Proportional Dynamics in Exchange Economies

Abstract

We study the Proportional Response dynamic in exchange economies, where each player starts with some amount of money and a good. Every day, players bring one unit of their good and submit bids on goods they like, each good gets allocated in proportion to the bid amounts, and each seller collects the bids received. Then every player updates the bids proportionally to the contribution of each good in their utility. This dynamic models a process of learning how to bid and has been studied in a series of papers on Fisher and production markets, but not in exchange economies. Our main results are as follows: