Market Equilibria in Polynomial Time for Fixed Number of Goods or Agents

We consider markets in the classical Arrow-Debreu model. There are n agents and m goods. Each buyer has a concave utility function (of the bundle of goods he/she buys) and an initial bundle. At an "equilibrium" set of prices for goods, if each individual buyer separately exchanges the initial bundle for an optimal bundle at the set prices, the market clears, i.e., all goods are exactly consumed. Classical theorems guarantee the existence of equilibria, but computing them has been the subject of much recent research. In the related area of Multi-Agent Games, much attention has been paid to the complexity as well as algorithms. While most general problems are hard, polynomial time algorithms have been developed for restricted classes of games, when one assumes the number of strategies is constant [20, 11]. For the Market Equilibrium problem, several important special cases of utility functions have been tackled. Here we begin a program for this problem similar to that for mult...

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Nikhil R. Devanur, Ravi Kannan
• Keywords: FOCS 2008, Initial Bundle, Polynomial Time, Theoretical Computer Science, Utility Functions