Ludovic A. Julien

Oligopoly Equilibria “à la Stackelberg” in Pure Exchange Economies

This paper introduces two equilibrium concepts which extend the notion of Stackelberg competition to cover a general equilibrium framework. From the benchmarks of Cournot-Walras economies and of strategic market games, the introduction of an active leader modifies the working of market power and the configuration of strategic interactions. In the context of a simple pure exchange economy, asymptotic identification and welfare results are thus obtained, about Stackelberg general equilibria, compared to Cournot general equilibria and to the competitive equilibrium. JEL Classification : D43, D51

On noncooperative oligopoly equilibrium in the multiple leader–follower game

In this paper, we provide new proofs of existence and uniqueness of a Stackelberg market equilibrium for a multiple leader–follower noncooperative oligopoly model in which heterogeneous firms compete on quantities. To this end, we consider a two-stage game of complete and perfect information in which many leaders interact strategically with many followers. The Stackelberg market equilibrium constitutes a pure strategy subgame perfect Nash equilibrium of this game. Existence and uniqueness are more difficult to handle in this framework, insofar as the presence of several leaders and followers displays a richer set of strategic interactions. Then, to prove existence, we notably provide a new procedure to determine (the conditions under which) the optimal behavior of the followers (may be written) as functions of the sole strategy profile of the leaders. Some examples outline our procedure and discuss our assumptions.

Noncooperative Oligopoly in Markets with a Cobb-Douglas Continuum of Traders

In this paper, we reconsider two models of noncooperative oligopoly in general equilibrium proposed by Busetto et al. ((2008), (2011)): a version of the Shapley’s window model for mixed exchange economies a la Shitovitz and its reformulation a la Cournot-Walras. We introduce the assumption that preferences of the traders belonging to the atomless part are represented by Cobb-Douglas utility functions. This assumption permits us to prove the existence of a Cournot-Nash equilibrium of the Shapley’s window model - called Cobb-Douglas-Cournot-Nash equilibrium - without introducing further assumptions on atoms’ endowments and preferences previously used by Busetto et al. (2011). Then, we show that the set of the Cobb-Douglas-Cournot-Nash equilibrium allocations coincides with the set of the Cournot-Walras equilibrium allocations. JEL Classification: C72, D51.

A Generalized Oligopoly Model with Conjectural Variations

This paper considers a generalization of the Stackelberg model to cover a T-stage framework with several leaders and followers who compete on quantities. Assuming a linear demand function and constant marginal costs, we introduce constant conjectural variations in order to capture various structures of competition. First, we characterize the equilibrium market outcome. Second, we study the influence of conjectures on welfare. We notably propose a welfare comparison for six symmetric equilibria. Third, we consider convergence analysis, and we also show that the competitive equilibrium is a consistent oligopoly equilibrium.

Market Price Mechanisms and Stackelberg General Equilibria: An Example

This paper considers Stackelberg competition in a general equilibrium framework with a productive sector. The working of market power and the configurations of strategic interactions are complexified by the presence of a leader. Two market price mechanisms are studied: one is associated with the Stackelberg–Walras equilibrium and the other is linked to the Stackelberg–Cournot equilibrium. Throughout the example of a two commodity economy, several results are obtained about equilibria mergings and about welfare comparisons.

Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities.

We show the existence of a Cournot–Nash equilibrium for a mixed version of the Shapley window model, where large traders are represented as atoms and small traders are represented by an atomless part. Previous existence theorems for the Shapley window model, provided by Sahi and Yao (1989) in the case of economies with a finite number of traders and by Busetto et al. (2011) in the case of mixed exchange economies, are essentially based on the assumption that there are at least two atoms with strictly positive endowments and indifference curves contained in the strict interior of the commodity space. Our result does not require this restriction. It relies on the characteristics of the atomless part of the economy and exploits the fact that traders belonging to the atomless part have an endogenous “Walrasian” behavior.

From Imperfect to Perfect Competition: A Parametric Approach Through Conjectural Variations

This paper features perfect competition under a parametric approach. We consider conjectural variations in a pure exchange economy where strategic interactions hold. We show, through an example, that the conjectural general equilibrium can coincide with the competitive equilibrium, independently of a replication procedure or an asymptotic identification. Additionally, the competitive equilibrium is a locally consistent conjectural general equilibrium. Perfect competition is defined at equilibrium.

A Review of Heinrich Von Stackelberg's Book: ‘Market Structure and Equilibrium’

type=main> In this note, we review the recent translation in English by Bazin et al. of Stackelbergs book ‘Marktform und Gleichgewicht’ (1934). (This abstract was borrowed from another version of this item.)

Exploring Duopoly Markets with Conjectural Variations

In this article, the authors investigate competitive firm behaviors in a two-firm environment assuming linear cost and demand functions. By introducing conjectural variations, they capture the different market structures as specific configurations of a more general model. Conjectural variations are based on the assumption that each firm believes its own strategy influences its rivals strategy. Firms derive their optimal choice from these exogenous conjectures, under the form of a conjectural best-response function. The authors’ approach fully encompasses the standard measures of market power (the Lerner Index) and concentration (the Herfindahl Index), both depending on the conjectural variations. They finally represent, analytically and graphically, the equilibrium strategies and the associated indexes in a unified framework for any level of competition, ranging from perfect competition to collusion.