms of both the inverse demand functions and the distributioon of firm technologies is introduced and it is shown that all markets sufficiently far along the sequence have a cournot equilibrium and all the cournot equilibria converge to the perfectly competitive equilibrium of the limit market

approximate bertrand equilibria in a replicated industry this paper considers the existence and properties of approximate bertrand equilibria in a replicated industry price setting firms produce a homogeneous product with weakly convex costs the main results are that a given e 0 an e equilibrium exists if the industry is large enough b if the e is small enough and the industry large enough any e equilibrium is approximately competitive these results depend on how contingent demand is specified

the elasticity of scale and the shape of average costs different concepts of returns to scale the first which is most widely used for defining returns to scale is the relative increase in output as all input quantities are increased proportionally along a ray through the origin the second which is the more relevant concept for micro economic analysis is the increase in output relative to costs for variations along the expansion path where input prices are constant and costs are minimized at every output 2 as it turns out these two concepts yield equal measures for the elasticity of scale3 e at every minimum cost point in the input space however the change in e with output is generally different for the two concepts 4 since expansion paths do not coincide with rays unless the production function is homothetic 5 but it is the change of e along the expansion path and not along the raywhich determines the shape of the average cost curve ac and which is therefore relevant for the analysis of firms and industry behavior under competition 6 these relations are stated and analyzed below it is shown that assumptions made in the literature7 which are related to the behavior of e along rays or to the slope of the technically optimal surface where returns to scale are locally constant are irrelevantbeing neither necessary nor sufficient for implying classical u shaped average cost curves the following definitions and results are used here

bertrand edgeworth equilibria with unobservable output uncoordinated consumers and large number of firms abstract we examine a bertrand edgeworth model of price competition where the output levels of the firms are unobservable and consumers are uncoordinated we show that if the number of firms is large enough then any price greater than the competitive one can be sustained as a pure strategy nash equilibrium

the existence of equilibrium in discontinuous economic games i theory the article presents information about the existence of equilibrium in discontinuous economic games in this paper and its sequel presents study the existence of nash equilibrium in games where agents payoff functions are discontinuous the enquiry is motivated by a number of recent studies that have uncovered serious existence problems in seemingly innocuous economic games in the sequel to this paper authors have explained the utility function in the economic games referred to earlier are neither continuous nor quasi concave however they demonstrate that the payoff functions in mildly modified versions of these constructs exhibit two weaker forms of continuity which together with the requirement of quasi concavity suffice for the existence of an equilibrium from this one may conclude that at least in the modified versions of these models discontinuities in the payoff functions are not the real source of the problem rather it is the failure of the payoff functions to the quasi concave which is responsible for the non existence of equilibrium these observations bear on the existence of nash equilibrium in pure strategies

the existence of mixed strategy equilibria in a price setting oligopoly with convex costs this paper shows that a mixed strategy equilibrium will exist in an industry producing a homogeneous product with perfectly informed consumers if firms are identical and have weakly convex costs this generalises an earlier result by dasgupta and maskin

on the strategic importance of prices versus quantities in this article i investigate three single shot models of differentiated products oligopoly in each model firms choose both output and price the demand cost and spillover demand specifications are quite general and there are three main results first with simultaneous choice there is no pure strategy noncooperative equilibrium second with output chosen first and announced to all firms before the choice of price equilibrium sometimes exists and when it does it is the same as in a quantity only model third with price chosen and announced first equilibrium always exists and is the same as in a price only model

existence of pure strategy nash equilibrium in bertrand edgeworth oligopolies abstract this article is searching for necessary and sufficient conditions which are to be imposed on the demand curve to guarantee the existence of pure strategy nash equilibrium in a bertrand edgeworth game with capacity constraints

micro adjustment toward long term equilibrium abstract a dynamic model is constructed in which the behavior of economic agents is based on adjustment decisions are made in disequilibrium prices respond to differences between supply and demand inventories capital is moved according to profitability differentials and money is issued by a bank which reacts to the general price level a proof of local stability of long term equilibrium with production prices is demonstrated we further distinguish between two aspects of the stability problem concerning the allocation of capital and relative prices stability in proportions and with respect to the general levels of activity and prices stability in dimension

a test of dual labor market theory despite substantial differences in their views of the appropriate policy response to the existence of poverty neither the proponents of dual market theory nor its critics have proposed potentially conclusive tests of the dual market hypothesis this paper presents a test of the two central propositions of dual market theory 1 the existence of two distinct labor markets with different wage setting mechanisms and 2 the existence of barriers to mobility between the labor markets we find considerable support for both hypothesis estimation of a switching model of wage determination with unknown regimes yields two distinct wage equations the one which most workers are associated with closely resembles the standard human capital regression with significant returns to education and experience the other equation is flat with no returns to human capital these two equations resemble the predictions of dual market theory for the primary and secondary markets respectively further we present evidence that at least some non white workers are involuntarily confined to the secondary market this crowding of minority workers into the low wage labor market accounts for a substantial portion of white non white wage differences we interpret these results as providing empirical support for the dual market hypothesis and for recent theoretical work on efficiency wagemodels in addition combining the efficiency wage argument with the observation that much of the white non white wage difference is explained by the exclusion of non whites from the primary sector suggests an explanation for the persistance of wage differences this abstract was borrowed from another version of this item

pricing in revenue management for multiple firms competing for customers abstract we consider the pricing strategies of multiple firms providing the same service in competition for a common pool of customers in a revenue management context the firms have finite capacity and the demand at each firm depends on the selling prices charged by all firms each of which satisfies demand up to a given capacity limit we use game theory to analyze the systems when firms face either a deterministic demand or a general stochastic demand the existence and uniqueness conditions of a nash equilibrium are derived and we calculate the explicit nash equilibrium point when the demand at each firm is a linear function of price we also conduct sensitivity analysis of the equilibrium prices with respect to cost and capacity parameters

iterated elimination of dominated strategies in a bertrand edgeworth model we consider a bertrand edgeworth model of price competition firms have identical and constant marginal costs and finite exogeneous capacities firms choose prices our interest is in the set of those prices which are left over after the iterated elimination of dominated strategies we show that in two circumstances this set will be close to the set containing only the marketclearing walrasian price i if any n 1 out of n firms assumed to be in the market have sufficient capacity to cover demand at marginal costs ii if any given total capacity is owned by a very large number of very small firms

production location decision and free entry oligopoly abstract this paper presents a simple oligopolistic model of location in which all firms in an imperfectly competitive industry are assumed to produce a homogeneous output and make cournot conjectures about their rivals input and location decisions within this framework this paper points out that the key difference between oligopoly and monopoly is the following in the case of monopoly a positive shift in demand requires that a monopolist increase his output but in the case of oligopoly an increase in industry output may or may not increase output per firm because of the number of firms at free entry equilibrium is not constant it is shown that in an oligopoly model of location that allows free entry the demand condition plays an important role on the determination of industrial location

collusion in a price quantity oligopoly abstract in the context of an infinitely repeated oligopoly game we study collusion among firms that simultaneously choose prices and quantities we compare a price cartel with a price quota cartel and analyze when and why firms prefer the latter to the former output quota may be required to solve coordination and incentive problems when market demand is sufficiently elastic if market demand is sufficiently inelastic then the cartel faces a trade off between increasing prices and the amount of costly overproduction we find that a price cartel prices consistently below the monopoly price to mitigate excessive production in this case a quota arrangement allows firms to avoid overproduction and to sustain the monopoly price from a policy perspective our findings suggest that an overall price increase in conjunction with more stable prices and market shares is indicative of collusion in industries where production precedes sales and outputs are imperfectly observable

market size and substitutability in imperfect competition a bertrand edgeworth chamberlin model competition is often associated with the idea that there are many traders in the market or that each price maker is small as compared to the market this paper introduces this notion of market size in a model of price competition with imperfect substitutes by constructing a model which creates a bridge between the chamberlin and bertrand edge worth lines of work on price competition we investigate the role of two fundamental parameters in the existence of an equilibrium the market size given by the number n of competitors and the degree of substitutability we prove that a for a given number of n 2 of competitors a sufficiently large but finite degree of substitutability entails nonexistence this thus generalizes the bertrand edgeworth nonexistence result which applies only to perfect substitutes b conversely for a given upper bound on the degree of substitutability a sufficiently large number of competitors ensures existence which thus introduces a significant role for market size in models of imperfect competition we finally investigate the proximity of an equilibrium when it exists to a competitive outcome and we find that both high substitutability and large market size are a condition for competitiveness

nonuniform bertrand competition the feasibility of bertrand undercutting with nonuniform prices is established and properties are derived for bertrand equilibrium in nonuniform price strategies with free entry equilibrium entails zero profit minimum average cost production if there is more than one producing firm all prices collapse to a minimum average cost uniform price an existence condition is compared to conditions from uniform price theory without free entry equilibrium prices may not collapse to a uniform price positive profit may occur but all firms earn equal profit and incur equal marginal cost while consumers pay average outlay no greater than marginal cost copyright 1992 by the econometric society

location and the theory of the imperfectly competitive firm under demand uncertainty there is a large and growing literature on location and the theory of the firm in a heterogeneous space i e in the space where markets are given at discrete points such as weber 22 isard 7 moses 15 sakashita 18 19 bradfield 3 emerson 5 woodward 23 khalili mathur and bodenhorn 8 miller and jensen 14 mathur 13 eswaran kanemoto and ryan 6 and mai and shieh 11 what is perhaps surprising is that within this large body of literature nothing has been said about how the firm would and should locate theoretically under conditions of uncertainty it only with webber 21 and mai 10 that any real indication is given that uncertainty due to imperfect market information may exert an influence on locational choice in particular mai 10 presented a formal mathematical model to show that the results and implications of the optimum location of the firm under demand uncertainty is different from that applicable to the state of certainty however mai s analytical framework is restricted to the case of pure competition where price is given all buyers are assumed to be concentrated at given market point and each firm seeks to minimize expected cost and is thus risk neutral the purpose of this paper is to extend the location theory of the competitive firm under demand uncertainty to the case where the imperfectly competitive quantity setting firms are not risk neutral and are interested in maximizing expected utility from profit including cost and demand factors 2 this expected utility approach will provide a more general formulation of the firm s attitude toward risk for analyzing its location decisions the basic model evaluating the firm s location and input choices is presented in section ii section iii examines the overall impacts of demand uncertainty on the optimum location and input demands the effect of a marginal increase in demand uncertainty on the optimum location is investigated in section iv section v analyzes the effect on the optimum location of a change in the expected output price section vi then evaluates the

market making oligopoly this paper analyzes price competition between market makers who set costly capacity constraints before they intermediate between producers and consumers the unique equilibrium outcome with pure strategies at the capacity stage is the cournot outcome the paper thus provides a rationale for cournot type competition between market makers this contrasts with previous findings in the literature where due to the absence of capacity constraints that are set ex ante the bertrand result typically obtains

bertrand edgeworth equilibria when firms avoid turning customers away this paper provides a simple solution to the problem of nonexistence of pure strategy equilibria in bertrand edgeworth models with strictly convex costs the voluntary trading constraint in standard bertrand edgeworth models is generalized to allow for there being costs incurred when customers are turned away so long as the industry is sufficiently large the presence of such costs ensures that the competitive price will be an equilibrium there will be other single price equilibria but if the offense costs are small all equilibria will be close to the competitive outcome

walrasian equilibria as limits of noncooperative equilibria part ii pure strategies abstract we examine the connection between walrasian equilibria of a limit economy with infinitesimal firms and noncooperative cournot equilibria of approximating finite economies with significant firms nonconvex production sets decreasing returns in the aggregate and endogenous determination of the number of active firms are allowed a walrasian equilibrium is a limit of pure strategy noncooperative equilibria only if a condition loosely analogous to downward sloping demand in the partial equilibrium constant returns to scale case holds the condition is also sufficient to guarantee the existence of a robust sequence of pure strategy noncooperative equilibria which converges to the walrasian equilibrium

bertrand edgeworth equilibrium with a large number of firms abstract we examine a model of price competition with strictly convex costs where the firms simultaneously decide on both price and quantity are free to supply less than the quantity demanded and there is discrete pricing if firms are symmetric then for a large class of residual demand functions there is a unique equilibrium in pure strategies whenever for a fixed grid size the number of firms is sufficiently large moreover this equilibrium price is within a grid unit of the competitive price the results go through to a large extent when the firms are asymmetric or they are symmetric but play a two stage game and the tie breaking rule is weakly manipulable

entry and price dynamics in a perfect foresight model abstract this paper studies firms entry and price dynamics in a model that combines the assumptions of free entry and perfect foresight with the hypothesis of consumer s loyalty postulated by phelps and winter the analysis of the transition to long run equilibrium reveals that in such a model the entry of firms is related to the difference between current prices and costs in relation to the growth of the firms output it is shown that the model is consistent with gibrat s law finally it is shown that the size distribution of firms approaches asymptotically a pareto distribution

bertrand edgeworth oligopoly in large markets the relation between perfectly competitive and monopolistically competitive equilibria is analysed for a bertrand edgeworth model of a single market in which capacity constrained firms choose prices as strategies the market always has a nash equilibrium in pure or mixed strategies as the number of firms increases the corresponding equilibria converge in distribution to a perfectly competitive price this result provides a justification for perfect competition that is based on an explicit account of price formation however monopoly prices persist with a positive but vanishing probability regularity or well defined inverse demand functions are not required

pricing non storable perishable goods by using a purchase restriction with an application to airline fare pricing abstract the aim of this paper is to address the pricing problem of non storable perishable goods or services such as airline seats and hotel rooms by incorporating the use of purchase restrictions such as the advance booking requirement that is commonly used by airlines and hotels we will show that there exists an optimal pricing policy of at most three prices which can be obtained by solving a series of linear programming problems we will demonstrate that when applied to airline fare pricing the monotonicity condition of the model is equivalent to the requirement that business travelers are less price elastic than leisure travelers we will further illustrate the applicability of the model through a numerical example in the context of airline fare pricing by incorporating the impact of various fences

constrained choices under risk there has recently been a revival of interest in the implications of rationing for economic theory extending the work of samuelson 21 tobin and houthakker 24 and pollak 16 recent papers by bruno 3 howard 8 latham 13 and neary and roberts 15 have explored the theory of producer and consumer behavior under quantity rationing these developments have provided useful hypotheses in the investigation of economic behavior for example they have stimulated a reexamination of macroeconomic disequilibrium however previous work seems to have focused on economic models in the absence of uncertainty yet given that production decisions are often made before output prices are known and in the absence of complete contingent markets sandmo 22 batra and ullah 2 and others have developed the theory of the competitive firm under price uncertainty under the expected utility maximization hypothesis such a theory provides useful information about the influence of changing economic conditions or of risk behavior on production decisions but because of the presence of short run adjustment costs leading to short run input fixity or because of regulatory or institutional constraints quantity rationing often influences production decisions in order to evaluate how rationing influences such decisions there is a need to develop a conceptual model of constrained choices of the firm under risk the objective of this paper is to explore the implications of quantity rationing in the context of production theory under price uncertainty by introducing risk and risk behavior it extends the classical analysis of quantity constrained production decisions 3 21 the implications of quantity constraints for risk responsive choice functions are derived using the concepts of compensated choice functions and virtual prices it is shown that expected price effects can be decomposed into substitution effects and wealth effects the substitution effects measure the effects of a change in expected price on the compensated choice functions the compensation being made through a change in initial wealth holding expected utility constant the wealth effects characterize risk preferences since a non zero wealth effect reflects a departure from an arrow pratt constant absolute risk aversion utility function the influence of rationing on the properties of ordinary as well as compensated choice functions is analyzed in details by deriving the implications of quantity constraints for firm behavior under uncertainty the paper presents a number of useful results concerning the influence of risk or technology on economic behavior under rationing for example a

the contestable outcome as a bertrand equilibrium abstract we consider a bertrand duopoly with increasing returns to scale where firms simultaneously decide on their prices and outputs the unique equilibrium of this game yields the contestable outcome

bubbles and crashes gradient dynamics in financial markets abstract fund managers respond to the payoff gradient by continuously adjusting leverage in our analytic and simulation models the base model has a stable equilibrium with classic properties however bubbles and crashes occur in extended models incorporating an endogenous market risk premium based on investors historical losses and constant gain learning when losses have been small for a long time asset prices inflate as fund managers increase leverage then slight losses can trigger a crash as a widening risk premium accelerates deleveraging and asset price declines

list pricing and discounting in a bertrand edgeworth duopoly list or retail pricing is a widely used trading institution where firms announce a price that may be discounted at a later stage competition authorities view list pricing and discounting as a procompetitive practice we modify the standard bertrand edgeworth duopoly model to include list pricing and a subsequent discounting stage both firms first simultaneously choose a maximum list price and then decide whether to discount or not in a subsequent stage we show that list pricing works as a credible commitment device that induces a pure strategy outcome this is true for a general class of rationing rules further unlike the dominant firm interpretation of a price leader the low capacity firm may have incentives to commit to a low price and in this sense assume the role of a leader

behavioral heuristics and market patterns in a bertrand edgeworth game abstract this paper studies bertrand price setting behavior when firms face capacity constraints bertrand edgeworth game this game is known to lack equilibria in pure strategies while the mixed strategy equilibria are hard to characterize we explore families of heuristic rules for individual price setting behavior and the resulting market patterns through simulations of agent based models and laboratory experiments overall the individual pricing strategies observed experimentally can be represented approximately by a sales based simple rule in the experiments average market prices tend to converge from above and approach a state resembling a steady state with slow aggregate price variations and low price dispersion around an average near the competitive level however that configuration can be disturbed occasionally by excursions triggered by discrete price raises of some agents salient features of experimental results can be described by simulations where agents use sales based heuristics with parameters calibrated from the experiments the results obtained here suggest the existence of useful complementarities between analytical experimental and agent based simulation approaches

consumer choice and cournot behavior in capacity constrained duopoly competition in a two stage model of duopolistic capacity choice and subsequent price competition consumer switching costs can deter some consumers from seeking service at a low price firm that lacks sufficient capacity to serve the entire market in this setting firms residual demand functions are aggregatedfrom thefirm selection decisions of individual consumers based on firms prices and their induced degrees of service reliability if consumers are approximately risk neutral with respect to service reliability then capacity constrained duopoly competition has a unique subgame perfect equilibrium in which firms choose cournot capacities and prices the equilibrium robustness of cournot behavior extends to duopoly markets in which consumer switching costs are induced by subscription pricing