A Rational Convex Program for Linear Arrow-Debreu Markets

We give a new, flow-type convex program describing equilibrium solutions to linear Arrow-Debreu markets. Whereas convex formulations were previously known ([17, 15, 6]), 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 [21]. As a consequence we also obtain a simple new proof of Mertens’s [16] result that the equilibrium prices form a convex polyhedral set.