The English auction with differentiated commodities
The authors study an economy consisting of finite collections of objects and consumers. Each consumer is endowed with a utility function and with a sufficient amount of money. Under suitable assumptions on the utility functions, it is proved that prices converge to the smallest Walrasian price. The key ingredient of the proof is a determination of an excess demand set. It is also shown that truthful revelation of demand is a perfect Bayesian equilibrium if the smallest Walrasian prices correspond to the Vickrey-Clarke-Groves payments. The main technical tool used in the paper is the matroid theory and submodular optimization.
scientific article; zbMATH DE number 1496286