Algorithms Column: The Computation of Market Equilibria

The market equilibrium problem has a long and distinguished history. In 1874, Walras published the famous “Elements of Pure Economics”, where he describes a model for the state of an economic system in terms of demand and supply, and expresses the supply equals demand equilibrium conditions [62]. In 1936, Wald gave the first proof of the existence of an equilibrium for the Walrasian system, albeit under severe restrictions [61]. In 1954, Nobel laureates Arrow and Debreu proved the existence of an equilibrium under milder assumptions [3]. This existence result, along with the two fundamental theorems of welfare are the pillars of modern equilibrium theory. The First Fundamental Theorem of Welfare showed the Pareto optimality of allocations at equilibrium prices, thereby formally expressing Adam Smith’s “invisible hand” property of markets and providing important social justification for the theory of equilibrium. We describe a model of the so-called exchange economy, an important special case of the model considered by Arrow and Debreu [3]. The exchange economy does not include