Book ChapterDOI
Existence of an equilibrium for a competitive economy
Kenneth J. Arrow,Gerard Debreu +1 more
TLDR
In this article, a simplification of the structure of the proofs has been made possible through use of the concept of an abstract economy, a generalization of that of a game, and proofs of the existence of an equilibrium are given for an integrated model of production, exchange and consumption.Abstract:
A. Wald has presented a model of production and a model of exchange and proofs of the existence of an equilibrium for each of them. Here proofs of the existence of an equilibrium are given for an integrated model of production, exchange and consumption. In addition the assumptions made on the technologies of producers and the tastes of consumers are significantly weaker than Wald's. Finally a simplification of the structure of the proofs has been made possible through use of the concept of an abstract economy, a generalization of that of a game. Introduction L. Walras [ 24 ] first formulated the state of the economic system at any point of time as the solution of a system of simultaneous equations representing the demand for goods by consumers, the supply of goods by producers, and the equilibrium condition that supply equal demand on every market. It was assumed that each consumer acts so as to maximize his utility, each producer acts so as to maximize his profit, and perfect competition prevails, in the sense that each producer and consumer regards the prices paid and received as independent of his own choices. Walras did not, however, give any conclusive arguments to show that the equations, as given, have a solution.read more
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Book
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
Posted Content
The Mechanisms of Governance
TL;DR: The Mechanisms of Governance as discussed by the authors is an important work in the field of transaction cost economics, a branch of the New Institutional Economics with which Oliver Williamson is especially associated.
Book
Proximal Algorithms
Neal Parikh,Stephen Boyd +1 more
TL;DR: The many different interpretations of proximal operators and algorithms are discussed, their connections to many other topics in optimization and applied mathematics are described, some popular algorithms are surveyed, and a large number of examples of proxiesimal operators that commonly arise in practice are provided.
Journal ArticleDOI
Existence and uniqueness of equilibrium points for concave n-person games
TL;DR: In this paper, the existence and uniqueness of equilibrium points for concave n-person games is studied in a dynamic model for nonequilibrium situations, where the equilibrium points are chosen by the players.
Journal ArticleDOI
Towards an economic theory of the multiproduct firm
TL;DR: In this paper, a theory of the multiproduct firm is presented, in which profit seeking firms are seen to diversify in order to avoid the high transactions costs associated with using various markets to trade the services of various specialized assets.
References
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Journal ArticleDOI
Equilibrium points in n-person games
TL;DR: A concept of an n -person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n -tuple ofpure strategies, one strategy being taken for each player.
Book
Foundations of Economic Analysis
TL;DR: Recent statistical techniques, including nonlinear programming, have been added to a basic survey of equilibrium systems, comparative statistics, consumer behavior theory, and cost and production theory as discussed by the authors, and they have been used in a variety of applications.
Book
The Coefficient of Resource Utilization
TL;DR: In this article, a numerical evaluation of the "dead loss" associated with a non-optimal situation (in the Pareto sense) of an economic system is sought and the intrinsic price systems associated with optimal situations of whose existence a noncalculus proof is given.
Journal ArticleDOI
A Social Equilibrium Existence Theorem.
TL;DR: The existence theorem presented here gives general conditions under which there is for such a social system an equilibrium, i.e., a situation where the action of every agent belongs to his restricting subset and no agent has incentive to choose another action.