Capacity precommitment,price competition and forward markets

The Cournot model can be seen as a reduced form of a more realistic model of capacity choice followed by price competition. We show that this is not the case if forward markets are added as their pro-competitive effects no longer hold.     

Cournot competition and endogenous firm size

The paper studies the dynamics of firm size in a repeated Cournot game with unknown demand function. We model the firm as a type of artificial neural network. Each period it must learn to map environmental signals to both a demand parameter and its rival’s output choice. However, this learning game is in the background, as we focus on the endogenous adjustment of network size. We investigate the long-run evolution of firm/network size as a function of profits, rival’s size, and the type of adjustment rules used.

Cournot competition in a differentiated oligopoly

This paper studies product-quantity equilibria in an oligopoly. Products are interpreted as “qualities” and each firm chooses a quality-quantity pair, simultaneously. It is well known that a pure-strategy equilibrium in product-price pairs does not exist in this model, but a pure-strategy equilibrium in product-quantity pairs exists. Furthermore, in an example widely studied in the literature, the equilibrium has nice asymptotic properties.     

The empirical content of Cournot competition

We consider the testable implications of the Cournot model of market competition. Our approach is nonparametric in the sense that we abstain from imposing any functional specification on market demand and firm cost functions. We derive necessary and sufficient conditions for (reduced form) equilibrium market price and quantity functions to be consistent with the Cournot model. In addition, we present identification results for the corresponding inverse market demand function and the firm cost functions. Finally, we use our approach to derive testable restrictions for the models of perfect competition, collusion and conjectural variations. This identifies the conditions under which these different models are empirically distinguishable from the Cournot model. We also investigate empirical issues (measurement error and omitted variables) related to bringing our testable restrictions to data.     

Winner-take-all price competition

Summary. We analyze an oligopoly model of homogeneous product price competition that allows for discontinuities in demand and/or costs. Conditions under which only zero profit equilibrium outcomes obtain in such settings are provided. We then illustrate through a series of examples that the conditions provided are “tight” in the sense that their relaxation leads to positive profit outcomes. Received: April 7, 2000; revised version: September 14, 2000     

Real business cycles with Cournot competition and endogenous entry

We introduce strategic interactions with quantity competition a` la Cournot and endogenous entry in an RBC model with homogenous goods. In the long run, the steady state mark up is decreasing in the capital share, in the discount factor and in the level of technology, while it is increasing in the rate of bankruptcy and in the entry cost. In the short run, a competition effect amplifies the propagation of the shocks and generates procyclical profits and countercyclical mark ups. We extend the model to different forms of competition (as imperfect collusion and Stackelberg competition). The analysis of technology and preference shocks and of the second moments suggests that the model outperforms the RBC in terms of variability of output, labor and, of course, profits and mark ups.     

Endogenous fluctuations under evolutionary pressure in Cournot competition

An evolutionary game theoretic model of Cournot competition is investigated. Individuals choose from a finite set of different behavioral rules. Each rule specifies the quantity to be produced in the current period as a function of past quantities. Using more sophisticated rules may require extra information costs. Based upon realized payoffs, the fractions of the population choosing a certain behavioral rule are updated according to the replicator equation with noise. The long-run behavior of the evolutionary system consisting of the population dynamics coupled with the quantity dynamics of the Cournot game may be complicated and endogenous fluctuations may arise. We consider a typical example where firms can choose between two rules: the Nash rule and the best-reply rule. We show that a homoclinic tangency between the stable and unstable manifold of the equilibrium occurs as evolutionary pressure increases, implying bifurcation routes to complicated dynamics and strange attractors.     

Strategic commitment and Cournot competition with labor-managed and profit-maximizing firms

This paper examines the behavior of a labor-managed income-per-member-maximizing firm and a profit-maximizing firm in a quantity-setting model with a strategic commitment. First, each firm independently decides whether or not to make a commitment to capacity. This capacity may subsequently be increased, but cannot be decreased. Hence, each firm’s investment choice changes its capital cost from a variable one into a fixed one. Second, each firm independently chooses its actual output. The paper examines the equilibrium of the quantity-setting mixed model and shows whether or not capacity investment is effective for the labor-managed firm and the profit-maximizing firm.     

Effect of credible quality investment with Bertrand and Cournot competition

We show how credible revelation and ability to commit to quality choice effect equilibrium qualities and welfare when product market is either Bertrand or Cournot competition. We show that results depend on the type of competition but not generally on the cost of quality function. We show that with Bertrand competition, the equilibrium qualities are lower with credible commitment. Competition is moderated and producer surplus is higher and consumer surplus lower. With Cournot competition, higher quality will be better but lower quality will be worse with credible commitment. Consumer surplus is always greater with credible commitment and if cost does not increase too quickly with quality, producer surplus will also increase. Thus credible commitment is a collusive device with Bertrand competition but it can improve social welfare with Cournot competition. Received: February 8, 2000; revised version: February 14, 2002 RID="*" ID="*" The idea of this paper originated in the weekly workshops of Mordecai Kurz at Stanford. I am forever in debted to Mordecai and fellow students – Luis Cabral, Peter DeMarzo, John Hillas, Michihiro Kandori, Steve Langois, Patrick McAllister, Steve Sharpe, Peter Streufert, Steve Turnbull and Gyu-Ho Wang – for their criticism and encouragement. I also benefited from comments from Yi-Heng Chen, Jin-Li Hu, Kala Krishna, Jinji Naoto, Thomas J. Prusa, and Shyh-Fang Ueng at various later stages of this work. Last but not least, I am grateful for the detailed comments of the referee.     

Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach

Summary. With few exceptions, the literature on the role of capacity as a strategic entry deterrent has assumed Cournot competition in the post-entry game. In contrast, this paper studies a model in which the incumbent and entrant sequentially precommit to capacity levels before competing in price. Interesting deterrence effects arise because firms need time to build, that is, cannot adjust capacity instantaneously in the post-entry game. This approach produces a simple and intuitive set of equilibrium behaviors and generates clear predictions about when these different outcomes are likely to arise. Our model also departs substantially from the existing literature in concluding that sunkness of capacity costs is neither necessary nor sufficient for capacity to have precommitment value. Received: August 25, 1999; revised version: October 15, 1999     

Downstream labeling and upstream price competition

This paper analyses the economic consequences of labeling in a setting with two vertically related markets. Labeling on the downstream market affects upstream price competition through two effects: a differentiation effect and a ranking effect. The magnitude of these two effects determines who in the supply chain will receive the benefits and who will bear the burden of labeling. For instance, whenever the ranking effect dominates the differentiation effect, the low-quality upstream firm loses from labeling while all downstream actors are individually better off. By decreasing the low-quality input price, the label acts as a subsidy and leads to an increase of the downstream market welfare. This analysis furthers our understanding of the economic consequences of labeling in cases like those of GMOs or restaurants.     

Differentiated credence goods and price competition

This paper analyses price competition between two firms producing horizontally and vertically differentiated goods. These are assumed to be credence goods, as consumers can hardly ascertain the quality of the commodities. To illustrate the model, we adapt it to represent a newspaper industry with two outlets, when the population of readers have preferences both on the political stance of the newspapers and on the accuracy of the news they dispatch.     

Collusive outcomes in price competition

In this paper we provide a sufficient condition for collusive outcomes in a single-shot game of simultaneous price choice in a homogeneous product market with symmetric firms and strictly convex costs. We also prove the counterintuitive result: if the second derivative of the cost function is nonincreasing in output, it is easier to sustain collusion when the number of firms increases.     

Location choice with delegation: Bertrand vs. Cournot competition

The conventional wisdom indicates that firms' optimal locations are sensitive to the modes of product-market competition, leading to a difficulty for firms to make concrete location decisions. This difficulty is especially crucial for the high entry-cost firms. The paper develops an uncovered-market model à la Economides (1984) to explore this sensitivity by taking into account a delegation game. It shows that firms' location configurations remain unchanged regardless of the modes of product-market competition as the owners offer the managers a contract with a relative-performance incentive scheme. Moreover, the paper shows that, by introducing a delegation game, the competition between managers under Bertrand competition is mitigated such that the managers have no incentive to choose price undercutting as they locate themselves far enough away from each other.     

Low-quality leadership in a vertically differentiated duopoly with Cournot competition

We model a vertically differentiated duopoly with quantity-setting firms as an extended game in which firms noncooperatively choose the timing of moves at the quality stage, to show that at the subgame, perfect equilibrium sequential play obtains, with the low-quality firm taking the leader’s role.     

Pricing and price competition in consumer markets

This paper offers a simple model of the price mechanism in markets where buyers take prices as given and prices are set by sellers, as in most consumer markets. It explains price competition by arguing that a market price goes down if—and only if—a price cut appears profitable to a firm even if its competitors follow suit. It also explains why markets do not always clear, that is, why production can be restricted by sales and not capacity at prices set by firms.     

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers’ surplus.     

On price competition with complementary goods

We consider a duopoly industry with two separate firms each selling an indivisible product. The joint consumption of these goods has a specific value for the consumers which exceeds the mere addition of utilities when products are consumed in isolation: the higher this excess, the larger the complementarity between the goods. We analyse price equilibria in this market as related to the degree of complementarity existing between the two products.     

Domestic and international mixed models with price competition

This article examines domestic (respectively, international) mixed competition in which a state-owned welfare-maximizing public firm competes on price with a domestic (respectively, foreign) profit-maximizing private firm. The article presents and compares the equilibrium outcomes of the two mixed models.     

Spatial Cournot competition in a circular city with more than two dispatches

This paper investigates spatial Cournot competition in a circular city, where the maximal service range of a vehicle is less than half of the perimeter, and a firm needs to initiate more than two dispatches to serve the whole market. We examine a multi‐stage game of location and transportation mode choices, and the subsequent quantity competition between duopoly firms. The findings reveal that non‐maximum dispersion is the unique location equilibrium when duopoly firms deliver products in different transportation modes or when the transportation mode decisions are made endogenously and the fixed cost of a transportation instrument is relatively high.