Equilibrium Theory in Infinite Dimensional Spaces

Journal Article HILDENBRAND (W.) and KIRMAN (A. P.). Introduction to Equilibrium Analysis Get access Introduction to Equilibrium Analysis. By W. Hildenbrand and A. P. Kirman. (Amsterdam: North-Holland Publishing Company, 1975. Pp. viii + 216. $18.50, Dfl. 45.00.) P. G. Hare P. G. Hare University of Stirling Search for other works by this author on: Oxford Academic Google Scholar The Economic Journal, Volume 87, Issue 345, 1 March 1977, Pages 152–153, https://doi.org/10.2307/2231845 Published: 01 March 1977

More on equilibria in competitive markets with externalities and a continuum of agents

On the Existence of Competitive Equilibrium in Frictionless and Incomplete Stochastic Asset Markets

A remark on the existence of equilibria in markets without ordered preferences and with a Riesz space of commodities

Experts against adverse selection: A note on the existence of equilibrium with costly appropriable information

Existence of competitive equilibrium under financial constraints and increasing returns

In this paper, we generalize the existence of Berge's strong equilibrium in Deghdak (see [7]) to discontinuous games in infinite dimensional space of srategy. Moreover, we prove that most of Berge's strong games are essential.

A new proof of the existence of a Walrasian equilibrium with an infinite dimensional commodity space is provided, which allows agents’ preferences to be discontinuous. The new theorems include as corollaries the existence results of Mas-Collel, Yannelis and Zame, Araujo and Monteiro, and Mas-Collel and Richard, among others.

Existence of Competitive Equilibrium in Unbounded Exchange Economies with Satiation: A Note

We are grateful to Jorg Laitenberger who allow us to take this chapter from his Ph.D. Thesis, Laitenberger [1999].

6 - Existence of competitive equilibria

This paper provides a price equilibrium existence theorem in economies where commodities may be indivisible and excess demand functions may not be continuous. We introduce a weak notion of continuity, called recursive transfer lower semi-continuity, which, together with Walras’ law, guarantees the existence of price equilibrium in economies with excess demand functions. The condition is also necessary, and thus our results generalize all the existing results on the existence of price equilibrium in economies where excess demand is a function.

Grid computing has emerged as an effective mechanism for allocating globally available surplus computational capacity to applications whose requirements exceed local capacity. It is often viewed as a commodity exchange with additional grid computing specific constraints that may arise due to requirements on multiple resources (e.g., disk space) in addition to computing power. These constraints are related to complementarity and substitution effects among resources, and significantly alter the assumptions typically used for demonstrating the existence of market equilibrium. However, prior work in grid computing has simply assumed that market equilibria exist. Our work fills this gap by studying the existence of market equilibrium under the grid computing environment. To do so, we first establish an economic framework that incorporates the grid computing specific constraints into a commodity market. We next derive some intuitive necessary conditions based on the computing requirements of individual agents. We finally establish the existence of regular markets as a competitive equilibrium, given that these necessary conditions are met and that the agents’ utility functions satisfy some minimal requirements. In the process, we also show existence of competitive equilibrium for the special case of grid computing as a pure exchange economy.

General Equilibrium Theory: An Introduction treats the classic Arrow-Debreu general equilibrium model in a form accessible to graduate students and advanced undergraduates in economics and mathematics. Topics covered include mathematical preliminaries, households and firms, existence of general equilibrium, Pareto efficiency of general equilibrium, the First and Second Fundamental Theorems of Welfare Economics, the core and core convergences, future markets over time and contingent commodity markets under uncertainty. Demand, supply, and excess demand appear first as (point-valued) functions, then optionally as (set-valued) correspondences. The mathematics presented (with elementary proofs of the theorems) includes a real analysis, the Brouwer fixed point theorem, and separating and supporting hyperplane theorems. Optional chapters introduce the existence of equilibrium with set-valued supply and demand, the mathematics of upper and lower hemicontinuous correspondences, and the Kakutani fixed point theorem. The treatment emphasizes clarity and accessibility to the student through use of examples and intuition.

This paper examines the existence of equilibria for double infinite eonomies. S.F. Richard and S. Srivastava have established the existence of equilibria for economies with infinitely countable consumers when commodity space isL ∞ (M, M, μ). However, most Banach Lattices as commodity spaces haven’t interior points in their positive cones, so their result can’t be applied to many cases. We here consider a general Banach Lattice as commodity space and introduce a concept of equiproperness on preferences. Under the assumption the existence of equilibrium for economy is established. Finally, we examine the existence of equilibria for production economies.