Walras Equilibrium Research Articles

Cournot–Nash equilibria in limit exchange economies with complete markets and consistent prices

In this paper, we analyse a model of non-cooperative exchange “à la Cournot–Nash”, proposed by Lloyd S. Shapley, in limit exchange economies. In contrast with the case with a finite number of traders, analysed by Sahi and Yao [Sahi, S., Yao, S., 1989, The non-cooperative equilibria of a trading economy with complete markets and consistent prices, Journal of Mathematical Economics 18, 325–346], we show that the non-uniqueness of market clearing prices induces an indeterminacy in traders' payoffs for individual deviations. In order to overcome this difficulty, we define a Cournot–Nash equilibrium concept by considering as possible equilibria only the strategy selections for which the aggregate bid matrix is irreducible. Then, we show an equivalence “à la Aumann” between the set of Cournot–Nash equilibrium allocations and the set of Walras equilibrium allocations under the assumption that the set of commodities in the economy is a net. Finally, we show the existence of a Cournot–Nash equilibrium as an easy corollary of the equivalence theorem.

Endogenous endowments and equilibrium starvation in a Walrasian economy

This paper deals with atomless exchange economies which do not fulfil the usual autarky assumption, meaning the endowments may lie outside the consumption set. I establish the existence of a Walras equilibrium, provided the economy is `heterogenous' (in some precise sense). Furthermore, the First Welfare Theorem is generalized to arbitrary, not necessarily autarkic, economies.

Intertemporal Cournot and Walras Equilibrium

In an intertemporal general equilibrium framework, we compare a Cournot equilibrium to the Walras equilibrium. The Cournot agents trade and invest less than the Walras agents. This generates an ineffciency which does not vanish as the number of Cournot agents tends to infinity. A larger number of strategic Cournot agents implies that the amount of trade (relative to their aggregate consumption) increases (i.e., moving towards the Walrasian amount), but their investment (relative to the stock) decreases (i.e., moving away from the Walrasian amount).

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.

Nash–Walras equilibria

At a Nash–Walras equilibrium, individuals exchange commodities competitively, and, simultaneously, they interact strategically. Under standard assumptions, Nash–Walras equilibria exist; equilibrium profiles of actions are, typically, determinate but pareto suboptimal, though not constrained pareto suboptimal: a transfer of revenue need not suffice for a pareto improvement in welfare.

Existence of Equilibria in Finitely Additive Nonatomic Coalition Production Economies

The existence of a Walras equilibrium is proved in the framework of a finitely economy with production. The theorem assumes the production set correspondence to be closed–valued and absolutely continuous with respect to the “weighting” finitely additive measure. The result is obtained by using the Kakutani's fixed point theorem and some convergence results stated for multifunctions.

A continuous double implementation of the constrained Walras equilibrium

We provide a continuous and feasible double implementation of the Walras equilibrium. In our game form the set of traders is partitioned intok subsets,k>-2, and for each member of the partition there is an (outside) auctioneer. Also, each agent announces a price-allocation pair so that all agents become price takers. The outcome allocation is defined as the feasible (and budget balanced) allocation which is closest to the aggregate announced allocation. No assumptions are made on the preferences of the traders.

A critical comment on Braun's “restricted access in exchange systems"*

In general this comment tackles the problems and difficulties potentially combined with an application of formal economic models and constructs, such as the Walras equilibrium and microeconmic demand theory, to pure sociological contexts. In particular, this is done by analyzing a further attempt, as recently suggested by Braun (1993 and 1994), to extend the well‐known Coleman Model by incorporating the embeddedness of social transactions in incomplete social network structures. “Pars pro toto” it is proved that Braun's conceptualization contains some weaknesses which imply that fundamental conclusions drawn in his article have to be revised.

Theory of Economic Equilibrium

New concepts of economics such as an average demand matrix of society, strategy of a firm and consumer behaviour, and others are introduced. We give sucient conditions for technological mapping under which there exist both the Walras equlibrium state and optimal Walras equilibrium one. We obtain the set of equations which equilibrium price vector solves. The theory of interindustry economic equilibrium is developed. The model of economy with regular interests of consumers is proposed.

Microeconomics. Institutions, Equilibrium and Optimality

Fundamental concepts. The consumer. The producer. Optimality and decentralization. Walras equilibrium. Fixed price equilibria. Imperfect competition. Externalities and public goods. Implementation. Large economies. Time and Allocation. Uncertainty and information. Remarks. Appendix. References. Index.

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.

Cournot Oligopoly: Characterization and Applications.

Preface Part 1. Introduction: 1. Introduction, purpose, and overview Andrew F. Daughety Part II. Background: 2. Of the competition of producers Augustin Cournot (translation by Nathanial T. Bacon) 3. Review of Walras's Theorie mathematique de la richesse sociale and Cournot's Reserches sur les principles mathematiques de la theorie des richesses Joseph Bertrand (translation by James W. Friedman) 4. Non-cooperative games John Nash Part III. Examining Cournot's Model: 5. On the existence of Cournot equilibrium William Novshek 6. Collusive behavior in non-cooperative epsilon-equilibria of oligopolies with long but finite lives Roy Radner 7. A non-cooperative equilibrium for supergames James W. Friedman 8. Reconsidering Cournot: the Cournot equilibrium is consistent Andrew F. Daughety 9. An experimental test of the consistent-conjectures hypothesis Charles A. Holt 10. Quantity precommitment and Bertrand competition yield Cournot outcomes David M. Kreps and Jose A. Scheinkman 11. On the efficiency of Bertrand and Cournot equilibria with product differentiation Xavier Vives 12. Price competition vs. quantity competition: the role of uncertainty Paul Klemperer and Margaret Meyer Part IV. Applications: 13. Cournot and Walras equilibrium William Novshek and Hugo Sonnenschein 14. Duopoly information equilibrium: Cournot and Bertrand Xavier Vives 15. Information transmission - Cournot and Bertrand equilibria Esther Gal-Or 16. Uncertainty resolution, private information aggregation, and the Cournot competitive limit Thomas R. Palfrey 17. Losses from horizontal merger: the effects of an exogenous change in industry structure on Cournot-Nash equilibrium Stephen W. Salant, Sheldon Switzer, and Robert J. Reynolds 18. Delegation and the theory of the firm John Vickers 19. A study of cartel stability: the Joint Executive Committee, 1880-1886 Robert H. Porter 20. Oligopoly and financial structure: the limited liability effect James A. Brander and Tracy R. Lewis.

On the second optimality theorem of welfare economics

To what extent does the second optimality theorem of welfare economics (every Pareto optimal allocation can be repesented as a Walras equilibrium allocation) remain valid when preferences are allowed to be locally satiated? It is always valid for an exchange economy, and is valid for a production economy if there is a consumer who is not locally satiated, but not in general for a production economy where all consumers are locally satiated. A generalized equilibrium is defined, which includes the Walras equilibrium as a special case. Every Pareto optimum can be represented as a generalized equilibrium allocation. Furthermore, every Pareto optimal utility distribution can be realized by a Walras equilibrium allocation.

Nash equilibria of market games: Finiteness and inefficiency

Publisher Summary This chapter discusses that under appropriate conditions, the Nash Equilibria of finite-player strategic market games are generically inefficient. The conditions are: (1) the dimension of each trader's strategy set is at most l — 1, where l is the number of commodities, (2) the mapping from strategies to net trades is sufficiently smooth, and (3) so are the traders' preferences. For concreteness, the chapter presents a specific model—the so-called sell-all model. The traders' preferences are quite standard and not particularly restrictive; a smooth mapping from strategies to net trades is necessary. The chapter presents the analogous finiteness results obtained for the Walras Equilibria of markets by Debreu, Smale, and others.

A note on the game theoretic interpretation of Walras equilibria

A note on the game theoretic interpretation of Walras equilibria

Introduction to Equilibrium Analysis.

Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.

Introduction to Equilibrium Analysis.

Advanced Textbooks in Economics, Volume 6: Introduction to Equilibrium Analysis: Variations on Themes by Edgeworth and Walras focuses on the approaches developed and instituted by Edgeworth and Walras in the study of equilibrium analysis. The book first underscores exchange economies, core of a game, and large economies. Discussions focus on economies with a continuum of agents, Walras equilibrium, prices and demand, balancedness, and commodity space. The manuscript then ponders on limit theorems for the core and existence of competitive equilibria. Topics include equilibria without convexity of preferences, existence of equilibria for economies with convex preferences, individual demand, emergence of prices, asymptotic equal treatment for most, uniform boundedness of core allocations, and limit theorems for type and replica economies. The publication examines continuous, upper, and lower hemi-continuous correspondences, fixed point theorems, and separation of convex sets. The book is a vital source of data for economists and researchers interested in equilibrium analysis.