Equilibrium locations in a mixed duopoly with sequential entry in real time

We investigate a mixed duopoly model where a public firm and a private firm enter a market sequentially over an infinite time horizon, with and without uncertainty over the follower's entry date. We assume that there is a unit-length linear city and show that, if the public firm moves first, equilibrium location falls inside the second and third quartiles. The later the follower is expected to enter, the closer the two firms are. However, if the private firm acts first, it moves aggressively to locate at the middle point (one-half), forcing the public firm to locate nearer the periphery (one-sixth), to minimize consumers' transportation cost. In addition, social welfare is strictly greater when the public firm moves as the leader.     

A public firm in a model of spatial duopoly with price discrimination

We visit the role of privatization in the location decision of firms in an industry where no firm can produce all varieties demanded. We demonstrate that the Nash equilibrium locations are socially optimal, in the presence of a publicly owned firm, notwithstanding the degree of privatization.     

Uncertain spatial demand and price flexibility: A state space approach to duopoly

Sufficient conditions for a unique price equilibrium, in terms of the uncertainty distribution and the state contingent consumer distributions, are given for spatial duopoly. Also considered are efficiency and endogenous locations for the symmetric case and comparative statics on price flexibility.     

NESTING VERTICAL AND HORIZONTAL DIFFERENTIATION IN TWO‐SIDED MARKETS

We merge the two‐sided markets duopoly model of Armstrong (2006) with the nested vertical and horizontal differentiation model of Gabszewicz and Wauthy (2012), which consists of a linear city with different consumer densities on the left and on the right side of the city. In equilibrium, the high‐quality platform sells at a higher price and captures a greater market share than the low‐quality platform, despite the indifferent consumer being closer to the high‐quality platform. The difference between market shares is lower than socially optimal. A perturbation that introduces a negligible difference between the consumer density on the left and on the right side of the city may disrupt existence of equilibrium in the model of Armstrong (2006).     

A spatial network approach to urban configurations

Abstract We propose a spatial network approach to studying urban configurations by modelling explicitly knowledge transmission, aggregation and spillovers via links formed, as well as by allowing the population and the locality role (‘core’ versus ‘periphery’) in each location to be endogenously determined in equilibrium. We establish conditions for the commonly assumed monocentric configuration to arise as the unique and efficient equilibrium outcome. We also illustrate under what circumstances a spatial equilibrium may feature multicentric, urban‐rural, or multiple (disconnected) urban areas and under what conditions each configuration is socially efficient. We further characterize the spatial equilibrium by performing various comparative statics.     

AIRPORT PRIVATIZATION AND INTERNATIONAL COMPETITION

We provide a simple theoretical model to explain the mechanism whereby the privatization of international airports can improve welfare. The model consists of a downstream (airline) duopoly with two inputs (landings at two airports) and two types of consumers. The airline companies compete internationally. We show that the outcome in which both airports are privatized is always an equilibrium, whereas that in which no airport is privatized is an equilibrium only if the degree of product differentiation is large. We also discuss airport congestion problems within the model framework.     

THE EXISTENCE OF EQUILIBRIUM IN A DIFFERENTIATED DUOPOLY WITH NETWORK EXTERNALITIES*

The existence of a pure‐strategy subgame‐perfect equilibrium in qualities and prices is investigated in a duopoly model of vertical differentiation where quality improvements require a quadratic variable cost and network externalities operate. We show that there exists a parameter region where the incentive to predate at the quality stage prevents firms from reaching a pure‐strategy non‐cooperative equilibrium with prices above marginal costs. If network externalities are sufficiently large, a Bertrand equilibrium with zero profits may arise, although the amount of product differentiation is strictly positive.     

Spatial Cournot Competition in a Linear City with Directional Delivery Constraints

This study investigates a sequential game of location and transportation mode choices, as well as the subsequent quantity choice. The results show that spatial Cournot competition with directional delivery constraints yields a richer set of spatial configurations, involving midpoint agglomeration, maximum differentiation and asymmetric dispersion, and a richer set of transportation mode selections, involving delivery in different directions, asymmetric delivery between duopoly firms, and delivery in two directions by each firm, depending on the fixed cost of a transportation instrument. This paper concludes with an investigation of welfare analysis on optimal locations and transportation modes.     

The Cournot-Bertrand model and the degree of product differentiation

We consider a duopoly model with a Cournot-type firm and a Bertrand-type firm. Both survive and the equilibrium is stable when there is sufficient product differentiation. With no differentiation, only the Cournot-type firm survives, and the outcome is perfectly competitive.     

QUALITY DIFFERENTIATION,WELFARE, AND THE MODE OF COMPETITION IN A VERTICALLY DIFFERENTIATED PRODUCT MARKET: A NOTE*

We analyse the implications of quality differences in a vertically differentiated product market for social welfare by employing an endogenous quality choice model. We find that in of Bertrand and Cournot duopolies, the degree of quality differentiation at equilibrium in an unregulated market is larger or smaller, respectively, than that of the socially second‐best optimum. This implies that a reduction in quality difference, respectively, increases or decreases social welfare in the case of Bertrand or Cournot duopolies.     

A note on free entry under uncertainty: The role of asymmetric information

In a model of competing managerial firms I show that the equilibrium number of firms decreases with uncertainty if entry is relatively more costly than monitoring. The result adds to the earlier contributions and is consistent with the available evidence.     

A NONCOOPERATIVE SHIPPING COURNOT DUOPOLY WITH LINEAR‐QUADRATIC TRANSPORT COSTS AND CIRCULAR SPACE*

The mixed strategy equilibria in a location quantity duopoly model with circular markets are investigated. We find that a continuum of equilibria exists when the transport cost function is linear. However, if costs are strictly concave or convex, most strategies fail to qualify as equilibria. For any integer n, there are nondegenerate mixed strategy equilibria in which each firm locates at n possible locations with equal probability. This result explains possible outcomes in which firms’ on‐path locations are not minimally or maximally differentiated.     

Shopping hours and price competition

This paper develops an argument why retail prices may rise in response to the deregulation of opening hours. We make this point in a model of imperfect duopolistic competition. In a deregulated market retailers view the choice of opening hours as a means to increase the degree of perceived product differentiation thus relaxing price competition. If the consumers’ preference intensity for time is sufficiently high the equilibrium configuration has asymmetric shopping hours where one retailer stays open for longer than the other. Both retailers charge higher prices than under regulation, and both are strictly better off.     

Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products

In this paper we consider a Cournot–Bertrand duopoly model with linear demand and cost functions and with product differentiation. We propose a dynamic framework for the study of the stability properties of this kind of mixed oligopoly game, a rather neglected topic in the existing literature despite its relevance. In particular, in this paper we highlight the role of best response dynamics and of an adaptive adjustment mechanism for the stability of the equilibrium.     

The dynamics of a differentiated duopoly with quantity competition

We analyse the dynamics of a Cournot duopoly with heterogeneous players to investigate the effects of micro-founded differentiated products demand on stability. The present study, which indeed modifies and extends Zhang et al. (2007) (Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148) and Tramontana, F., (2010) (Tramontana, F., 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling 27, 350–357), reveals that a higher degree of product differentiation may destabilise the market equilibrium. Moreover, we show that a cascade of flip bifurcations may lead to periodic cycles and ultimately chaotic behaviours. Since a higher degree of product differentiation implies weaker competition, then a theoretical implication of our findings, that also constitute a policy warning, is that a fiercer (weaker) competition tends to stabilise (destabilise) the unique positive Cournot–Nash equilibrium.     

Home-market vs. vote-market effect: Location equilibrium in a probabilistic voting model

This paper considers the location of manufacturing activities when regional policies are endogenous. We find that once the political economy of regional policy is explicitly taken into account, regional population size has an ambiguous effect on the level of regional subsidy, even though it plays a key role in determining the equilibrium spatial allocation of industry. In particular, the final allocation of firms depends both on the relative economic strengths of the two regions, as predicted by more orthodox economic geography models, as well as by their relative political strengths.     

PRICE FLOORS AND QUALITY CHOICE

This paper studies effects of price floors in a simple model of vertical product differentiation. We find that even non‐binding price floor (i.e., minimum price set below the lowest Nash equilibrium price in the baseline model) can increase quality on the market, if the cost of quality is sufficiently low. Where a binding price floor does not increase the equilibrium quality, it makes consumers worse off. There is also a possibility of over‐investment into quality as a result of the binding minimum price.     

SPATIAL DISCRIMINATION,PRODUCT SUBSTITUTABILITY AND WELFARE

The paper examines a quantity–location duopoly game in a spatial discrimination model in which the delivered goods are assumed to be imperfect substitutes or complements. By extending the range of the unit transportation cost analysed in the existing literature, it is shown that a dispersed equilibrium arises in which the choice of the optimal locations is affected by the degree of product substitutability. The interaction between the latter and the size of the transportation cost is also discussed in order to verify its welfare implications. In particular, it is shown that in this spatial framework imperfect substitutability may increase welfare.     

Congestion with heterogeneous commuters

We study a congestion model where a continuum of heterogeneous commuters make a binary choice between riding a bus and driving private vehicles for their commutes. Formulating the model as a large game, we establish the existence and uniqueness of a nontrivial Nash equilibrium and analyze how a gasoline tax affects the allocation of commuters between public transportation and private vehicles at the equilibrium. Based on the analysis, we provide a sufficient condition under which a gasoline tax is Pareto improving. We also prove the existence of a socially optimal policy that minimizes the aggregate loss to all commuters.     

Understanding the Role of Governments and Administrations in the Implementation of Community and Complementary Currencies

This text focuses on the role of governments and administrations in the emergence, spread, development and differentiation of community and complementary currency schemes (CCs), highlighting their role as potential support for experimentation. This support can take various forms: technical, financial, fiscal, official and/or legal recognition. We present first the role of governments, mostly local, in the emergence and development of four generations of CCs. We distinguish then a series of modes of action of governments at central and local levels. This leads to identify the interest of being supported (greater professionalism, greater complexity and possibly greater impact) while emphasizing the risks linked to public support as well.