Brouwer’s Fixed Point Theorem and Price Equilibrium
نویسنده
چکیده
This is an expository paper based on Border [1]. Starting from basic convexity results, I present a proof of the so-called Equilibrium Theorem, which states the existence of a free disposal equilibrium price vector in an Arrow-Debreu economy with a continuous excess demand function.
منابع مشابه
Proof of Constructive Version of the Fan-Glicksberg Fixed Point Theorem Directly by Sperner’s Lemma and Approximate Nash Equilibrium with Continuous Strategies: A Constructive Analysis
It is often demonstrated that Brouwer’s fixed point theorem can not be constructively proved. Therefore, Kakutani’s fixed point theorem, the Fan-Glicksberg fixed point theorem and the existence of a pure strategy Nash equilibrium in a strategic game with continuous (infinite) strategies and quasi-concave payoff functions also can not be constructively proved. On the other hand, however, Sperner...
متن کاملUndecidability of Uzawa equivalence theorem and LLPO (Lesser limited principle of omniscience)
The Uzawa equivalence theorem [H. Uzawa, Walras’s Existence Theorem and Brouwer’s Fixed Point Theorem, Economic Studies Quarterly 8 (1962) 59–62] showed (classically) that the existence of Walrasian equilibrium in an economy with continuous excess demand functions is equivalent to Brouwer’s fixed point theorem, that is, the existence of a fixed point for any continuous function from an n-dimens...
متن کاملCs294-1 Algorithmic Aspects of Game Theory 2.1 Overview 2.2 Sperner's Lemma
We begin by looking at a set of theorems from various disciplines and how they relate to one another. From combinatorics, we take Sperner’s Lemma which we can use to prove Brouwer’s Fixed Point Theorem from topology. Brouwer’s Fixed Point Theorem can be used to prove the Arrow-Debreu Theorem from economics which states that general equilibria exist, and can also be used to prove Kakutani’s Fixe...
متن کاملCS 294 - 1 Algorithmic Aspects of Game Theory Spring 2001 Lecture 2 : January 23
We begin by looking at a set of theorems from various disciplines and how they relate to one another. From combinatorics, we take Sperner’s Lemma which we can use to prove Brouwer’s Fixed Point Theorem from topology. Brouwer’s Fixed Point Theorem can be used to prove the Arrow-Debreu Theorem from economics which states that general equilibria exist, and can also be used to prove Kakutani’s Fixe...
متن کاملCompetitive Equilibrium in Piecewise Linear and Concave Exchange Economies and the non-symmetric Nash Bargaining Solution By
In this paper we show that for concave piecewise linear exchange economies every competitive equilibrium satisfies the property that the competitive allocation is a non-symmetric Nash bargaining solution with weights being the initial income of individual agents evaluated at the equilibrium price vector. We prove the existence of competitive equilibrium for concave piecewise linear exchange eco...
متن کامل