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.

This article summarizes the theory of markets under uncertainty that Arrow and Debreu created, its achievements and the critical issues that it raises. It focuses on the way Arrow introduced securities: how he de…ned them and what were the most useful developments of this theory. It mentions the theory of insurance that Arrow pioneered together with Malinvaud and others, and Arrow’s theory of r...

We show FIXP-hardness of computing equilibria in Arrow-Debreu exchange markets under Leontief utility functions, and Arrow-Debreu markets under linear utility functions and Leontief production sets, thereby settling these open questions [33]. As corollaries, we obtain FIXPhardness for piecewise-linear concave (PLC) utilities and for Arrow-Debreu markets under linear utility functions and polyhe...

The notion of ‘mathematical impossibility’ of group decision making is founded on errors in microeconomics, game theory, and related disciplines. We highlight mathematical errors that have been committed by von Neumann and Morgenstern, Pareto, Hicks, Samuelson, and Debreu which have been propagated throughout the social sciences. Applicability of Mathematical Operations

We study equilibrium computation for exchange markets. We show that the market equilibrium of either of the following two markets: 1. The Fisher market with several classes of concave non-homogeneous utility functions; 2. A mixed Fisher and Arrow-Debreu market with homogeneous and log-concave utility functions can be computed as convex programming and by interior-point algorithms in polynomial ...

We analyze the ex ante incentive compatible core for replicated private information economies. We show that any allocation in the core when the economy is replicated sufficiently often is approximately Walrasian for the associated Arrow–Debreu economy.  2004 Elsevier Inc. All rights reserved. JEL classification: C7; C71; D5

Arrow and Debreu showed in 1954 that, under mild conditions, a competitive economy always has an equilibrium. In this paper, we show that, given a competitive economy that fully respects all the conditions of Arrow-Debreu’s existence theorem, for any positive constant h > 0, it is PPAD-hard to compute a 1 nh -approximate competitive equilibrium.