We present polynomial-time interior-point algorithms for solving the Fisher and Arrow-Debreu competitive market equilibrium problems with linear utilities and n players. Both of them have the arithmetic operation complexity bound of O(n log(1/2)) for computing an 2-equilibrium solution. If the problem data are rational numbers and their bit-length is L, then the bound to generate an exact solut...

We introduce a new system of generalized vector quasiequilibrium problems which includes system of vector quasiequilibrium problems, system of vector equilibrium problems, and vector equilibrium problems, and so forth in literature as special cases.We prove the existence of solutions for this system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results...

The Scarf algorithm was the Þrst practical, almost surely convergent method for computing general equilibria of competitive models. The current focus of much computational research is computing equilibrium of dynamic stochastic models. While many of these models are examples of Arrow-Debreu equilibria, Scarf’s algorithm and subsequent homotopy methods cannot be applied directly since they have ...

We prove that a preference relation which is continuous on every straight line has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than theirs. JEL classific...

Recently, Jain, Mahdian and Saberi [5] had given a FPTAS for the problem of computing a market equilibrium in the Arrow-Debreu setting, when the utilities are linear functions. Their running time depended on the size of the numbers representing the utilities and endowments of the buyers. In this paper, we give a strongly polynomial time approximation scheme for this problem. Our algorithm build...

We introduce agent-based dynamics in a class of Arrow-Debreu economies with capital accumulation and technological progress. In this framework we confirm the results obtained by Gintis (2006, 2007) in an exchange economy: the micro-behavior of boundedly rational agents can lead to the emergence of equilibrium at the macro-level provided some form of collective optimization takes place via evolu...

We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets: 1. A mixed Fisher and ArrowDebreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can b...

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17–38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R2, <l)...

We consider the Arrow-Debreu market with linear utilities in which there is a set G of divisible goods and a set B of buyers. Each buyer starts with an initial endowment of goods. The buyer’s utility function is a linearly separable function of the goods that the buyer purchases. We develop a simple and efficient algorithm for determining an approximate market equilibrium. Our algorithm finds a...