On-line algorithms for market equilibria

Abstract

We consider a variation of the classical problem of finding prices which guarantee equilibrium in linear markets consisting of di-visible goods and agents with money. Specifically, we consider on-line algorithms for this problem in which goods are considered on-line, and each good is assigned an irrevocable price. Since exact equilibria will not be found in such a setting, we appeal to the concept of approximate equilibrium defined in previous studies of the problem, to characterize the quality of our solutions. We consider both deterministic and randomized algorithms for finding approximate equilibria. We prove a tight bound on the performance of deterministic algorithms, and show that under certain natural conditions, randomized algorithms lead to market prices which are closer to equilibrium. © Springer-Verlag Berlin Heidelberg 2005.