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.     

Secret information acquisition in Cournot markets

Summary. Two-stage game models of information acquisition in stochastic oligopolies require the assumption that firms observe the precision of information chosen by their competitors before determining quantities. This paper analyzes secret information acquisition as a one-stage game. Relative to the two-stage game firms are shown to acquire less information. Policy implications based on the two-stage game yield, therefore, too high taxes or too low subsidies for research activities. For the case of heterogeneous duopoly we briefly discuss comparative statics results. Received: August 9, 1999; revised version: May 31, 2000     

Cournot equilibrium in large markets under increasing returns

We consider Cournot partial equilibria in large markets where firms have decreasing average costs. It is shown that the outcome of competition is approximatelyefficient if entry is free.     

Cournot-Walras and Cournot equilibria in mixed markets: A comparison

Summary In this paper, we show that, in markets with a continuum of traders and atoms, the set of Cournot-Walras equilibria and the set of Cournot equilibria may be disjoint. We show also that, when the preferences of the traders are represented by Cobb-Douglas utility functions, the set of Cournot-Walras equilibria and the set of Cournot equilibria have a nonempty intersection.I would like to thank R. Amir, B. de Meyer, J. J. Gabszewicz, J.-F. Mertens, H. Polemarchakis and L. Ventura for some helpful discussions about the questions examined in the present work.     

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.     

Policy futures markets with multiple goals

Previous work in monetary policy futures markets under a single policy goal have shown this approach to be effective at eliminating the circularity problem inherent with private-sector targeting strategies. We extend this monetary policy setting framework to a typical multiple goal policy objective: inflation and output stabilization. We also demonstrate how the prices in policy futures markets can help resolve debates over important policy questions.     

Collusive equilibria in oligopolies with finite lives

It is generally accepted that collusive agreements cannot be sustained in oligopolies with finite lives. In this paper it is shown that, provided the number of competitors is neither too small nor too large, the most restrictive output, i.e., the monopoly output, can be sustained as a perfect Nash equilibrium. If the number of firms is too small only sequences of the Nash equilibria of the constituent market game can appear as perfect Nash equilibria. If the number of firms is too large the power of the cartel falls sharply.     

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.     

Schumpeterian competition in heterogeneous oligopolies

The modeling of Schumpeterian competition as a process of innovation, imitation and selection was first presented by Nelson/Winter (1982) in a simulation study and further analyzed in a similar but general analytical formulation by Iwai (1984a, 1984b). Their results concerning the relations between the combination of the different forces of Schumpeterian competition and market structure respectively the distributions of profits are interesting, but restricted to competitive markets. Comparing rules of thumb and satisficing for the Ramp;D decisions the present study analyzes the process of Schumpeterian competition in a heterogeneous oligopoly. Firstly, the authors find for the Ramp;D-concentration relation results contrary to the traditional interpretation of Schumpeter. Secondly, Iwai’s (1984a, 1984b) qualitative results hold in this less restrictive modeling.     

Free and second-best entry in oligopolies with network effects

We compare the number of firms in equilibrium in a Cournot industry with positive network effects and complete compatibility, under free and second-best entry. Under free entry, the firms decide whether to enter the market or not; in the second-best problem, the number of firms is established by the regulator to maximize social welfare (the regulator controls entry but not production). We show that when individual equilibrium output decreases with entry (business-stealing competition), free entry may lead to more or less firms than the second-best problem. This contrasts with the standard (nonnetwork) Cournot oligopoly model, wherein with business-stealing competition, free entry leads to an excessive number of firms compared with the second-best solution.     

Product differentiation in successive vertical oligopolies

Abstract.  This is a successive oligopoly model with two varieties of a final product. Downstream firms choose one variety to sell on a final market. Upstream firms specialize in the production of one input specifically designed for one variety, but they also produce the input for the other variety at an extra cost. We show that as more downstream firms choose one particular variety, more upstream firms specialize in the input specific to that variety, and vice‐versa. Multiple equilibria may result, and the softening effect of product differentiation on competition might not be strong enough to induce maximal differentiation. JEL Classification: L11, L13, L23     

Counterintuitive number effects in experimental oligopolies

Recent theoretical research on oligopolistic competition suggests that under certain conditions prices increase with the number of competing firms. However, this counterintuitive result is based on comparative-static analyses which neglect the importance of dynamic strategies in naturally-occurring markets. When firms compete repeatedly, supra-competitive prices can become sustainable but this is arguably more difficult when more firms operate in the market. This paper reports the results of laboratory experiments investigating pricing behavior in a setting in which (static) theory predicts the counterintuitive number effect. Under a random matching protocol, which retains much of the one-shot nature of the model, the data corroborates the game-theoretic prediction. Under fixed matching duopolists post substantially higher prices, whereas prices in quadropolies remain very similar. As a result, the predicted effect is no longer observed, and towards the end the reverse effect is observed.

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Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.      

Cournot games with biconcave demand

Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for the uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either “nearly linear” or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.     

Labor-managed Cournot oligopoly with product differentiation

Two dynamic systems of labor adjustments are formulated for labor-managed firms in Cournot oligopoly with product differentiation. The global stability conditions are derived for two types of Cournot equilibria corresponding to the stationary points of the two dynamic systems.The author is grateful to two referees of this Journal for helpful comments, which have led to a radical revision of an earlier version.     

Cournot duopoly with two production periods

We modify the Cournot model by allowing for two production periods before the market clears. The firms choose outputs simultaneously in the first period. These outputs become common knowledge and then the firms choose how much more to produce in the second period before the market clears. Any outcome on the outer envelope of the best-response functions between and including the firms' smallest Stackelberg outcomes is sustainable as a subgame perfect Nash equilibrium.     

Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives

In a game of a finite number of repetitions of a Cournot-type model of an industry, if firms are satisfied to get close to (but not necessarily achieve) their optimal responses to other firms' sequential strategies, then in the resulting noncooperative “equilibria” of the sequential market game, (1) if the lifetime of the industry is large compared to the number of firms, there are equilibria corresponding to any given duration of the cartel, whereas (2) if the number of firms is large compared to the industry's lifetime, all equilibria will be close (in some sense) to the competitive equilibrium.     

On the efficiency of indirect taxes in differentiated oligopolies with asymmetric costs

This paper shows that unit taxation can be welfare superior to ad valorem taxation in asymmetric and differentiated oligopolies if the goods are sufficiently differentiated, the cost variance is sufficiently large and the ad valorem tax rate is sufficiently high. Moreover, this result holds under either Cournot competition or Bertrand competition.      

Do short-term laboratory experiments provide valid descriptions of long-term economic interactions? A study of Cournot markets

One key problem regarding the external validity of laboratory experiments is their duration: while economic interactions out in the field are often lengthy processes, typical lab experiments only last for an hour or two. To address this problem for the case of both symmetric and asymmetric Cournot duopoly, we conduct internet treatments lasting more than a month. Subjects make the same number of decisions as in the short-term counterparts, but they decide once a day. We compare these treatments to corresponding standard laboratory treatments and also to short-term internet treatments lasting one hour. We do not observe differences in behavior between the short- and long-term in the symmetric treatments, and only a small difference in the asymmetric treatments. We overall conclude that behavior is not considerably different between the short- and long-term.     

Firm-specific information and explicit collusion in experimental oligopolies

We experimentally study the effect of information about competitors’ actions on cartel stability and firms’ incentives to form cartels in Cournot markets. As in previous experiments, markets become very competitive when individualized information is available and participants cannot communicate. In contrast, when communication is possible, results reverse: markets become less competitive and cartels become more stable when individualized information is available. We also observe that the extra profits that firms obtain thanks to the possibility to communicate are higher when individualized information is present, suggesting that firms have greater incentives to form cartels in that situation.