The incentives for takeover in oligopoly

We present a model of takeover where the target optimally sets its reserve price. Under relatively standard symmetry restrictions, we obtain a unique equilibrium. The probability of takeover is only a function of the number of firms and of the insiders' share of total industry gains due to the increase in concentration. Our main application is to the linear Cournot and Bertrand models. A takeover is more likely under Bertrand competition if goods are substitutes, and more likely under Cournot competition if goods are complements.     

Computing welfare losses from data under imperfect competition with heterogeneous goods

We study the percentage of welfare losses (PWL) yielded by imperfect competition under product differentiation. When demand is linear, even if prices, outputs, costs and the number of firms can be observed, PWL is arbitrary in both Cournot and Bertrand equilibria. If in addition the elasticity of demand (resp. cross elasticity of demand) is known, we can calculate PWL in a Cournot (resp. Bertrand) equilibrium. When demand is isoelastic and there are many firms, PWL can be computed from prices, outputs, costs and the number of firms. We find that price–marginal cost margins and demand elasticities may influence PWL in a counterintuitive way. We also provide conditions under which PWL increases or decreases with concentration.     

On the endogeneity of Cournot, Bertrand, and Stackelberg competition in oligopolies

In many industries, firms pre-order input and forward sell output prior to the actual production period. It is known that forward buying input induces a “Cournot-Stackelberg endogeneity” (both Cournot and Stackelberg outcomes may result in equilibrium) and forward selling output induces a convergence to the Bertrand solution. I analyze the generalized model where firms pre-order input and forward sell output. First, I consider oligopolists producing homogenous goods, generalize the Cournot-Stackelberg endogeneity to oligopoly, and show that it additionally includes Bertrand in the generalized model. This shows that the “mode of competition” between firms may be entirely endogenous. Second, I consider duopolies producing heterogenous goods. The set of equilibrium outcomes is characterized and shown not to contain the Bertrand solution anymore. Yet, forward sales increase welfare also in this case, notably even when goods are complements.     

Price and quantity experimentation: A synthesis

This paper compares experimentation about product differentiation in a linear setting under four market structures: quantity-setting and price-setting monopoly, Cournot and Bertrand duopoly. Quantity-setting firms always experiment by raising their quantities and the monopolist experiments relatively more than the duopolists. A price-setting monopolist does not experiment. The value of information to Bertrand duopolists may be positive or negative depending on the degree of product differentiation. When information is valuable, price-setting duopolists experiment by lowering prices. A numerical example indicates that the intensity of experimentation is higher in a Cournot duopoly than in a Bertrand duopoly.     

Common ownership,market power,and innovation

I examine the effects of overlapping ownership on market power when there are external effects across firms. This is done in an oligopoly model with cost-reducing innovation with technological spillovers where firms have an overlapping ownership structure based largely on López and Vives (2019). The model allows for Cournot competition with homogeneous product and for Bertrand with differentiated products as well as for strategic effects of R&D investment. It derives positive testable implications and normative results to inform policy.     

Horizontal integration in the Dutch financial sector

In this paper, the consequences of cross-shareholding in an n-firm industry are analyzed. Our attention focuses on the case where firms have silent interests in each other. These interests can be direct or indirect. We analyze the effects of cross-shareholding on the price–cost margins in a Cournot and a Bertrand setting. In all cases, competition is reduced due to shareholding interlocks. As an empirical example the Dutch financial sector is used. Comparing the case of shareholding with the case of no-shareholding, the price–cost margins are found to be up to 2% higher in a Bertrand market, and at least 8% higher in a Cournot market.     

On Welfare under Cournot and Bertrand Competition in Differentiated Oligopolies

Häckner (2000, Journal of Economic Theory 93, 233–239) shows that in a differentiated oligopoly with more than two firms, prices may be higher under Bertrand competition than under Cournot competition, implying that the classical result of Singh and Vives (1984, Rand Journal of Economics, 15, 546–554) that Bertrand prices are always lower than Cournot prices is sensitive to the duopoly assumption. Häckner (2000, Journal of Economic Theory, 93, 233–239), however, leaves unanswered the important question of whether welfare may be lower under price competition. This note shows that in Häckner’s model both consumer surplus and total surplus are higher under price competition than under quantity competition, regardless of whether goods are substitutes or complements.     

Oligopoly intermediation,relative rivalry and market conduct

We consider two firms that compete against each other jointly in upstream and downstream markets under two pricing games: Purchasing to stock (PTS), in which firms select input prices prior to setting consumer prices; and purchasing to order (PTO), in which firms sell forward contracts to consumers prior to selecting input prices. The antitrust implications of the model depend on the relative degree of oligopoly rivalry in the upstream and downstream markets. Firms strategically precommit to setting prices in the less rivalrous market, which serves to soften competition in the more rivalrous market, resulting in anticompetitive effects. Bertrand prices emerge in equilibrium when the markets are equally rivalrous, while Cournot outcomes arise with upstream monopsony or downstream monopoly markets. The slope of firm reaction functions depends on relative rivalry, a feature we use to derive testable hypotheses for antitrust analysis of a wide variety of industry practices.     

MARKET COMPETITION,R&D AND FIRM PROFITS IN ASYMMETRIC OLIGOPOLY*

We investigate a Cournot model with strategic R&D investments wherein efficient low‐cost firms compete against less efficient high‐cost firms. We find that an increase in the number of high‐cost firms can stimulate R&D by the low‐cost firms, while it always reduces R&D by the high‐cost firms. More importantly, this force can be strong enough to compensate for the loss that arises from more intense market competition: the low‐cost firms' profits may indeed increase with the number of high‐cost firms. An implication of this result is far‐reaching, as it gives low‐cost firms an incentive to help, rather than harm, high‐cost competitors. We relate this implication to a practice known as open knowledge disclosure, especially Ford's strategy of disclosing its know‐how publicly and extensively at the beginning of the 20th century.     

Vertical Contract Disclosure in Three-Tier Industries*

Consider a three-tier industry with a monopolist supplying a manufacturer which sells its product to final consumers through two retailers. Contracts are linear and secret. Hence, upon receiving an out-of-equilibrium offer, each retailer must form a belief about the identity of the deviating upstream firm. This beliefs' specification problem wipes out if an Open Book Accounting (OBA) policy is implemented, whereby the input price is disclosed to retailers. Under Cournot (Bertrand) competition, OBA increases industry profits and consumer surplus if retailers believe that any out-of-equilibrium offer is more likely to reflect a deviation by the upstream supplier (by the manufacturer).     

Timing of technology adoption and product market competition

This paper examines how product market competition affects firms' timing of adopting a new technology, as well as whether the market provides sufficient adoption incentives. It demonstrates that adoption dates differ, not only among symmetric firms, but also among markets with different market features. More specifically, technology adoption can occur earlier in a market with Cournot competition than in a market with Bertrand competition. It can also occur earlier in a market in which goods are not too close substitutes. Therefore, this paper shows that competition toughness does not always reinforce adoption incentives. When goods are sufficiently differentiated, adoption occurs later than is socially optimal.     

Input Price Discrimination and Allocation Efficiency

This research examines the effects of input price discrimination on allocation efficiency and social welfare. Instead of assuming constant marginal costs, we allow downstream firms to produce under increasing marginal costs. When downstream firms operate in separate markets, even though total output remains unchanged, consumer surplus and social welfare could be greater under discriminatory pricing than under uniform pricing. Moreover, the social desirability of input price discrimination can still hold true when downstream firms compete either in Cournot or Bertrand fashion.

     

The Aggregate Relation between Profits and Concentration is Consistent with Cournot Behavior

An important and controversial stylized fact inindustrial organization is the positive correlationbetween industry profit and concentration. Oneinterpretation of this finding is based on thetheories of Chamberlin and Stigler, which imply thatconcentrated industries facilitate collusion. Butnon-cooperative profit maximizing behavior can alsogenerate a positive correlation. This paperpresents an equilibrium model of oligopoly whichnests the behavioral assumptions of Bertrand,Cournot, and Chamberlin. Simulations of the modelunder the Cournot assumption yield regressioncoefficients for the profits-concentration relationthat are very close to the estimated coefficients inthe literature.     

The incentives for cost reduction in a differentiated industry

This paper investigates how the incentives for cost reduction in a differentiated industry depend upon the degree of product substitutability. When goods are imperfect substitutes, both Cournot and Bertrand competition result in underinvestment in the sense that a social planner would be willing to pay more for a given cost reduction than a profit-maximizing firm. Overinvestment may occur when the goods are sufficiently close substitutes. Similarly, Cournot competition provides a stronger incentive to innovate than Bertrand competition if the degree of substitutability is low, and a weaker incentive if this degree is high.     

Comparing Cournot and Bertrand Equilibria in the Presence of Spatial Barriers and R&D

Review of Industrial Organization - We compare the equilibria under Bertrand and Cournot competition in the spatial barbell model where spatial barriers and process R&D are involved. We...     

Local network externalities and market segmentation

This paper models interaction between groups of agents by means of a graph where each node represents a group of agents and an arc represents bilateral interaction. It departs from the standard Katz–Shapiro framework by assuming that network benefits are restricted only amongst groups of linked agents. It shows that even if rival firms engage in Bertrand competition, this form of network externalities permits strong market segmentation in which firms divide up the market and earn positive profits. The analysis also shows that some graphs or network structures do not permit such segmentation, while for others, there are easy to interpret conditions under which market segmentation obtains in equilibrium.     

When is it rational for firms to acquire silent interests in rivals?

The cartelizing effects of firms' shareholding in rivals have been well established theoretically, yet empirical instances of such are rate to nonexistent. It is argued here that if the stock market is efficient in the sense that share prices reflect post-share trading product market equilibria, then acquiring shares in rivals is not subgame perfect for Cournot oligopolies but is subgame perfect for some Bertrand oligopolies. Acquiring a silent interest in a rival is an example of the “fat cat ploy”. That the stock market is not a cartel maker is consistent with Cournot having wide empirical application, but not with Bertrand.     

Optimal bid disclosure in patent license auctions under alternative modes of competition

The literature on patent license auctions in oligopoly assumed that the auctioneer reveals the winning bid and stressed that this gives firms an incentive to bid high in order to signal an aggressive output strategy in a downstream Cournot market game, and conversely bid low to signal acquiescent pricing in a Bertrand market game. The present paper examines the information revealed by publishing the winning or the losing or no bid, assuming an oligopoly with differentiated goods. We rank disclosure rules and find that it is not optimal for the innovator to disclose the winning bid, regardless of the mode of competition.     

Proof of nonparticipation in a price fixing conspiracy

When a group of firms colludes on price, the industry price will rise even when there are some firms that do not participate in the conspiracy. If the government or private parties file antitrust suits, the noncolluders face the problem of establishing their innocence since their prices rise along with those of the colluders. We propose a simple output test. Under various models of oligopoly pricing—Bertrand, Cournot, and Stackelberg—we show that the colluders restrict their output while the noncolluders take advantage of the higher price by expanding their outputs. Thus, distinguishing between colluders and noncolluders involves simply observing the output behavior of the industry members.The authors appreciate the support of the Public Policy Research Center at the University of Florida. We regret that B&R Associates is purely imaginary as is the industry.     

Non-Nash equilibria of Darwinian dynamics with applications to duopoly

Consider a symmetric, differentiated duopoly. If firms’ strategy choices, in the repeated game, follow a stochastic Darwinian process, then they cluster around a strategy profile that is typically not a one-shot Nash equilibrium. This profile is invariant under a broad class of transformations of the strategy space (e.g. Bertrand vs. Cournot); this implies that mixing imitative and rational decision-makers can produce purely imitative outcomes. The evolution of objectives consistently distorts behavior toward revenue maximization, and the distortion increases in ‘good times’ of high demand and low costs. We generalize the results beyond duopoly to symmetric, two-player games.