Location choice with delegation: Bertrand vs. Cournot competition

The conventional wisdom indicates that firms' optimal locations are sensitive to the modes of product-market competition, leading to a difficulty for firms to make concrete location decisions. This difficulty is especially crucial for the high entry-cost firms. The paper develops an uncovered-market model à la Economides (1984) to explore this sensitivity by taking into account a delegation game. It shows that firms' location configurations remain unchanged regardless of the modes of product-market competition as the owners offer the managers a contract with a relative-performance incentive scheme. Moreover, the paper shows that, by introducing a delegation game, the competition between managers under Bertrand competition is mitigated such that the managers have no incentive to choose price undercutting as they locate themselves far enough away from each other.     

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.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

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.     

R&D games in a Cournot duopoly with isoelastic demand functions: A comment

In a recent paper, Tramontana (Economic Modelling, 27; 350-357, 2010) investigates the stability properties of a Cournot Duopoly game when the demand function is isoelastic. In this note, we show that for some well known applications of two-stage Cournot games (D. Aspremont and Jacquemin, American Economic Review, 78, 1122-1137, 1988) an isoelastic demand function can guarantee both the existence and the uniqueness of a Nash Equilibrium even in cases where existence is not obtained with linear demands.     

Product customization

The advent of the Internet has revolutionized the way companies advertise, develop and distribute products. Firms can now customize their advertising messages and products to the particular characteristics and needs of customers. Customers themselves can create their own products. We investigate investments by firms in product-customization capabilities within a duopoly model of horizontal product differentiation. We find that (i) if brand name effects are not too strong, one firm emerges as a leader in product customization—firms make asymmetric investments in product-customization technologies in order to reduce price competition, (ii) if brand name effects are strong, both firms make extensive investments in product customization, and (iii) the possibility of product customization can raise industry profits if brand names are weak, but not when they are strong.     

Customer information sharing among rival firms

The recent rapid growth of the Internet as a medium of communication and commerce, combined with the development of sophisticated software tools, are to a large extent responsible for producing a new kind of information: Databases with detailed records about consumers’ preferences. These databases have become part of a firm's assets, and as such they can be sold to third parties. This possibility has raised numerous concerns from consumer privacy advocates and regulators, who have entered into a heated debate with business groups and industry associations about whether the practice of customer information sharing should be banned, regulated, or left unchecked. This paper investigates the incentives of rival firms to share their customer-specific information and evaluates the welfare implications if such exchanges are banned, in the context of a perfect price discrimination model.     

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.     

Mixed pricing in oligopoly with limited monopoly

We analyze price competition between two brands. Buyers consist of switchers and two segments of customers with limited brand loyalty. We identify a unique symmetric mixed-strategy price equilibrium and find that competition is most relaxed when there exists some switchers.     

Geographical separation of oligopolists can be very competitive

A given number of single, differentiated product oligopolists locate in one of two separate market-places, which consumers access at a cost. Firms set prices and the CES consumers choose purchases at one or both market-places. Firm agglomeration in one market-place produces positive profits because of product differentiation. But if consumer access costs are homogeneous and products are sufficiently good substitutes, geographical separation of firms produces prices analogous to homogeneous product Bertrand, and is “very competitive”, the reverse of textbook Hotelling. Hence a novel explanation emerges for the geographical agglomeration of firms producing very similar products.     

The impact of bargaining on markets with price takers: Too many bargainers spoil the broth

In this paper we study how bargainers impact on markets in which firms set a list price to sell to those consumers who take prices as given. The list price acts as an outside option for the bargainers, so the higher the list price, the more the firms can extract from bargainers. We find that an increase in the proportion of consumers seeking to bargain can lower consumer surplus overall, even though new bargainers receive a lower price. The reason is that the list price for those who do not bargain and the bargained prices for those who were already bargaining rise: sellers have a greater incentive to make the bargainers’ outside option less attractive, reducing the incentive to compete for price takers. Competition Authority exhortations to bargain can therefore be misplaced. We also consider the implications for optimal seller bargaining.     

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.     

The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

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.     

Platform intermediation in a market for differentiated products

We study a two-sided market where a platform attracts firms selling differentiated products and buyers interested in those products. In the subgame perfect equilibrium of the game, the platform fully internalises the network externalities present in the market and firms and consumers all participate in the platform with probability one. The monopolist intermediary extracts all the economic rents generated in the market, except when firms and consumers can trade outside the platform, in which case consumers obtain a rent that corresponds to the utility they would get if they did trade outside the platform. The market allocation is constraint-efficient in the sense that the monopoly platform does not introduce distortions over and above those arising from the market power of the differentiated product sellers. An increase in the number of retailers increases the amount of variety in the platform but at the same time increases competition. As a result, the platform lowers the firm fees and raises the consumer charges. In contrast, an increase in the extent of product differentiation raises the value of the platform for the consumers but weakens competition. In this case, the platform raises both the charge to the consumers and the fee for the firms.     

Consumer search with asymmetric price sampling

We explore asymmetries in the way consumers sample prices in a simple sequential search framework. In equilibrium, the price distribution of a firm catering to more local consumers first-order stochastically dominates that of its rival. Prices rise in the degree of asymmetry.     

Low-quality leadership in a vertically differentiated duopoly with Cournot competition

We model a vertically differentiated duopoly with quantity-setting firms as an extended game in which firms noncooperatively choose the timing of moves at the quality stage, to show that at the subgame, perfect equilibrium sequential play obtains, with the low-quality firm taking the leader’s role.     

Unilateral effects of mergers with general linear demand

We derive the formula for the unilateral price effects of mergers of two products with linear demand in the general asymmetric situation. The formula uses the same information required to calculate upward pricing pressure in the 2010 Horizontal Merger Guidelines.     

Buyer search and price dispersion: a laboratory study

We study markets with costly buyer search in which sellers simultaneously post prices. Buyers costlessly observe one or (with probability 1−q) two of the posted prices, and can accept one or pay to search again. The experiment varies q, the search cost, and the number of buyers. Equilibrium theory predicts a unified very low (high) price for q=0 (q=1) and predicts specific distributions of dispersed prices for q=1/3 and 2/3. Actual prices conform closely to the predictions in some treatments. Buyers’ reservation prices are biased away from the extremes, however, and sellers’ prices have positive autocorrelation and cross-sectional correlation.