Perfectly competitive markets as the limits of cournot markets

A perfectly competitive, partial equilibrium market for a single homogeneous good with a (bounded) continuum of infinitesimal firms is considered. Cost functions are essentially unrestricted and are allowed to vary smoothly across firms. A sequence (net) of Cournot markets (each with a finite number of firms) which converge smoothly to the perfectly competitive limit in terms of both the inverse demand functions and the distributioon of firm technologies is introduced and it is shown that all markets sufficiently far along the sequence have a Cournot equilibrium and all the Cournot equilibria converge to the perfectly competitive equilibrium of the limit market.     

Coordination in Oligopoly

The private and social efficiency of two "behavioral" coordination mechanisms is examined in this paper. In Cournot oligopoly, firms prefer immediate coordination on the Nash equilibrium (interpreted as a preplay communication) over the best-reply dynamics (and fictitous play) which converge to the equilibrium, but with delay (interpreted as a decentralized learning process). In Bertrand oligopoly, firms prefer the learning process. These results indicate that firms have incentives to create institutions, such as trade associations or informal meetings, to facilitate coordination of production capacities, but not prices. Moreover, quantity agreements may even increase social welfare.     

Competition with Congestible Networks

We analyse competition between two network providers when the quality of each network depends negatively on the number of customers connected to that network. With respect to price competition we provide a sufficient condition for the existence of a unique pure strategy Nash equilibrium. Comparative statics show that as the congestion effect gets stronger quantities will decrease and prices increase, under both Bertrand and Cournot competition. In an example with endogenous capacities it turns out that equilibrium capacities are at first increasing and then decreasing in the strength of congestion. Furthermore, capacities are higher under Cournot competition. Welfare comparisons between Bertrand and Cournot competition are unambiguous for fixed capacities, but may turn around for endogenous capacities.     

TO REGULATE OR TO DEREGULATE? THE ROLE OF DOWNSTREAM COMPETITION IN UPSTREAM MONOPOLY VERTICALLY LINKED MARKETS

This paper attempts to cast light to the effect of monopoly regulation in Cournot markets compared to its effect in Bertrand markets. To this purpose, we use a simple model of a vertically linked market, where an upstream regulated natural monopoly is trading via two‐part tariff contracts with a downstream duopoly. Combining our results to those of the existing literature on deregulated markets, we argue that when the downstream competition is in prices, efficiency dictates regulating the monopoly with a marginal cost based pricing scheme. However, this type of regulation leads to significant welfare loss, when the downstream market is characterized by Cournot competition.     

Behavioral convergence properties of Cournot and Bertrand markets: An experimental analysis

This paper reports an experiment that examines the relative convergence properties of differentiated-product Cournot and Bertrand oligopolies. Overall, Bertrand markets tend to converge to Nash equilibrium predictions more quickly and more completely than Cournot markets. Further, when products are close substitutes Bertrand markets respond more quickly to an announced nominal shock. As products become weaker substitutes, however, an increased tendency for tacit collusion degrades convergence in Bertrand markets. This effect is particularly pronounced following a nominal shock. Our results suggest that in an oligopoly context variations in decision error costs dominate a ‘Strategic Substitutes Effect’ isolated in previous experimental research.     

Economic natural selection in Bertrand and Cournot settings

We study economic natural selection in classical oligopoly settings. When underlying pure strategies consist of a finite number of prices, convex monotonic dynamics always converge under a weak condition to the smallest price in the support of the initial state that exceeds marginal cost. When underlying pure strategies consist of a finite number of quantities, monotonic dynamics always converge under a specific condition to a quantity equal or similar to classical Cournot equilibrium.     

Nonlinear incentive provision in Walrasian markets: a Cournot convergence approach

The paper studies insurance with moral hazard in a system of contingent-claims markets. Insurance buyers are modelled as Cournot monopolists or oligopolists. The other agents condition their expectations on market prices, as in models of rational-expectations equilibrium with asymmetric information. Thereby they correctly anticipate accident probabilities corresponding to effort incentives induced by insurance buyers’ net trades. When there are many agents to share the insurance buyers’ risks, Cournot equilibrium outcomes are close to being second-best. In contrast, if insurance buyers are price takers, equilibria fail to exist or are bounded away from being second-best.     

EXPERIMENTAL WORK ON SUBSIDIES,MORAL HAZARD,AND MARKET POWER IN AGRICULTURAL MARKETS

Laboratory markets are created to capture the important features of agricultural commodity markets. Sellers make production decisions and hold inventories before goods are sold. In a posted‐bid auction environment, price supports create a moral hazard for sellers. Part of the price‐support subsidy is transferred to buyers in the form of lower prices, which are close to those predicted by the buyers' Cournot level. The subsidy program is expensive for this reason. Lump‐sum payments correct the moral hazard problem and are better at transferring income to sellers. However, transfers made at the beginning of each production period cause a decline in production levels. (JEL D44, C92)     

Stability of supply function equilibria implications for daily versus hourly bids in a poolco market

We consider a supply function model of a poolco electricity market where demand varies significantly over a time horizon such as a day and also has a small responsiveness to price. Although there are equilibria yielding prices at peak that are close to Cournot prices, it is known that the wider the range of demand uncertainty the narrower the range of such supply function equilibria. Here we show that such equilibria are also typically unstable and consequently would be difficult to sustain in practice. This strengthens the results of Green and Newbery by ruling out many equilibria that have high prices. We demonstrate this result both theoretically under somewhat restrictive assumptions and also numerically using both a three-firm example system and a five-firm example system having generation capacity constraints. Hence, this reinforces the conclusion that the market outcome is significantly influenced by a requirement that offers into the poolco be consistent over the time horizon. This result contrasts with markets where bids can be changed on an hourly basis, where Cournot prices are possible outcomes. The stability analysis has important policy implications for the design of day-ahead electricity markets. The stability perspective also provides a narrowing of the equilibrium selection that strengthens empirical analysis.      

An experimental study of coordination and learning in iterated two-market entry games

Summary. Tacit coordination in large groups is studied in an iterated market entry game with complete information and multiple market capacities that are varied randomly from period to period. On each period, each player must decide independently whether to enter any of the markets, and if entering, which of the two markets to enter. Across symmetric and asymmetric markets, we find remarkable coordination on the aggregate level, which is accounted for by the Nash equilibrium, together with considerable individual differences in frequency of entry and decision rules. With experience, the decisions of most players converge to decision rules with cutoff values on the combined market capacity that determine whether or not to enter but not which of the two markets to enter. This latter decision is determined probabilistically by the differential market capacities. The aggregate and individual results are accounted for quite well by a reinforcement-based learning model that combines deterministic and probabilistic elements.     

Capacity precommitment and price competition yield the Cournot outcome

We introduce a simple model of oligopolistic competition where firms first build capacity, and then, after observing the capacity decisions, choose a reservation price at which they are willing to supply their capacities. This model describes many markets more realistically than the model of Kreps and Scheinkman [Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell J. Econ. 14, 326–337]. We show that in this new model every pure strategy equilibrium yields the Cournot outcome, and that the Cournot outcome can be sustained by a pure strategy subgame perfect equilibrium.     

International trade in genetically modified products

This paper investigates competition between two markets that sell close substitutes: a traditional product and a genetically modified (GM) product. Tightening an import quota on the GM product raises the prices of both goods and hurts consumers. Two scenarios are considered under free trade: Cournot–Nash equilibrium and Stackelberg equilibrium. A Stackelberg type monopolist produces more, and the competitive traditional firms produce less, than in Cournot–Nash equilibrium. In the long run, an import ban on the GM product does not help competitive producers of the genetically modified organism (GMO)-free products but benefits only the landowners in Europe.     

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     

Coalition-proof supply function equilibria under capacity constraints

Whereas in the absence of capacity constraints the Cournot outcome is the unique coalition-proof supply function equilibrium outcome, the presence of capacity constraints may enlarge the set of equilibrium outcomes. Interestingly, if capacities are sufficiently asymmetric the new equilibrium prices are below the Cournot price. These results have important implications for merger and privatization policies: specifically, capacity divestiture will not necessarily imply lower market prices.This article is based on the second chapter of my PhD dissertation. I benefited from the comments and suggestions of Diego Moreno and Bill Hogan. I thank three anonymous referees for helpful comments. Seminar audiences at Carlos III and Harvard are gratefully acknowledged. The author is currently a Repsol YPF fellow at the Harvard John F. Kennedy School of Government. I am grateful to the Repsol YPF-Harvard Fellowship Program for financial support.     

Kreps & Scheinkman with Product Differentiation

Kreps and Scheinkman (1983)’s celebrated result is that in a two-stage model of a market with homogeneous products in which firms noncooperatively pick capacities in the first stage and set prices in the second stage, the equilibrium outcome is that of a one-shot Cournot game. This note derives capacity best response functions for the first stage and extends the Kreps and Scheinkman result to the case of differentiated products.     

Price and Quantity Competition in a Differentiated Duopoly With Network Compatibility Effects

We consider the efficiency of price and quantity competition in a network products market, where we observe product compatibility with network externalities (hereafter, network compatibility effects). In particular, if network compatibility effects between firms are sufficiently asymmetric, the Cournot equilibrium is more efficient than the Bertrand equilibrium in terms of larger consumer, producer and total surpluses. Then, we consider an endogenous choice of the strategic variables, price and quantity. If the degree of network compatibility effects of the rival firm is larger (smaller) than the degree of product substitutability, then choosing prices (quantities) is a dominant strategy for the firm. Thus, if the network compatibility effects of both firms are larger (smaller), the Bertrand (Cournot) equilibrium arises. Furthermore, if the network compatibility effects between the firms are sufficiently asymmetric, the firm with a larger (smaller) network compatibility effect than a certain level of product substitutability chooses quantities (prices). In this case, the Cournot–Bertrand equilibrium arises, which is less (more) efficient than the Cournot equilibrium in terms of consumer (producer) surplus.     

COMMUNICATION AND MARKET SHARING: AN EXPERIMENT ON THE EXCHANGE OF SOFT AND HARD INFORMATION

We study the role of communication in collusive market sharing. In a series of Cournot oligopoly experiments with multiple markets, we vary the information that firms can exchange: hard information—verifiable information about past conduct—and soft information—unbinding information about future conduct. We find that the effect of communication on the firms' ability to collude depends on the type of information available: Whereas market prices increase only slightly with hard information, the price raise due to soft information is substantial. Our results point to the types and contents of communication that should be of particular concern to antitrust authorities.     

Equilibrium prices in the Bertrand and Cournot oligopolies

The equilibrium prices for the Bertrand and Cournot oligopolies with product differentiation are compared. If all firms have linear demand and cost functions, and if, in addition, the Jacobian matrix of the demand functions has a dominant negative diagonal, the Cournot equilibrium prices are not lower than the Bertrand ones. The general condition for the comparison of the Bertrand and Cournot equilibrium prices can be derived even if the nonlinearity is involved in the cost and/or demand functions.     

Competition,strategic delegation and delay in technology adoption

This paper examines how strategic managerial delegation affects firms' timing of adoption of a new technology under different modes of product market competition. It demonstrates that strategic delegation has differential impacts on adoption dates under Cournot and Bertrand competitions. Strategic delegation with ‘own-performance’-based incentive schemes always leads to early adoption in markets with Bertrand competition compared to that under no-delegation, but not necessarily so in markets with Cournot competition. It also shows that under strategic delegation with ‘own-performance’-based incentive schemes, adoption occurs earlier (later) in markets with Cournot competition than in markets with Bertrand competition, if the degree of product differentiation is high (low). In contrast, under strategic delegation with ‘relative-performance’-based incentive schemes, adoption dates do not differ across markets with different modes of competition. It also analyses implications of firms' choice over types of managerial incentive schemes on the speed of diffusion of new technology.     

Stackelberg Beats Cournot — On Collusion and Efficiency in Experimental Markets

We report on an experiment designed to compare Stackelberg and Cournot duopoly markets with quantity competition. We implement both a random matching and a fixed-pairs version for each market. Stackelberg markets yield, regardless of the matching scheme, higher outputs than Cournot markets and, thus, higher efficiency. For Cournot markets, we replicate a pattern known from previous experiments. There is stable equilibrium play under random matching and partial collusion under fixed pairs. We also find, for Stackelberg markets, that competition becomes less intense when firms remain in pairs but we find considerable deviations from the subgame perfect equilibrium prediction which can be attributed to an aversion to disadvantageous inequality.