Substitute goods, auctions, and equilibrium

This paper identifies two notions of substitutes for auction and equilibrium analysis. Weak substitutes, which is the usual price-theory notion, guarantees monotonicity of tâtonnement processes and convergence of clock auctions to a pseudoequilibrium, but only strong substitutes, which treats each unit traded as a distinct good with its own price, guarantees that every pseudo-equilibrium is a Walrasian equilibrium, that the Vickrey outcome is in the core, and that the “law of aggregate demand” is satisfied. The paper provides several primal and dual characterizations and properties of weak and strong substitutes. When goods are divisible, weak substitutes along with concavity guarantees all of the above properties, except for the law of aggregate demand.