Convergence of T\^atonnement 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. T\^atonnement, 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 t\^atonnement process, a problem that recently attracted considerable attention of computer scientists. We prove that the simple t\^atonnement process that we consider converges (efficiently) to equilibrium prices and allocation in markets with nested CES-Leontief utilities, generalizing some of the previous convergence proofs for more restricted types of utility functions.