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

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

finding all pure strategy nash equilibria in a planar location game in this paper we deal with a planar location price game where firms first select their locations and then set delivered prices in order to maximize their profits if firms set the equilibrium prices in the second stage the game is reduced to a location game for which pure strategy nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the customer and the facility from which it is served we present characterizations of local and global nash equilibria then an algorithm is shown in order to find all possible nash equilibrium pairs of locations the minimization of the social cost leads to a nash equilibrium an example shows that there may exist multiple nash equilibria which are not minimizers of the social cost

durable goods monopolists durable goods monopolists face special problems because the sale of their products creates a secondhand market not controlled by the monopolist to the extent the monopolist is able to rent his product rather than sell it or to make binding promises about his future production such problems are ameliorated given the inability to do the above the monopolist is led to producing goods less durable than those produced by either competitive firms or monopolist returns a reverse averch johnson result that monopolist sellers may invest less in fixed costs including plant modernization and research and development than would the renters is shown it is also shown that even though sellers have less monopoly power than renters and nondurable goods monopolists it is possible that the seller will cause a greater deadweight loss than the other types of monopolies

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

multiproduct monopoly regulation and firm costs regulation of public utiilties has traditionally been justified on the grounds that firm long run average costs fall with increased output in these industries for this reason it has been argued that cost efficiency dictates that a single firm supply the product ideally regulation of public utilities prevents monopolistic pricing while still permitting the most cost efficient industrial structure a large amount of theoretical and applied research has shown however that regulation in these industries generally does not guarantee that regulated firm costs are held at the lowest possible level for a given amount of output it seems then that regulation results in a tradeoff between cost savings from efficient industrial organization and cost inefficiencies generically known as x inefficiencies in this paper a new dimension of this tradeoff is examined specifically the paper explores whether cost efficiencies that are thought to characterize multiproduct public utilities are offset by increased costs permitted by a lack of inter energy competition in the next section a framework is constructed that is capable of identifying the cost structure for multiproduct firms and its relationship to efficient industrial structure section iii examines the sources of multiproduct economies and diseconomies for regulated multiproduct public utilities the cost structure is then estimated in section iv for single and multiproduct electricity and natural gas utilities section v considers the implications of the empirical analysis

foundations of dynamic monopoly and the coase conjecture subgame perfect equilibria are characterized for a market in which the seller quotes a price each period assume zero costs positive interest rate continuum of buyers and some technical conditions if buyers valuations are positive then equilibrium is unique buyers strategies are stationary and the price sequence is determinant along the equilibrium path but possibly randomized elsewhere otherwise a continuum of stationary equilibria can exist but at most one with analytic strategies coase s conjecture is verified for stationary strategies reducing the period length drives all prices to zero or the least valuation connections to bargaining models are described journal qf economic literature classification

the distribution of school leaver unemployment within scottish cities this paper examines the phenomenon of intra urban unemployment in the context of school leaver unemployment in scottish cities unlike much of the previous work in this area the paper avoids the ecological fallacy by utilising data on individual school leavers from the 1981 scottish school leavers survey in conjunction with detailed small area statistics from the 1981 decennial census probit analysis is employed to avoid certain statistical problems the results indicate that in terms of employment probabilities there is little evidence of any area effects within scottish cities in this sense there is one urban labour market in which personal characteristics matter but where area of residence is of little import these findings were found to hold in aberdeen dundee edinburgh and glasgow within each of these cities the effects of inter city variations in unemployment rates was found to fail disproportionately on the less qualified and less advantaged young job seekers

countervailing power revisited abstract the paper uses the nash bargaining concept to study the predictions of the theory of countervailing power within two theoretical models a cournot model and a model of perfect competition within the cournot model a decrease in the number of retailers unambiguously leads to an increase in equilibrium consumer prices in the model of perfect competition the reverse is true one may thus conclude that countervailing power can have positive effects for the consumers only if competiton at the retail level is very fierce

survival at the center the stability of minimum differentiation abstract we model a hotelling market with multidimensional product differentiation in an evolutionary framework both evolutionary stability in the sense of schaffer 1989 and stochastic stability following kandori et al 1993 young 1993 are analyzed it is shown that firms move towards the center in product space i e a principle of minimum differentiation on all dimensions of the product space applies

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

a nonparametric test for economies of scope this paper presents a simple test for economies of scope using nonparametric methods rather than elaborate estimation techniques the test reveals that nonporfit hospitals diversified into psychiatric services realize neither economies nor diseconomies of scope the test may be useful for policy markers concerned about whether diversification activities by certain groups of firms enhance efficiency or produce anticompetitive effects

x inefficiency and interfirm rivalry evidence from the electric utility industry competition from the natural gas industry is shown to increase the efficiency of the work force of electric power utilities this conclusion is qualified to the extent that duopoly rivalry does not represent perfect competition in a free market as natural gas reserves decline however the impetus to improve efficiency will diminish but this will be offset by technological advances in both power generation and power transmission if regulators develop policies to encourage competitive interplay utility performance is more likely to improve 38 references 3 tables dck

bargaining and boldness abstract we study a multiperson bargaining problem with general risk preferences through the use of shaked s game of cycling offers with exogenous breakdown if preferences are smooth then as the risk of breakdown vanishes the limiting outcome is one in which bargainers are equally marginally bold where a bargainer s marginal boldness measures his willingness to risk disagreement in return for a marginal improvement in his position under smoothness any ordinal nash solution is an equally marginally bold outcome however unlike the concept of the ordinal nash solution a unique equally marginally bold outcome exists in natural cases in particular if all bargainers have risk averse preferences of the rank dependent expected utility type for these preferences the equally marginally bold outcome maximizes a bargaining power adjusted asymmetric nash product where the degree of asymmetry is determined by the disparity in the marginal valuation of certainty among bargainers journal of economic literature classification numbers c72 c78 d81

let me talk to my manager haggling in a competitive environment although negotiating over prices with sellers is common in many markets such as automobiles furniture services consumer electronics etc it is not clear how a haggling price policy can help a firm gain a strategic advantage or whether it is even sustainable in a competitive market in this paper we explore the implications of haggling and fixed prices as pricing policies in a competitive market we develop a model in which two competing retailers choose between offering either a fixed price or haggling over prices with customers there are two consumer segments in our analysis one segment thehagglers has a lower opportunity cost of time and a lower haggling cost than the other segment thenonhagglers when both retailers follow the same pricing policy then a haggling policy is more profitable than a fixed price policy only when the proportion of nonhagglers is sufficiently high we find two kinds of prisoners dilemma under some conditions a more profitable haggling policy can be broken by a fixed price policy and under other conditions a fixed price policy can be broken by a haggling policy surprisingly we show that under some conditions an asymmetric outcome with one retailer haggling and the other offering a fixed price is also an equilibrium

digital pricing with piracy and variety seeking abstract this paper aims to explore behavioral digital pricing which incorporates realistic consumer behavior into firms pricing and anti piracy investment models we consider a duopoly market with an original company and a pirated group selling digital products the demand is sensitive to both parties prices we extend the traditional hotelling model by taking into account the effects of externality on both parties we then propose three types of price competition games i cournot model ii stackelberg model with the original company as the leader and iii the stackelberg model with the pirated group as the leader in model ii if the value of externality effects is lower than a threshold the original company will benefit from the government anti piracy policy that tolerates some piracy finally we investigate the behavior of consumer variety seeking in a two period cournot model with the presence of variety seeking both the original and pirated parties will adopt higher prices in the first period surprisingly variety seeking brings higher profits to both parties in two periods

equilibrium in a market with sequential bargaining this paper considers a market where pairs of agents who are interested in carrying out a transaction are brought together by a stochastic process and upon meeting initiate a bargaining process over the terms of the transaction the basic bargaining problem is treated with the strategic approach the paper derives the steady state equilibrium agreements analyzes their dependence on market conditions such as the relative numbers of agents of different types and discusses their relations with the competitive equilibrium outcome and other results in the search equilibrium literature this paper considers a market that operates in the following way pairs of agents who have mutual interest in carrying out a transaction are brought together by a stochastic process when two agents meet they initiate a bargaining process over the terms of the transaction if two agents reach an agreement a transaction takes place and they leave the market of course the bargaining positions and hence the agreement reached in any particular meeting will be affected by the conditions prevailing in the market these will include the chances that each of the negotiating parties have of meeting other partners in the event that the agreement in the current negotiations is delayed also the expected length of time required to achieve an alternative transaction and the expected behavior of alternative partners the study of such a market mechanism is of interest for two reasons firstly it captures some realistic aspects of the trade in certain specific markets e g asset markets such as housing and some labor markets secondly it contributes to an understanding of the micro mechanisms of price formation and their role in shaping market outcomes in both cases the features studied are largely neglected in the traditional market equilibrium analyses the related literature includes the articles by diamond 4 5 diamond and maskin 6 mortensen 8 9 and zusman and bell 13 these articles consider markets of the type described above in which transactions are concluded at pairwise meetings of agents the major difference between our work and these articles is in the approach to the basic bargaining problem in the cited articles it is assumed that a meeting is concluded with an instantaneous agreement which divides the associated surplus in an arbitrary predetermined way when the surplus is assumed to be divided equally the division rule is in fact nash s axiomatic bargaining solution in contrast the present paper treats the basic bargaining problem with the strategic approach see rubinstein 19 which constitutes an attempt to look into the bargaining black box this approach explicitly models the time dimension of the bargaining process describes in detail the bargaining procedure and justifies the agreement as a perfect equilibrium in

price competition for an informed buyer abstract this paper investigates price competition with private information on the demand side two sellers each offer a different variety of a good to a buyer endowed with a private binary signal on their relative quality the model provides an informational foundation to differentiation in hotelling s price competition game equilibrium comparative statics is performed with respect to the prior belief and the precision of the private information competition is fierce when the prior strongly favors one seller and private signals are relatively uninformative sellers equilibrium profits may fall with the revelation of public information and are nonmonotonic in the prior belief journal of economic literature classification numbers c72 d43 d82 l15

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

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

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

spatial competition with heterogeneous firms i model endogenous horizontal and vertical product differentiation with arbitrarily many heterogeneous firms firms are asymmetric in that they differ in their marginal costs i prove that under an equilibrium refinement all economically relevant firm outcomes are uniquely determined across all strict subgame perfect nash equilibria there are two central results first a firm s price market share and profit are independent of its neighbors marginal costs conditional on the average marginal cost in the market second more productive firms are more isolated all else equal in particular the distance between two firms is strictly decreasing in their average marginal cost

bargaining with incomplete information an infinite horizon model with two sided uncertainty the resolution of any bargaining conflict depends crucially on the relative urgency of the agents to reach agreement and the information each agent has about the others preferences this paper explores within the context of an infinite horizon bargaining model with two sided uncertainty how timing and information affect the rational behaviour of agents when commitment is not possible since the bargainers are uncertain about whether trade is desirable they must communicate some of their private information before an agreement can be reached this need for learning due to incomplete information about preferences results in bargaining inefficiencies trade often occurs after costly delay thus the model provides an explanation for the inefficient bargaining behaviour that appears to occur often in practice

noncooperative bargaining and spatial competition the article develops a bargaining model of spatial competition sellers compete by choosing locations in a market region consumers face a cost to moving from one place to another the price of the good is determined as the perfect equilibrium of a bargaining game between seller and buyer in this game the buyer has the outside option to move to another seller and so the prices at all stores are interdependent existence of a location price equilibrium is established the outcome approaches the perfectly competitive one if the consumer s cost of traveling becomes negligible or if the number of sellers tends to infinity copyright 1989 by the econometric society

recent advances in oligopoly theory from a game theory perspective abstract this paper surveys the contribution that recent developments in game theory have made to the understanding of oligopoly theory it is argued that conventional models suffer from the problem that there are a number of solution concepts offered with little guidance as to which should be selected and this is related to the static nature of the models employed one important development in game theory has been the analysis of repeated games and when applied to oligopoly theory this suggests that outcomes may be more cooperative than conventional theory suggests related to this is the requirement that firms employ credible threats to punish cheating from cooperative outcomes and the paper examines the extent to which imperfect information may restrict the scope of firms to employ such punishments one way in which firms may seek to make threats credible is through strategic investments for example in production capacity and the paper explores how competition over price or output is integrated with competition over instruments for strategic investment

bargaining search costs and equilibrium price distributions this paper studies a bargaining model of equilibrium price distributions consumers choose a seller at random and face search costs to switching to another store in the market equilibrium the prices at all stores are determined simultaneously as the perfect equilibrium of a bargaining game in this game the buyer has the outside option to search for another seller differences between the sellers types create price dispersions typically the number of active sellers increases with higher search costs the market equilibrium converges to the competitive equilibrium under perfect information when search costs become small

urban unemployment a causal modelling approach intra urban variations in male unemployment are hypothesised to depend on residential variations in the personal characteristics of adult males age marital status family size skill level housing tenure and local characteristics manufacturing employment the number of married working women and unemployment in previous years a causal modelling approach is adopted in which the nature and direction of the causal relationships between the highly correlated personal and local characteristics are carefully specified a priori the hypothesised linkages between the standardised variables are tested in a systematic manner using step wise regression yielding beta coefficients post code sector data for 29 scottish cities and towns from the small areas statistics of the 1971 and 1981 censuses of population were analysed as a whole and in seven subsets 4 cities strathclyde excluding glasgow new towns and the rest of scotland the typical pattern suggests that unemployment is related to lack of

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

non cooperative bargaining theory an introduction the paper provides an informal introduction to some of the main themes of the recent literature on non cooperative or sequential bargaining models it focuses in particular on the relationship between the new approach and the traditional axiomatic approach exemplified by nash bargaining theory it illustrates the new insights offered by the non cooperative approach by reference to a detailed analysis of the manner in which the presence of an outside option available to one of the parties will affect the negotiated outcome finally the difficulties which arise in extending this analysis to two person bargaining with incomplete information and to n person bargaining are discussed this is a revised version of the fourth review of economic studies lecture presented in april 1985 at the joint meeting of the association of university teachers of economics and the royal economic society held in oxford the choice of lecturer is made by a panel whose members are currently professors hahn mirrlees and nobay and the paper is refereed in the usual way this paper aims to provide an informal and elementary introduction to an approach to bargaining which has received a great deal of attention over the past few years the approach involves writing down some particular sequence of moves offers and replies to be made over time in the course of negotiations and then looking for a non cooperative equilibrium in the game thus specified in practice a perfect equilibrium or in games of incomplete information a sequential equilibrium while the approach appears at first sight to be very different in spirit from the traditional axiomatic approach in which a bargaining solution is specified by appealing to a number of general requirements which are deemed appropriate on the basis of some a priori considerations the two approaches are in fact complementary while the

a bargaining model of financial intermediation abstract in a financial market the investor searches for investment projects and bargains with the entrepreneur about the financial contract alternatively he may delegate search and bargaining to a financial intermediary delegation generates a commitment advantage in bargaining it may however induce excessively risky investments because the investor cannot monitor the intermediary s search behavior this restricts the parameter constellations under which equilibrium intermediation occurs competition may not reduce the intermediaries profits to zero because of incentive restrictions

elections with platform and valence competition abstract we study a game in which candidates first choose platforms and then invest in costly valences e g engage in campaign spending the marginal return to valence depends on platform polarization the closer platforms are the more valence affects the election outcome consequently candidates without policy preferences choose divergent platforms to soften valence competition moreover exogenous increases in incentives for valence accumulation lead to both increased valence and increased polarization the latter because candidates seek to avoid the costs of extra valence as a result the increase in valence is smaller than it would have been with exogenous platforms finally the model highlights the overlooked substantive importance of common modeling assumptions changing the source of uncertainty in our model from noise around the median voter s ideal point to a shock to one candidate s valence as is common in the literature leads to complete platform convergence for all parameter values

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

theory and experiments on spatial competition we present theoretical and experimental results on spatial competition between two firms firms choose locations simultaneously along a line representing a linear market identical consumers with non increasing demand functions are uniformly distributed along this line we solve for symmetric equilibrium payoffs in an infinitely repeated game for the case of linear demand and an arbitrary discount factor the set of equilibriums found includes both competitive and collusive payoffs in laboratory experiments in which the final period was unknown to the players in advance we observed both competitive and collusive outcomes non binding communication led to collusion

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

a bargaining model with incomplete information about time preferences etude d un jeu de negociation strategique sequentiel avec information incomplete caracterisation d une classe d equilibres sequentiels appeles equilibres sequentiels de negociation et demonstration de l unicite de cet equilibre

market efficiency with combinable products abstract we allow consumers to combine products to obtain a mix of their characteristics we show there is a unique sub game perfect equilibrium in a product location price game such that all consumers are able to attain their desired product mix this solution is the socially optimal one in stark contrast to location models where combinability is debarred by assumption

why do all the flights leave at 8 am competition and departure time differentiation in airline markets abstract theoretical models of spatial product differentiation indicate that firms face two opposing incentives 1 minimize differentiation in order to steal customers from competitors and 2 maximize differentiation in order to reduce price competition using data on u s airline departure times from 1975 when fares were regulated and 1986 when fares were not regulated we empirically estimate the effect of competition on differentiation we find a negative relationship in both periods in 1986 however reductions in exogenous scheduling constraints increase differentiation implying that firms may be differentiating their products where possible to reduce price competition this effect is not apparent in the 1975 data

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

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

spatial price discrimination and the locations of firms with different product selections or product varieties abstract the equilibrium locations of two firms are partially centralized to the socially optimal extent if there is spatial price discrimination and if each firm has two out of three products or else one variety of a differentiated product with some consumers indifferent between varieties

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

on the nature of equilibria in a downsian model with candidate valence abstract i analyze mixed strategy equilibria in a downsian model with two office motivated candidates in which one candidate is endowed with a sufficiently large valence advantage that a voter might prefer this candidate even if the voter strictly prefers the other candidate s policies there is a discrete one dimensional policy space and the preferences of the median voter are uncertain i show that there is a range of moderate policies with no gaps that are optimal for the advantaged candidate there is also a range of liberal policies with no gaps and a corresponding range of conservative policies with no gaps that are optimal actions for the disadvantaged candidate the upper and lower bounds on these ranges of policies vary in predictable ways with the size of the advantaged candidate s advantage

technology adoption and the emergence of regional asymmetries the model explains the emergence of asymmetric productive structures among regions based on adoption of a quality improving technology firms products are diierentiated both in location and quality location is given we characterize symmetric and asymmetric equilibria of the two stage game in price and adoption asymmetric equilibria display partial adoption frequencies and regular geographical patterns of adoptions the asymmetry of the economy has often a reverse u shaped relation with the innovation size market integration is an obstacle for the full adoption of the new technology and favours the emergence of regional asymmetries i introduction regional income inequalities in the european community are very large the following gures reported by dunford 1993a f rom the regio database give an idea about their magnitude in 1989 per capita output in nuts 2 1 regions measured in purchasing power standards pps varied between 177 to 40 of the ec average or between 199 and 26 if measured in ecu over 18 of the population of the ec lived in areas with a per capita gdp of less than 75 of the community average a further 36 lived in areas with a per capita gdp below the community average at the other end of the distribution 10 of the population of the community lived in areas with an average per capita gdp 53 above the community average these leading regions form an area also de ned as the blue banana which extends from greater london to groningen in the netherlands hamburg darmstadt bremen oberbayern and stuttgart in germany the i le de france in france down to lombardia and emilia romagna in italy

global and local players in a model of spatial competition abstract we analyze equilibrium configurations of hotelling location games where some players compete on several markets with the same product such global players tend to lower product diversity across markets the model is consistent with recent empirical findings on preference externalities

spatial competition and strategic firm relocation firms compete spatially for customers who have some degree of brand loyalty the number and attractiveness of the alternatives available to these customers dictates the level of competition facing firms in this study data on ticket pricing in four professional sports leagues are used to empirically examine the existence of spatial competition in sports and the impact of space on team relocations results allowing for structural breaks over time while using spatial autoregressive techniques suggest that sports franchises spatially compete when pricing their tickets and that spatial characteristics including the level of spatial competition have influenced the relocation of teams jel d40 l11 r30 l83

sequential bargaining with incomplete information this paper describes a simple two person two period bargaining game and solves it using the concept of perfect bayesian equilibrium in which the actions of each player convey information which is used by his opponent the paper examines the effects of changes in bargaining costs the size of the contract zone and the length of the bargaining process on such aspects of the solution as the probability of impasse and the likelihood of concessions the combination of information transfer and the lack of pre commitment embodied in perfectness yields many surprising results common perceptions about the effects of parameter changes on bargaining processes are suspect and should be checked in the particular game being discussed

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

efficient spatial competition abstract game theoretic models of spatial competition usually assume that firms set prices after their choices of locations rather than make this assumption this paper uses the core to model the competition between the firms two conditions are shown to be sufficient for efficient spatial competition the first is that the firms location choices satisfy a no externalities condition the second is that the second stage game satisfy a separable value condition namely that the value gains from trade can be created on a buyer by buyer basis this approach yields two further benefits first efficient location can be stable in situations with arbitrary distributions of buyers arbitrary willingness to pay functions and completely general location spaces second efficiency in location games can be shown to be related to the second welfare theorem

product differentiation decisions under ambiguous consumer demand and pessimistic expectations abstract this paper studies product differentiation decisions in a spatial duopoly with limited information on consumer demand in particular a situation is discussed in which the firms do not know the exact distribution of the random location of consumer demand and its responsiveness to price changes measured by the scale of transport costs but resolve the resulting ambiguity using the maxmin or minimax regret criteria when the firms are sufficiently pessimistic is high enough results are in contrast with the existing literature in particular an increase of demand location uncertainty decreases the equilibrium product differentiation intensifying the second stage competition in prices although the effect is dampened by uncertainty about transport costs endogenizing the choice of objective function leads to the dominance of an extreme form of pessimism which turns out to be socially optimal

hotelling competition with demand on parallel line abstract this paper discusses equilibria in hotelling competition under assumption of the demand being on a line parallel to the firms location line when the distance between two lines is large enough the game has spe in pure strategies