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.     

Rational conjectures in the theory of oligopoly

The paper employs the notion of rational conjectural equilibrium to remove the arbitrary nature of conjectures about rivals' reactions which characterises the traditional non-cooperative theory of oligopoly. A general definition of these equilibria is given, and the concept is then applied to a simple duopoly model. The standard models of perfect competition, monopoly, limit-price dominant firms are shown to emerge as special cases of rational conjectural equilibria.     

Strategic segmentation of a market

When competing firms target information towards specific consumers through direct marketing activities, complete segmentation of markets can result. We analyze a two-stage duopoly where, prior to price competition, each firm targets information to specific consumers and only consumers informed by a firm can buy from it. This has the effect of endogenously determining market segments in a model of ‘sales'. In equilibrium, pure local monopoly emerges; firms target and sell to mutually exclusive market segments. When the cost of marketing approaches zero, market shares reflect relative production efficiency (equal shares when firms are symmetric); this may not be the case when marketing cost is high.     

PRODUCT IMPROVEMENT AND TECHNOLOGICAL TYING IN A WINNER‐TAKE‐ALL MARKET*

In a winner‐take‐all duopoly for systems in which firms invest to improve their products, a vertically integrated monopoly supplier of an essential system component may have an incentive to advantage itself by technological tying. If the vertically integrated firm is prevented from technologically tying, there is an equilibrium in which the more efficient firm invests and serves the entire market. However, another equilibrium may exist in which the less efficient firm wins the market. Technological tying enables a vertically integrated firm to foreclose its rival. The welfare implications of technological tying are ambiguous and depend on equilibrium selection.     

Collusion in a price-quantity oligopoly

In the context of an infinitely repeated oligopoly game, we study collusion among firms that simultaneously choose prices and quantities. We compare a price cartel with a price-quota cartel and analyze when and why firms prefer the latter to the former. Output quota may be required to solve coordination and incentive problems when market demand is sufficiently elastic. If market demand is sufficiently inelastic, then the cartel faces a trade-off between increasing prices and the amount of costly overproduction. We find that a price cartel prices consistently below the monopoly price to mitigate excessive production. In this case, a quota arrangement allows firms to avoid overproduction and to sustain the monopoly price. From a policy perspective, our findings suggest that an overall price increase in conjunction with more stable prices and market shares is indicative of collusion in industries where production precedes sales and outputs are imperfectly observable.     

Risky quality choice

In vertical product differentiation with a stochastic research technology, firms should target their research at different quality levels for efficiency. In a natural monopoly where the top firm finds it most profitable to sell to the whole market, the incentives for risk-taking and for firms to differentiate their targeted qualities are optimal. In a natural oligopoly (which results when there is sufficient dispersion of tastes), the relationship between a firm’s payoff and its quality improvement over other firms is weakened. This diminishes the firms’ incentives to differentiate and the targeted qualities are too low and too close together.     

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.     

Lanchester market structures: A. Japanese approach to the analysis of business competition

Japanese consultants have used Lanchester's military models to define monopoly, premium, duopoly, oligopoly and polyopoly market structures in which competitive conditions differ. These situations are investigated using the PIMS database. The findings refute the idea that monopoly and premium structures are more stable than the others. Instead movements between structures seem to follow a Markov process.     

Speculative storage in imperfectly competitive markets

Markets for many commodities are characterized by imperfectly competitive production as well as substantial storage by speculators who are attracted by significant price volatility. We examine how speculative storage affects the behavior of an oligopoly producing a commodity for which demand is subject to random shocks. Speculators compete with consumers when purchasing the commodity and then subsequently compete with producers when selling their stocks, resulting in two opposing incentives: on the one hand, producers would like to increase production to capture future sales in advance by selling to speculators; while on the other hand, they would like to withhold production to deter speculation, thereby eliminating the additional supply from speculators in future periods. We find that the incentive to sell to speculators can be quite strong, potentially resulting in prices sufficiently high to drive consumers from the market. Furthermore, these incentives are non-monotonic in the number of producers: speculative storage occurs more frequently in a relatively concentrated oligopoly than in the extremes of monopoly or perfect competition.     

Equilibrium Real Options Exercise Strategies with Multiple Players: The Case of Real Estate Markets

This article derives a closed-form solution for an equilibrium real options exercise model with stochastic revenues and costs for monopoly, duopoly, oligopoly and competitive markets. Our model also allows one option holder to have a greater production capacity than others. Under a monopolistic environment we find that the optimal option exercise strategy in real estate markets is dramatically opposite to that in a financial (warrant) market, indicating the importance of paying attention to the institutional details of the underlying market when analyzing option exercise strategies. Our model can be generalized to the pricing of convertible securities and capital investment decisions involving both stochastic revenues and costs under different types of market structures.     

Informative Externalities and Pricing in Regulated Multiproduct Industries

This paper addresses the issue of how to organise a two-product industry with interdependent demands when the regulator cannot observe the demand level of the goods produced. Two industry structures are compared: a multiproduct monopoly, in which an informed firm produces both goods, and a differentiated duopoly, where two firms control one good each but the level of demand is known by one firm only. Focusing on the informative costs of regulation, the paper shows that, if goods are substitutes, the regulator may achieve a better performance through integration of production. With complements, instead, decentralisation tends to be preferred.     

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.     

Resale and Collusion in A Dynamic Market for Semidurable Goods

The paper studies the incentives to form collusive agreements when goods can be traded in second‐hand markets. It will be shown that such incentives crucially depend on the rate of depreciation of the durable good and on consumer heterogeneity. The main contribution of the paper shows that an active second‐hand market may strengthen the incentives to collude, as do policies that affect the functioning of the second‐hand market (e.g., leasing policy and buy‐back). It will also be argued that the oligopoly incentives to adopt strategies that strengthen collusion often differ from the monopoly incentives to increase profits.     

COLLUSION AND FIGHTS IN AN EXPERIMENT WITH PRICE‐SETTING FIRMS AND ADVANCE PRODUCTION*

We present results from 50‐round duopoly and triopoly experiments. Firms decide repeatedly both on price and quantity of a perishable good. Each firm has capacity to serve the whole market. The stage game does not have an equilibrium in pure strategies. Most markets evolve either to monopolies as a consequence of bankruptcies or to collusion at the monopolistic price. Evolution is faster in markets with two than in those with three firms. Therefore, over time average price is lower with three than with two. Consumer surplus is higher with three firms, but efficiency is lower in markets with three firms.     

Price behavior in tight oligopoly

The study examines price behavior in tight oligopoly. The investigation proceeds from the premise that tacit cooperation is the rational response of firms comprising tight oligopoly. The study’s thesis is that cooperative conduct in tight oligopoly will reflect one of two general pricing patterns: (1) shared monopoly pricing, or (2) mark-up pricing. A unique empirical test of this dual price hypotheses is developed. The test focuses on the nature of price responses to cost and demand changes as reflected in a price equation that is estimated for each of fifty four-digit SIC industries. The study’s results indicate infrequent, but still notable, instances of shared monopoly pricing. More common is evidence of mark-up pricing, a general category within which demand proved to be significant in roughly half of the industries examined. Theoretical implications of these findings are discussed.     

Investment timing and vertical relationships

We show that the standard analysis of vertical relationships transposes directly to investment dynamics. Thus, when a firm undertaking a project requires an outside supplier (e.g., an equipment manufacturer) to provide it with a discrete input to serve a growing but uncertain demand, and if the supplier has market power, investment occurs too late from an industry standpoint. The distortion in firm decisions is characterized by a Lerner-type index. Despite the underlying investment option, greater volatility can result in a lower value for both firms. We examine several contractual alternatives to induce efficient timing, a novel vertical restraint being for the upstream to sell a call option on the input. We also extend the model to allow for downstream duopoly. When downstream firms are engaged in a preemption race, the upstream firm sells the input to the first investor at a discount such that the race to preempt exactly offsets the vertical distortion, and this leader invests at the optimal time. These results are illustrated with a case study drawn from the pharmaceutical industry.     

Quantity competition with access fees

We analyze an oligopoly model where firms choose both quantities and access fees. Per unit prices are determined endogenously to equate quantity demanded with quantity supplied at each firm. In a Nash equilibrium of the game played by firms, the per unit prices equal marginal cost and access fees may or may not extract all consumer surplus. As the number of firms increases, access fees fall below net consumer surplus and toward zero. Existence is guaranteed if Marshallian consumer surplus is not too concave. With open entry, quantity competition with access fees may be less efficient than without access fees.     

Industry structure and the choice of product reliability

Epple and Raviv (1979) and Saving (1982) argued that product reliability may be independent of market structure. Using a two period oligopoly model we show that this conclusion is correct only if the firms are risk-neutral and output is rented. If either of these conditions is violated, the firm's reliability will not be socially optimal. Our results provide further rationale for Avinger's (1981) empirical findings on product obsolescence in the vacuum tube and electric lamp industries. We do find, however, that the independence result can be reestablished in sales markets if firms are required to provide warranties.     

The Number of Firms and Production Capacity in Relation to Market Size

Many oligopoly theories predict a positive correlation between market size and the equilibrium number of firms and some also imply that competition is more intense in larger markets. We test these predictions on a sample of driving schools in 250 Swedish regional markets by estimating the relation between the number of firms, production capacity, and market size. The number of firms increases less than proportionally with market size. Market size per capacity unit is smaller in large markets. Since firms produce a fairly homogenous good, we argue that this is evidence that profits per capita is decreasing in market size.     

Conjectural variations strategies in accelerated cournot games

A family of constant conjectural variations strategies is defined and examined in the natural context of infinitely repeated Cournot duopoly games with discounting. It is shown that any pair of linear reaction functions in the family gives rise to a unique pair of quantities in stationary equilibrium. As the conjectures and discount parameter vary, the sum of the stationary quantities will vary anywhere between the competitive and the monopoly outcomes. Equilibrium is strongly stable and credible (in the sense of exhibiting a variation of Selten's subgame perfection) provided that firms can react quickly enough to one another's actions.