ON THE SUSTAINABILITY OF COLLUSION IN A DIFFERENTIATED OLIGOPOLY WITH A CARTEL AND A FRINGE

We discuss the effects of the existence of non‐colluding (fringe) firms on cartel sustainability. We obtain, using trigger strategies, that with product differentiation collusion is always more easily sustained when firms compete in prices than when firms compete in quantities. This is true basically because (i) price competition is more intense than quantity competition, and (ii) fringe firms exacerbate the fact that cartel firms have more incentives to deviate from the agreement under quantity competition. This result reverses previous findings where, in the absence of fringe firms, product differentiation plays a crucial role in determining the effectiveness of price or quantity competition in sustaining collusion.     

ON THE PRICE EFFECTS OF HORIZONTAL MERGERS: A THEORETICAL INTERPRETATION

Horizontal mergers are usually under the scrutiny of antitrust authorities due to their potential undesirable effects on prices and consumer surplus. Ex‐post evidence, however, suggests that these effects do not always take place and even relevant mergers may end up having negligible price effects. The analysis of mergers in the context of non‐localized spatial competition may offer a further interpretation to the ones proposed in the literature: in this framework both positive and zero price effects are possible outcomes of the merger activity.     

BERTRAND Vs. COURNOT COMPETITION WITH UPSTREAM FIRM INVESTMENT

This paper compares Bertrand and Cournot competition in a vertical structure in which the upstream firm sets the input price and makes R&D investments. We show that from the downstream firms’ point of view, Cournot competition has the advantage of a more monopolistic effect, leading to the setting of a higher price, but has the disadvantage of inducing a lower incentive for the upstream firm to invest. On the other hand, Bertrand competition has the advantage of providing a greater incentive for the upstream firm to invest but has the disadvantage of a more competitive effect, leading to the setting of a lower price. Our main findings are as follows. First, R&D investment level is greater under Bertrand competition than under Cournot competition. Second, from the standpoint of the upstream firm and industry, Bertrand competition is more efficient than Cournot competition. Third, from the standpoint of the downstream firms, Bertrand competition is more efficient than Cournot when investment is sufficiently efficient and products are sufficiently differentiated.     

HORIZONTAL MERGERS: A SOLUTION OF THE INSIDERS' DILEMMA

We show that in a three‐firm infinitely repeated Cournot game, there exists a stick and carrot strategy equilibrium in which an exogenous bilateral horizontal merger is profitable and the incentive to remain out of the merger disappears. In this sub‐game perfect equilibrium, the merged entity produces the duopoly quantity and the outsider limits its production to half the duopoly quantity. Our stick and carrot strategy entails that the merged entity threatens to produce twice the triopoly quantity for two periods if the outsider does not produce half the duopoly quantity. In this equilibrium, the aggregate price remains high enough to make the merger profitable for the insiders. Also, the quantity produced by the outsider is sufficiently low to eliminate the difference between the profit of the outsider and the merging firm.     

ALTERNATIVE STRATEGIES OF A PUBLIC ENTERPRISE IN OLIGOPOLY REVISITED: AN EXTENSION TO STACKELBERG COMPETITION

This paper revisits De Fraja and Delbono (1989), which is the seminal paper on mixed oligopoly, in order to pay more attention to Stackelberg competition. First, we show that, even in Cournot competition, if the number of private firms is sufficiently small, privatization necessarily reduces social welfare. Second, we demonstrate that when a public firm is a Stackelberg leader before and after privatization, privatization necessarily reduces welfare irrespective of the number of private firms. Moreover, we show that even when a public firm remains a follower, privatization reduces welfare if the number of private firms is relatively small.     

PRIVATIZATION AND EFFICIENCY GAIN IN AN INTERNATIONAL MIXED OLIGOPOLY WITH ASYMMETRIC COSTS*

This paper examines two policy instruments, privatization of the domestic public firm and imposition of a tariff on foreign private firms in an international mixed oligopolistic model with asymmetric costs. It first demonstrates that different orders of moves of firms will imply different government decisions on optimal tariff and on privatization policy. Following Hamilton and Slutsky (1990 ), this paper then uses an extended game to discuss endogenous roles. It indicates that the efficiency gain that highlights the importance of foreign competition is crucial in determining the welfare improving privatization policy. Moreover, the endogenous equilibria are associated with different government decisions on privatization.     

HORIZONTAL MERGERS WITH CAPITAL ADJUSTMENT: WORKERS' COOPERATIVES AND THE MERGER PARADOX

We study the incentives towards horizontal merger among firms when the amount of capital is the strategic variable. We focus on workers' cooperatives, but our conclusions apply also to employment‐constrained profit maximizers. Within a simple oligopoly model, we prove that the horizontal merger, for any merger size, is: (i) privately efficient for insiders as well as for outsiders; (ii) socially efficient if market size is large enough, even in the case of merger to monopoly.     

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.     

FREE VERSUS SECOND‐BEST ENTRY IN COURNOT OLIGOPOLIES WITH FIRM‐SPECIFIC NETWORKS

This paper endogenizes the number of firms in an industry with positive network effects, complete incompatibility, and firms that compete in quantity. To this end, we compare two possibilities: free entry and second‐best number of firms (the one that maximizes social welfare). We show that with business‐stealing competition, free entry yields, in general, more firms than the socially optimal solution. In addition, we find that by the nature of the industry with firm‐specific networks, total production may be greater or lower under free entry than with a regulator; moreover, some industries attain their maximum social welfare with a monopoly.     

STRATEGIC BUDGET CONSTRAINTS IN A UNIONIZED MIXED OLIGOPOLY

This paper considers the budget‐constraint problem where the government decides whether or not to impose a budget constraint on the public firm, assuming the public firm is less efficient than private firms. We find that imposing budget constraints on the public firm is the preferred choice because of the welfare‐improving effect. Our model suggests that the wage levels of the public firm can be lower or higher than those of private firms depending upon the degree of inefficiency. These results differ from Ishida and Matsushima's findings that in a unionized mixed duopoly, tight budget constraints can enhance social welfare when the public firm is as efficient as private firms.     

A Theory of Mergers and Merger Waves

We consider a sequential merger game between Cournot firms with homogeneous product and quadratic cost. A large slope of the marginal cost function or a small slope of inverse market demand are both predicted to increase the incentive to merge. The profitability of any merger increases with the number of mergers having already taken place. Thus, mergers tend to occur in waves in industries that have experienced exogenous shocks affecting firms’ cost or demand. We also show some mergers that are not profitable for merged firms in the short-run may take place in the early stage of a wave.     

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.     

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).     

WELFARE ENHANCING COORDINATION IN CONSUMER COOPERATIVES UNDER MIXED OLIGOPOLY

The recent globalization of world economies has led the retail markets of developed countries towards increasing levels of integration and strategic interdependence. A non negligible share of retail and food markets is currently served by co‐operative societies. Consistently with this trend, the consumer cooperatives have recently experienced increasing levels of integration. The main aim of this paper is to study the welfare effects of coordination among consumer cooperatives competing in quantities in a mixed oligopoly against profit‐maximizing firms. We show that, in absence of agency problems, under increasing or constant returns to scale a higher output coordination of the consumer cooperatives does not affect the total welfare as long as a nonnegative profit constraint holds in these firms. On the other hand, under decreasing returns to scale, the consumer cooperatives contribute more to social welfare when acting on behalf of all consumers. This is because, by coordinating consumers’ preferences, these firms can reduce their market output, thus helping the market to come closer to the first best. All together these results seem to provide an argument in favour of the recent process of integration involving consumer cooperatives in many developed countries.     

N‐FIRM OLIGOPOLY WITH GENERAL ISO‐ELASTIC DEMAND

In this note oligopoly with iso‐elastic demand is analysed. Unlike previous studies we consider general iso‐elastic demand rather than the case of unit elasticity. An n‐firm Nash‐Cournot equilibrium for the case of heterogeneous constant marginal costs is derived. The main result is a closed‐form solution that shows the dependency of the equilibrium on the elasticity of demand and the share of industry costs. The result has applications to a wide range of areas in oligopoly theory by allowing comparisons across markets with different elasticities of demand.     

Bertrand versus Cournot competition in a downstream mixed oligopoly with foreign ownership

Focusing on foreign ownership in the private firm, we examine the Cournot-Bertrand comparison in a mixed oligopolistic market with vertical market structure. We have found that if public and private firms were charged with uniform price for their inputs, then Cournot-Bertrand ranking in market outcomes confirms those obtained by Ghosh and Mitra (2010). This implies that under uniform pricing in the upstream sector, the vertical market structure does not have substantial influences on Cournot-Bertrand ranking. However, if discriminatory pricing is adopted, firm's profits, output, and social welfare are often reversed to those obtained from uniform pricing in the upstream sector. Given the closeness of products, if the share of foreign ownership is sufficiently low, social welfare in Cournot competition can exceed that of Bertrand competition, contrasting with the standard welfare ranking that Bertrand welfare is strictly higher than Cournot. This implies that Cournot competition can be more socially desirable than Bertrand in mixed oligopoly with vertical market structure if discriminatory pricing scheme is adopted by foreign upstream monopolists.     

INSUFFICIENT ENTRY OF EMPLOYEE‐CONTROLLED FIRMS IN A FREE‐ENTRY OLIGOPOLY

This study is a theoretical examination of whether employee‐controlled firms (ECFs) enter a free‐entry oligopolistic market excessively or insufficiently, from the viewpoint of welfare maximization. The excess entry theorem is well known in oligopoly theory. According to this theorem, a greater number of profit‐maximizing firms enter a free‐entry oligopolistic market than is optimal for welfare maximization. We demonstrate the possibility that insufficient entry arises when ECFs compete in a free‐entry market. In particular, we show that if both the demand and cost functions are convex, insufficient ECF entry necessarily occurs. Our results suggest that competition among firms seeking purposes other than profit might lead to insufficient entry because differences in competing firms’ objectives affect the intensity of market competition.     

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.     

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.     

EQUILIBRIUM SELECTION IN THE YANO MODEL OF PRICE LEADERSHIP

Abstract. A number of studies have provided a theoretical explanation for the fact that the technologically superior firm becomes a price leader in a duopoly market for a homogeneous product. While previous studies show that the state in which the technologically superior firm becomes a price leader is a Nash equilibrium (superior leader equilibrium), they do not eliminate the possibility that the state in which the technologically inferior firm becomes a price leader is also a Nash equilibrium (inferior leader equilibrium). We demonstrate that an inferior leader equilibrium can be eliminated by the iterative elimination of weakly dominated strategies.