Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

General Equilibrium

2002; Deng, Papadimitriou, Safra
  • Li-Sha Huang
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_160

Keywords and Synonyms

Competitive market equilibrium  

Problem Definition

This problem is concerned with the computational complexity of finding an exchange market equilibrium. The exchange market model consists of a set of agents, each with an initial endowment of commodities, interacting through a market, trying to maximize each's utility function. The equilibrium prices are determined by a clearance condition. That is, all commodities are bought, collectively, by all the utility maximizing agents, subject to their budget constraints (determined by the values of their initial endowments of commodities at the market price). The work of Deng, Papadimitriou and Safra [3] studies the complexity, approximability, inapproximability, and communication complexity of finding equilibrium prices. The work shows the NP-hardness of approximating the equilibrium in a market with indivisible goods. For markets with divisible goods and linear utility functions, it develops a pseudo-polynomial time...


Utility Function Equilibrium Price Market Equilibrium Initial Endowment Indivisible Good 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Arrow, K.J., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica 22(3), 265–290 (1954)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Codenotti, B., McCune, B., Varadarajan, K.: Market equilibrium via the excess demand function. In: Proceedings STOC'05, pp. 74–83. ACM, Baltimore (2005)CrossRefGoogle Scholar
  3. 3.
    Deng, X., Papadimitriou, C., Safra, S.: On the complexity of price equilibria. J. Comput. Syst. Sci. 67(2), 311–324 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Devanur, N.R., Papadimitriou, C.H., Saberi, A., Vazirani, V.V.: Market equilibria via a primal-dual-type algorithm. In: Proceedings of FOCS'02, pp. 389–395. IEEE Computer Society, Vancouver (2002)Google Scholar
  5. 5.
    Eaves, B.C.: Finite solution for pure trade markets with Cobb-Douglas utilities, Math. Program. Study 23, 226–239 (1985)Google Scholar
  6. 6.
    Garg, R., Kapoor, S.: Auction algorithms for market equilibrium, In: Proceedings of STOC'04, pp. 511–518. ACM, Chicago (2004)CrossRefGoogle Scholar
  7. 7.
    Jain, K.: A polynomial time algorithm for computing the Arrow-Debreu market equilibrium for linear utilities. In: Proceeding of FOCS'04, pp. 286–294. IEEE Computer Society, Rome (2004)Google Scholar
  8. 8.
    Nenakhov, E., Primak, M.: About one algorithm for finding the solution of the Arrow-Debreu Model. Kibernetica 3, 127–128 (1983)Google Scholar
  9. 9.
    Ye, Y.: A path to the Arrow-Debreu competitive market equilibrium, Math. Program. 111(1–2), 315–348 (2008)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Li-Sha Huang
    • 1
  1. 1.Department of Computer Science and TechnologyTsinghua UniversityBeijingChina