Cournot-Walras Equilibrium Research Articles

Cournotian duopolistic firms may be Walrasian: a case in the Gabszewicz and Vial model

In this paper, we present a refreshed version of the original model proposed by Gabszewicz and Vial (J Econ Theory 4:381–400, 1972) and we use their main example to review the main theoretical issues related to the notion of Cournot-Walras equilibrium. We compute, in the Gabszewicz and Vial main example, two different Cournot-Walras equilibria associated with different normalization rules. Moreover, in the same example, we compute a Utility-Cournot-Walras equilibrium as defined by Grodal (in: Allen (ed) Economics in a changing world, Macmillan, London, 1996) and we show that it coincides with the unique Walras equilibrium. Furthermore, using a proposition proved by Grodal (1996), we build a normalization rule with respect to which there is a Cournot-Walras equilibrium that coincides with the Utility-Cournot-Walras equilibrium and hence with the unique Walras equilibrium. To the best of our knowledge, this example provides the first case of Cournotian duopolistic firms being Walrasian in a production economy.

Towards the theory of general economic equilibrium

The paper proposes a model of general economic equilibrium, when some firms can influence prices by their actions. Their primitives (that is, the description of production, distribution, and consumption) of the proposed model are the same as those of the Arrow–Debreu model. The difference lies in the behavior of oligopolistic firms: it is assumed that they (as in the original Cournot model) assign their production plans. The main innovation is the description of the decision-making process on production plans by oligopolistic firms. In previous models, it was assumed that oligopolistic firms seek to maximize profits at current prices. Here, a more natural assumption is made that oligopolistic firms make decisions about production plans through a vote of shareholders. It is shown how the Arrow–Debreu model can be modified to account for this circumstance. The concept of Condorcet–Cournot–Walras equilibrium is introduced, combining the ideas of these three classics. The question of the existence of equilibria is discussed. A simplified version of the model is also considered, in which each firm is owned by one agent. The simplification is that there is no need to turn to the voting.

General Equilibrium Oligopoly and Ownership Structure

We develop a tractable general equilibrium framework in which firms are large and have market power with respect to both products and labor, and in which a firm's decisions are affected by its ownership structure. We characterize the Cournot–Walras equilibrium of an economy where each firm maximizes a share‐weighted average of shareholder utilities—rendering the equilibrium independent of price normalization. In a one‐sector economy, if returns to scale are non‐increasing, then an increase in “effective” market concentration (which accounts for common ownership) leads to declines in employment, real wages, and the labor share. Yet when there are multiple sectors, due to an intersectoral pecuniary externality, an increase in common ownership could stimulate the economy when the elasticity of labor supply is high relative to the elasticity of substitution in product markets. We characterize for which ownership structures the monopolistically competitive limit or an oligopolistic one is attained as the number of sectors in the economy increases. When firms have heterogeneous constant returns to scale technologies, we find that an increase in common ownership leads to markets that are more concentrated.

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

Équilibres non coopératifs à la Cournot sur les marchés avec un continu d’agents : le cas Cobb-Douglas Dans cet article, nous considérons les deux modèles d’oligopole équilibre général analysés dans Busetto et al. (2008), (2011). Ces modèles constituent deux transpositions dans le cadre d’analyse des marchés mixtes rationalisés par Shitovitz : la première est une version du modèle de Shapley et la deuxième une reformulation du modèle Cournot-Walras. Nous supposons que les agents dont la taille est négligeable ont des préférences représentées par des fonctions de type Cobb-Douglas. Cette hypothèse nous permet de construire un concept d’équilibre général stratégique, l’équilibre de Cobb-Douglas Cournot-Nash. Nous prouvons l’existence d’un tel équilibre. De plus, nous montrons l’ensemble des allocations associées à l’équilibre de Cobb-Douglas Cournot-Nash coïncide avec l’ensemble des allocations de l’équilibre Cournot-Walras. Classification JEL : C72, D51.1.

Three Models of Noncooperative Oligopoly in Markets with a Continuum of Traders

SummaryIn this paper, we reconstruct the main developments of the theory of noncooperative oligopoly in general equilibrium, by focusing on the analysis of three prototypical models for pure exchange economies: the model of Cournot-Walras equilibrium of Codognato and Gabszewicz (1991); the model of Cournot-Nash equilibrium originally proposed by Lloyd S. Shapley and known as window model; the model of Cournot-Walras equilibrium of Busetto et al. (2008). We establish, in a systematic way, the relationship between the three notions of equilibrium proposed in these models and the notion of Walras equilibrium. Then, we investigate the relationships among those three notions of equilibrium.

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

SummaryIn 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.

Stackelberg-Walras and Cournot-Walras Equilibria in Mixed Markets: A Comparison

In this note, we compare two strategic general equilibrium concepts: the Stackelberg-Walras equilibrium and the Cournot-Walras equilibrium. We thus consider a market exchange economy embodying atoms and a continuum of traders. It is shown that, when the preferences of the small traders are represented by Cobb-Douglas utility functions, the Stackel-berg-Walras and the Cournot-Walras equilibria can coincide only if 1) the endowments and preferences of atoms are identical and 2) the elasticity of the followers’ best response functions are equal to zero in equilibrium.

Cournot–Walras equilibrium as a subgame perfect equilibrium

In this paper, we investigate the problem of the strategic foundation of the Cournot–Walras equilibrium approach. To this end, we respecify à la Cournot–Walras the mixed version of a model of simultaneous, noncooperative exchange, originally proposed by Lloyd S. Shapley. We show, through an example, that the set of the Cournot–Walras equilibrium allocations of this respecification does not coincide with the set of the Cournot–Nash equilibrium allocations of the mixed version of the original Shapley’s model. As the nonequivalence, in a one-stage setting, can be explained by the intrinsic two-stage nature of the Cournot–Walras equilibrium concept, we are led to consider a further reformulation of the Shapley’s model as a two-stage game, where the atoms move in the first stage and the atomless sector moves in the second stage. Our main result shows that the set of the Cournot–Walras equilibrium allocations coincides with a specific set of subgame perfect equilibrium allocations of this two-stage game, which we call the set of the Pseudo–Markov perfect equilibrium allocations.

Specialized oligopolies in a pure exchange economy: The symmetric Cournot–Walras equilibrium

This paper explores the symmetric Cournot–Walras equilibrium (SCWE) as an alternative concept to the asymmetric Cournot–Walras equilibrium (ACWE) à la Codognato–Gabszewicz. All agents have specialized initial endowments but generalized consumption activities: they are strategic suppliers of the only good they own and competitive demanders of all the other ones. Two kinds of results are showed in the framework of an example. First, the asymptotic identification of this strategic equilibrium with the competitive equilibrium when all markets are replicated and its asymptotic identification with the ACWE when all markets but one are replicated. Second, when the SCWE is compared to the Walrasian equilibrium (WE), two results are obtained in terms of welfare.

Existence and optimality of oligopoly equilibria in linear exchange economies

Summary. We consider a linear exchange economy and its successive replicas. We study the notion of Cournot-Walras equilibrium in which the consumers use the quantities of commodities put on the market as strategic variables. We prove that, generically, if the number of replications is large enough but finite, the competitive behaviour is an oligopoly equilibrium. Then, under a mild condition, which may be interpreted in terms of market regulation and/or market activity, we show that any sequence of oligopoly equilibria of successive replica economies converges to the Walrasian outcome and furthermore that every oligopoly equilibrium of large, but finite, replica is Pareto optimal. Consequently, under the same assumptions on the fundamentals of the economy, one has an asymptotic result on the convergence of oligopoly equilibria to the Walras equilibrium together with a generic existence result for the Cournot-Walras.

Diversification and Competition: Financial Intermediation in a Large Cournot–Walras Economy

An economy with partially diversified imperfectly competitive (Cournot) intermediaries is replicated. The Cournot–Walras equilibrium converges to the perfectly competitive equilibrium with no uncertainty. Despite the convergence, the tension between diversification and competition persists when the economy becomes large, and is manifested in the rates of convergence of price, quantities, and per capita welfare to their respective limits. To maximize the rate of convergence of per capita welfare, resources must be allocated in a particular way that balances the gains from better diversified intermediaries and the gains from more competition in the intermediation sector.Journal of Economic Literature classification numbers: D43, D61, D89, G10, G21, L10, L16, O16.

Équilibres de Cournot-Walras dans une économie d'échange

Équilibres de Cournot-Wakas dans une économie d'échange Nous introduisons la notion d'équilibre Cournot-Walras pour une économie d'échange. Sur base d'un exemple, nous étudions en premier lieu la relation entre la notion d'équilibre « à la Cournot » proposée par Shapley et Shubik et l'équilibre de Cournot-Walras, tout en démontrant qu'ils coïncident asymptotiquement. Ensuite, nous démontrons, par le même exemple, que l'équilibre de Cournot-Walras converge par « replication » vers l'équilibre walrasien.