A Fast and Simple Algorithm for Computing Market Equilibria

  • Lisa Fleischer
  • Rahul Garg
  • Sanjiv Kapoor
  • Rohit Khandekar
  • Amin Saberi
Conference paper

DOI: 10.1007/978-3-540-92185-1_11

Volume 5385 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Fleischer L., Garg R., Kapoor S., Khandekar R., Saberi A. (2008) A Fast and Simple Algorithm for Computing Market Equilibria. In: Papadimitriou C., Zhang S. (eds) Internet and Network Economics. WINE 2008. Lecture Notes in Computer Science, vol 5385. Springer, Berlin, Heidelberg

Abstract

We give a new mathematical formulation of market equilibria using an indirect utility function: the function of prices and income that gives the maximum utility achievable. The formulation is a convex program and can be solved when the indirect utility function is convex in prices. We illustrate that many economies including
  • Homogeneous utilities of degree α ∈ [0,1] in Fisher economies — this includes Linear, Leontief, Cobb-Douglas

  • Resource allocation utilities like multi-commodity flows

satisfy this condition and can be efficiently solved.

Further, we give a natural and decentralized price-adjusting algorithm in these economies. Our algorithm, mimics the natural tâtonnement dynamics for the markets as suggested by Walras: it iteratively adjusts a good’s price upward when the demand for that good under current prices exceeds its supply; and downward when its supply exceeds its demand. The algorithm computes an approximate equilibrium in a number of iterations that is independent of the number of traders and is almost linear in the number of goods. Interestingly, our algorithm applies to certain classes of utility functions that are not weak gross substitutes.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lisa Fleischer
    • 1
  • Rahul Garg
    • 2
  • Sanjiv Kapoor
    • 3
  • Rohit Khandekar
    • 2
  • Amin Saberi
    • 4
  1. 1.Dartmouth College 
  2. 2.IBM T.J. Watson Research Center 
  3. 3.Illinois Institute of Technology 
  4. 4.Stanford University