A Rational Convex Program for Linear Arrow-Debreu Markets

Abstract: We give a new, flow-type convex program describing equilibrium solutions to linear Arrow-Debreu markets. Whereas convex formulations were previously known [Nenakov, Primak 83; Jain 07; Cornet '89], our program exhibits several new features. It gives a simple necessary and sufficient condition and a concise proof of the existence and rationality of equilibria, settling an open question raised by Vazirani. As a consequence we also obtain a simple new proof of Mertens's result that the equilibrium prices form a convex polyhedral set.