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.     

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.     

Bertrand Competition Under Uncertainty

We look at a Bertrand model in which each firm may be inactive with a known probability, so the number of active firms is uncertain. The model has a mixed-strategy equilibrium, in which industry profits are positive and decline with the number of firms, the same features which make the Cournot model attractive. Unlike those in a Cournot model with similar uncertainty, Bertrand profits always increase in the probability that firms are inactive. Profits decline more sharply than in the Cournot model, the pattern found empirically in Bresnahan and Reiss [1991].     

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.     

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.     

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.     

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.     

Endogenous capacities and price competition: The role of demand uncertainty

We analyze the role of demand uncertainty in markets of fixed size, in which firms take long-run capacity decisions prior to competing in prices. We characterize the set of subgame perfect Nash equilibria under various assumptions regarding the nature and timing of demand uncertainty. In order to prove equilibrium existence, we identify a sufficient condition for the capacity choice game to be submodular. This condition resembles the standard downward-sloping marginal revenue condition used in Cournot games. A robust conclusion of the analysis is that equilibrium capacity choices are asymmetric, even when firms are ex-ante identical. Concerning the equivalence between the capacity-price game and the Cournot game, we find that with inelastic demands, the equilibria of the former belong to the equilibrium set of the latter. However, as compared to the Cournot game, the capacity-price game leads to lower prices and generates price dispersion.     

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.

     

An Asymmetric Oligopolist can Improve Welfare by Raising Price

We demonstrate that, in Bertrand/Cournot equilibrium, a firm with a relatively small market share may improve social welfare by raising its price. This could be because the price increase can mitigate an output-structure distortion: if there are two goods which have the same marginal cost, then, under some conditions, the good in higher demand (the efficient good) will have a higher markup rate than the other good (the inefficient good). This suggests that the output structure is distorted in favor of the inefficient good, since the higher markup rate of the efficient good should lead to a considerable increase in demand for the inefficient good.     

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.     

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.     

Welfare losses under Cournot competition

In a market for a homogeneous good where firms are identical, compete in quantities and produce with constant returns, the percentage of welfare losses (PWL) is small with as few as five competitors for a class of demand functions which includes linear and isoelastic cases. We study markets with positive fixed costs and asymmetric firms. We provide exact formulae of PWL and robust constructions of markets were PWL is close to one in these two cases. We show that the market structure that maximizes PWL is either monopoly or dominant firm, depending on demand. Finally we prove that PWL is minimized when all firms are identical, a clear indication that the assumption of identical firms biases the estimation of PWL downwards.     

The Strategic Effect of Bundling: A New Perspective

This paper investigates the strategic effect of the bundling strategy that is adopted by a multi-product firm that produces two complementary goods and faces one single-product rival in each market. I consider both the Cournot and Bertrand cases. When firms compete in quantities, bundling is completely ineffective. Under price competition, selling as a package is profitable when market competition is particularly tough. In such circumstances, the multi-product firm resorts to bundling to dampen the negative impact of low brand differentiation and/or scarce product complementarity. However, overall prices increase as a result of bundling, and not only consumer surplus, but also total social welfare, shrink.     

Elasticity of demand and behaviour-based price discrimination

Behaviour-based price discrimination (BBPD) is typically analysed in a framework characterised by perfectly inelastic demand. This paper provides a first assessment of the role of demand elasticity on the profit, consumer and welfare effects of BBPD. We show that the demand expansion effect, that is obviously overlooked by the standard framework with unit demand, plays a relevant role. In comparison to uniform pricing, we show that firms are worse off under BBPD, however, as demand elasticity increases the negative impact of BBPD on profits gets smaller. Despite a possible slight increase in the average prices charged over the two periods in comparison to uniform pricing, we show that BBPD boosts consumer surplus and that this benefit is independent of elasticity. In contrast to the welfare results derived under the unit demand assumption, where BBPD is always bad for welfare, the paper shows that BBPD can be welfare enhancing if demand elasticity is sufficiently high.     

Distributional assumptions in the theory of oligopoly information exchange

We analyze the profitability of information sharing among Cournot oligopolists receiving private information about random demand. In this setting, previous authors showed information exchange to be unprofitable when firms' marginal costs are constant and outputs are perfect substitutes. We introduce a measure of the increase in the accuracy of firms' demand forecasts when information is shared. We provide two examples showing when this measure is large, information exchange is profitable, even though firms' marginal costs are constant and outputs are perfect substitutes. Moreover, we show that in the linear-conditional-expectations framework, which has been standard in the literature, this measure reveals these accuracy gains to be severely limited.     

Distributional assumptions in the theory of oligopoly information exchange

We analyze the profitability of information sharing among Cournot oligopolists receiving private information about random demand. In this setting, previous authors showed information exchange to be unprofitable when firms' marginal costs are constant and outputs are perfect substitutes. We introduce a measure of the increase in the accuracy of firms' demand forecasts when information is shared. We provide two examples showing when this measure is large, information exchange is profitable, even though firms' marginal costs are constant and outputs are perfect substitutes. Moreover, we show that in the linear-conditional-expectations framework, which has been standard in the literature, this measure reveals these accuracy gains to be severely limited.     

Asymmetric price adjustments: A supply side approach

Using a model of dynamic price competition, we provide an explanation from the supply side for the well-established observation that output prices react faster in response to input cost increases than to decreases. When costs decline, the opportunity of profitable storing in anticipation of higher future costs allows competitive firms to coordinate on prices above current marginal costs. The initial price response is only partial and profitable storing relaxes competition. Conversely, when costs rise, storing is not beneficial in anticipation of lower future costs and firms immediately adjust their prices to current marginal costs, which entails the standard Bertrand outcome. Our results shed new light on the empirical evidence about asymmetric pricing and can stimulate further empirical investigation on this puzzle.     

Cournot and Bertrand equilibria compared: substitutability,complementarity and concavity

This paper assesses the view that Bertrand equilibrium is intrinsically more competitive than Cournot equilibrium. We consider an oligopoly model with linear demand, and a mixture of substitute and complementary products. Our results provide support for the conventional wisdom, and also indicate its limitations. We provide counter-examples showing that no clear-cut comparison of prices and quantities is possible without strategic complementarity in either of the two games. However, price competition is indeed more competitive according to the following criteria: lower mark-up/output ratios, larger average output, and lower average price.     

Bertrand under Uncertainty: Private and Common Costs*

Does asymmetric information about costs in a homogeneous-good Bertrand model soften competition? Earlier literature has shown that the answer (perhaps counter-intuitively) is “no,” while assuming (i) private (i.e., independent) cost draws and (ii) no drastic innovations. I first show, in a fairly general setting, that by relaxing (i) and instead allowing for sufficiently much common (interdependent) cost draws, asymmetric information indeed softens competition. I then study a specification that yields a closed-form solution and show that relaxing (ii) but not (i) does not alter the result in the earlier literature. While relying on specific functional forms, this specification is quite rich and might be useful in applications. It allows for any (positive) degree of interdependence between the cost draws, for any demand elasticity, and for any number of firms. The closed-form solution is simple and in pure strategies.