Introduction

Economists using games to represent oligopolistic competition debated the relative merits of models using prices or quantities as firms' strategic variables from as early as Bertrand's (1883) criticism of Cournot (1838). The extent to which firms can choose price or quantity must, of course, crucially affect the nature of competition. If they have some choice, however, the extent to which firms want to choose price or quantity may be important.

A common way of analyzing multiperiod oligopoly models without dynamic interactions in the payoff structure is to compute a Nash equilibrium for each period taken separately. Many economists believe that behavior in a repeated market game cannot be predicted accurately with a period-by-period sequence of such “static” Nash equilibria, but an explicitly dynamic analysis can be extremely difficult unless the class of feasible dynamic strategies is restricted.

There is an embarrassing multiplicity of alternative oligopoly “solutions” that are computationally less complex than game-theoretic approaches to multiperiod games. Many of these alternative solutions can be classified as conjectural variations models in which firms are assumed to conjecture that changes in their own decisions will induce reactions by other firms. These reactions are typically assumed to be characterized by functions that are locally linear. Almost any configuration of decisions can be an equilibrium for some conjectured reaction functions, so these models have little empirical content unless the reaction functions themselves are determined endogenously.

Timothy Bresnahan (1981) has proposed a consistency condition that can often be used to determine specific conjectured reactions. Martin Perry provides a clear explanation of this consistency condition in the context of a duopoly in which firms' decisions are output quantities:

This paper examines the existence of n-firm Cournot equilibrium in a market for a single homogeneous commodity. It proves that if each firm's marginal revenue declines as the aggregate output of other firms increases (which is implied by concave inverse demand) then a Cournot equilibrium exists, without assuming that firms have nondecreasing marginal cost or identical technologies. Also, if the marginal revenue condition fails at a “potential optimal output”, there is a set of firms such that no Cournot equilibrium exists. The paper also contains an example of nonexistence with two nonidentical firms, each with constant returns to scale production.

Introduction

Cournot equilibrium is commonly used as a solution concept in oligopoly models, but the conditions under which a Cournot equilibrium can be expected to exist are not well understood. The nature of each firm's technology, whether all firms have identical technologies, and restrictions on the market inverse demand vary from model to model, and are all important for the existence of Cournot equilibrium. This paper examines the question of existence of (pure strategy) Cournot equilibrium in a single market for a homogeneous good. In this context there are two known types of existence theorems. The first type allows general (downward sloping) inverse demand and shows the existence of Cournot equilibrium when there are n identical firms with convex technologies (nondecreasing marginal cost and no avoidable fixed costs). See McManus [1962, 1964] and Roberts and Sonnenschein [1976].

The literature on financial structure and the literature on oligopoly have at least one common feature: they both place relatively little emphasis on the strategic relationships between financial decisions and output market decisions. In financial theory, the product market is typically assumed to offer an exogenous random return which is unaffected by the debt-equity positions of the firms in the market. Correspondingly, in the economic analysis of oligopoly, the firm's obligations to debt holders and the possibility of financial distress are usually ignored in modeling the strategic interaction between producers in the output market.

This approach of focusing separately on financial and output decisions is clearly useful in understanding certain aspects of both financial structure and strategic output market behavior. It seems equally clear, however, that there are important linkages between financial and output decisions.

The choice of financial structure can affect output markets in the following way, which we refer to as the limited liability effect of debt financing. As firms take on more debt, they will have an incentive to pursue output strategies that raise returns in good states and lower returns in bad states.

Introduction

In a stimulating paper, Wilson (1977) makes an observation about how a particular market mechanism is able to process diverse imperfect information in a very efficient way.

Introduction

It is a well-established idea that Bertrand (price) competition is more efficient than Cournot (quantity) competition. In fact with an homogenous product and constant marginal costs the Bertrand outcome involves pricing at marginal cost. This is not the case with differentiated products where margins over marginal cost are positive even in Bertrand competition. Shubik showed in a model with a linear and symmetric demand structure that the margin over marginal cost is larger in Cournot competition, and that, under certain conditions, as the number of varieties grows equilibrium prices go to marginal cost in either Bertrand or Cournot competition (see Shubik [16, Chaps. 7 and 9]).

This article uses an infinite-regress model of firm-level decisions to find a rational expectations equilibrium for a duopoly and to relate concepts of conjectural variations and consistency to the Cournot equilibrium. The model derives a conjectural variation instead of assuming it. In particular, the Cournot equilibrium is shown to be consistent in the usual sense of the literature. The conflict between notions of consistent conjectures and the Cournot equilibrium results from a compounding problem inherent in the earlier models. We extend these results to the n-firm problem. Alternatively, the article can be viewed as providing a purely static model that generates the Cournot equilibrium without reference to conjectures or quasi dynamics.

Introduction

Recently, the use of the Cournot model as a valid equilibrium solution in noncooperative oligopoly settings has been questioned in a variety of articles using the concept of a consistent conjectural variation (see, e.g., Laitner (1980), Bresnahan (1981), Kamien and Schwartz (1983), Perry (1982), and Kalai and Stanford (1982). A conjectural variation is a conjecture by one firm about how the other firm will adjust its decision variable with respect to potential adjustments in the first firm's action. A consistent conjectural variation is a conjectural variation that is correct: predicted change (locally) in the relevant decision variable (output or price) on the part of one's competitor is what actually occurs. A consistent conjectures equilibrium is a consistent conjectural variation equilibrium, in the sense that no individual change in a decision variable is profitable.

Introduction

This paper unifies the two leading classical concepts of equilibrium for an economy: Walras equilibrium and Cournot equilibrium. The theory provides a fresh setting for the study of competitive markets, and leads to a description of economic equilibrium which differs in substance from the one offered by modern formal competitive theory (see, e.g., Debreu [3]).

Modern formal competitive theory does not permit free entry, hence the number of firms is fixed. Further, it is posited that firms behave in one of two ways. In one case, perfect competition is assumed: Firms act as if they have no effect on price; they maximize profit taking prices as given. In the other case, imperfect competition is assumed: Firms recognize and act on their ability to influence price. In the model we present, price and market power are determined by free entry and the size of efficient scale relative to demand. Several distinctive features of classical economic analysis occupy a central role in the development.

Specifically, we study a model in which the number of firms is determined endogenously; firms enter when it is profitable to enter, and the entry of firms is a driving force in the explanation of value. The presence of fixed costs (more precisely, the fact that the efficient scale of firms is bounded away from zero) places a limit on the number of firms which are “active” in an equilibrium.

Introduction

In 1838 Augustin Cournot introduced his model of market equilibrium, which has become known in modern game theory as a noncooperative (or Nash) equilibrium [1]. Cournot's model was intended to describe an industry with a fixed number of firms with convex cost functions, producing a homogeneous product, in which each firm's action was to choose an output (or rate of output), and in which the market price was determined by the total industry output and the market demand function. A Cournot-Nash equilibrium is a combination of outputs, one for each firm, such that no firm can increase its profit by changing its output alone.

Cournot thought of his model as describing “competition” among firms; this corresponds to what we call today the “noncooperative” character of the equilibrium.

Introduction

In the Cournot [1838] solution to the oligopoly problem, each firm's output choice is profit-maximizing given the outputs of the other firms. The Cournot approach is conventionally extended to industries with merged firms and cartels by treating each merged entity as a collective of plants under the control of a particular player in a noncooperative game. The payoff to each coalition is the sum of the profits that accrue to each of its members. For each exogenous specification of market structure (partition of plants into coalitions), outputs, profits, and market prices are endogenously determined.

The purpose of this article is to explore and evaluate an unnoticed comparative-static implication of such Cournot models: some exogenous mergers may reduce the endogenous joint profits of the firms that are assumed to collude.

Overview

This part rounds out the volume by presenting eight papers wherein the Cournot model plays a fundamental role in analyzing economic behavior. As indicated in the Introduction, there were literally hundreds of possible papers from which to choose. The organizing principle employed was to emphasize two aspects of this literature, applications of the Cournot model to provide insights about both the theoretical analyses of competitive behavior and the various observable outcomes of competitive behavior. The first five papers focus on three theoretical issues: obtaining Walrasian outcomes when firms have nonconvex technologies and some monopoly power; the incentives for competitors to implicitly correlate product market strategies via sharing of information when the ability to explicitly correlate via collusion is not possible; and the implications of strategic interaction for models that allow changes in the number of firms in an industry. The rest of the papers in this part use a Cournot model to understand seemingly contradictory behavior in the “real world.” Let us consider each topic area in turn.

Papers focusing on theoretical models of competitive behavior

It is probably universally true that the first model of competitive behavior a student encounters in a course in economics is that of perfect competition. Fundamental to the exposition is an assertion that firms take prices as given, or that even if they don't they somehow act as if they do.

Introduction

We examine how incentives for two duopolists to honestly share information change depending upon the nature of competition (Cournot or Bertrand) and the nature of the information structure. In contrast to earlier papers [Gal-Or (1985), Novshek and Sonnenschein (1982) and Vives (1984)], where uncertainty is about an unknown common demand intercept, in the present paper uncertainty is about unknown private costs. With an uncertain demand each firm observes a private signal of a parameter of the model which affects everyone's payoff function in the same way. With uncertain costs each firm observes a private signal of a parameter of the model which is different for each firm. While the first environment is called a “common value” problem in the auction literature, the second environment is called a “private values” problem in the same literature.

Overview

The eight papers in this part deal with various aspects of Cournot's model and analysis and thus focus on the model itself, as opposed to applications of the model. The first three papers explore the basic notion of noncooperative behavior embodied in Cournot's model and focus around two themes: existence and versatility. Novshek's paper provides existence. As discussed in the Introduction, this paper is especially appealing in that it specifically admits cost functions which are conceptually consistent with long-run oligopoly behavior, in stark contrast with the earlier existence literature which usually employed an assumption (such as convexity of all cost functions) that eliminated or severely restricted scale economies.

The versatility of the noncooperative model of multiagent behavior is best seen by considering collusion. At least since Adam Smith many economists have harbored the deep suspicion that, given the opportunity, firms in an industry will collude. The problem for the firms, of course, is how to make the collusion stick. For many years collusion was viewed as requiring individually irrational behavior on the part of the participants: short of enforcement via government intervention, individual maximizing behavior on the part of the agents should lead to defections from the collusive solution. Specifically, at least one firm would find it advantageous to expand output and cut price.

More generally, the strategies for firms that would support a collusive outcome do not form a Nash equilibrium in the one-shot game, since they do not reflect individual maximizing behavior.

Théorie mathématique de la richesse sociale, by Léon Walras, professor of political economy at the academy of Lausanne, Lausanne, 1883.

Recherches sur lesprincipes mathématiques de la théorie des richesses, by Augustin Cournot, Paris, 1838.

The title of these books seems to promise a new and secure path for the science of Adam Smith; however, the authors have received a very indifferent reception. A distinguished scholar, a skillful writer, endowed with an original and lofty intellect, Cournot was a master in the art of deduction. Mr. Walras does himself credit by being his disciple. “Mr. Cournot”, he says, “is the first person to have seriously attempted the application of mathematics to political economy; he did so in a work published in 1838 which no French author has ever criticized. I have insisted,” adds the learned professor of Lausanne, “upon mentioning the author of a remarkable endeavor upon which, I repeat, no judgment has been brought and to which I dare say justice has not been rendered.”

This reproach, publicly addressed to Cournot's fellow countrymen, gave me a reason for re-reading a thoroughly forgotten work which, in spite of the well deserved reputation of the author, has not left a favorable impression upon all of those who have read it. “The title of my work,” says Cournot in his preface, “not only announces theoretical research, it indicates that I intend to apply to it the forms and symbols of mathematical analysis.”

If control of my decisions is in the hands of an agent whose preferences are different from my own, I may nevertheless prefer the results to those that would come about if I took my own decisions. This has some interesting implications for the theory of the firm. For example, in markets where firms are interdependent, it is not necessarily true that maximum profits are earned by firms whose objective is profit-maximization.

This can be seen in a simple example of entry deterrence. Firm A is deciding whether or not to enter a market currently monopolized by firm B. If A enters, B (or rather its managers) must decide whether to respond aggressively or in an accommodating fashion. Entry is profitable for A if and only if B does not fight. Faced with the fact of entry, it is more profitable for B to accommodate than to fight, but B's profits are greater still if there is no entry.

Introduction

Industrial organization economists have recognized for some time that the problem of distinguishing empirically between collusive and noncooperative behavior, in the absence of a “smoking gun,” is a difficult one. This article exploits the model proposed in Green and Porter (1984). They consider an explicitly dynamic model in which the firms of an industry are faced with the problem of detecting and deterring cheating on an agreement. In particular, they assume that firms set their own production level and observe the market price, but do not know the quantity produced by any other firm. Firms' output is assumed to be of homogeneous quality, so they face a common market price. If the market demand curve has a stochastic component, an unexpectedly low price may signal either deviations from collusive output levels or a “downward” demand shock.

Every one has a vague idea of the effects of competition. Theory should have attempted to render this idea more precise; and yet, for lack of regarding the question from the proper point of view, and for want of recourse to symbols (of which the use in this connection becomes indispensable), economic writers have not in the least improved on popular notions in this respect. These notions have remained as ill-defined and ill-applied in their works, as in popular language.

To make the abstract idea of monopoly comprehensible, we imagined one spring and one proprietor. Let us now imagine two proprietors and two springs of which the qualities are identical, and which, on account of their similar positions, supply the same market in competition. In this case the price is necessarily the same for each proprietor. If p is this price, D = F(p) the total sales, D1 the sales from the spring (1) and D2 the sales from the spring (2), then D1 + D2 = D. If, to begin with, we neglect the cost of production, the respective incomes of the proprietors will be pD1 and pD2; and each of them independently will seek to make this income as large as possible.

Bertrand's model of oligopoly, which gives perfectly competitive outcomes, assumes that: (1) there is competition over prices and (2) production follows the realization of demand. We show that both of these assumptions are required. More precisely, consider a two-stage oligopoly game where, first, there is simultaneous production, and, second, after production levels are made public, there is price competition. Under mild assumptions about demand, the unique equilibrium outcome is the Cournot outcome. This illustrates that solutions to oligopoly games depend on both the strategic variables employed and the context (game form) in which those variables are employed.

Introduction

Since Bertrand's (1883) criticism of Cournot's (1838) work, economists have come to realize that solutions to oligopoly games depend critically on the strategic variables that firms are assumed to use. Consider, for example, the simple case of a duopoly where each firm produces at a constant cost b per unit and where the demand curve is linear, p = a–q. Cournot (quantity) competition yields equilibrium price p = (a + 2b)/3, while Bertrand (price) competition yields p = b.

In this article, we show by example that there is more to Bertrand competition than simply “competition over prices.” It is easiest to explain what we mean by reviewing the stories associated with Cournot and Bertrand.