Convergence of Tâtonnement in Fisher Markets

Analyzing simple and natural price-adjustment processes that converge to a market equilibrium is a fundamental question in economics. Such an analysis may have implications in economic theory, computational economics, and distributed systems. Tâtonnement, proposed by Walras in 1874, is a process by which prices go up in response to excess demand, and down in response to excess supply. This paper analyzes the convergence of a time-discrete tâtonnement process, a problem that recently attracted considerable attention of computer scientists. We prove that the simple tâtonnement process that we consider converges (efficiently) to equilibrium prices and allocation in Eisenberg-Gale markets satisfying some mild and widely applicable assumptions. Our simple proof of convergence applies to essentially all utility functions for which previous results showed that discrete tâtonnement converges. It also applies to some utility functions for which there was no previous proof of convergence. Yahoo! Labs Haifa, MATAM, Haifa 31095, Israel. Email: [email protected] The Rachel and Selim Benin School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel. Email: [email protected]. Research supported by Israel Science Foundation grant number 856-11 and by the Israeli Center of Excellence on Algorithms. Part of this work was done while visiting Microsoft Research. Computer Science Department, Technion—Israel Institute of Technology, Haifa 32000, Israel. Email: [email protected]. This work was supported in part by the Israel Ministry of Industry, Trade, and Labor under the Net-HD Consortium, and by Microsoft.