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Algorithms for Equilibrium Prices in Linear Market Models

  • Kurt Mehlhorn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)

Abstract

Near the end of the 19th century, Leon Walrus [Wal74] and Irving Fisher [Fis91] introduced general market models and asked for the existence of equilibrium prices. Chapters 5 and 6 of [NRTV07] are an excellent introduction into the algorithmic theory of market models. In Walrus’ model, each person comes to the market with a set of goods and a utility function for bundles of goods. At a set of prices, a person will only buy goods that give him maximal satisfaction.1 The question is to find a set of prices at which the market clears, i.e., all goods are sold and all money is spent. Observe that the money available to an agent is exactly the money earned by selling his goods. Fisher’s model is somewhat simpler. In Fisher’s model every agent comes with a predetermined amount of money. Market clearing prices are also called equilibrium prices. Walrus and Fisher took it for granted that equilibrium prices exist. Fisher designed a hydromechanical computing machine that would compute the prices in a market with three buyers, three goods, and linear utilities [BS00].

Keywords

Equilibrium Price Polynomial Time Algorithm Market Model Price Vector Market Clearing Price 
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.

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References

  1. [AD54]
    Arrow, K.J., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)CrossRefzbMATHMathSciNetGoogle Scholar
  2. [BS00]
    Brainard, W.C., Scarf, H.E.: How to compute equilibrium prices in 1891. Cowles Foundation Discussion Papers 1272, Cowles Foundation for Research in Economics, Yale University (August 2000)Google Scholar
  3. [DM13]
    Duan, R., Mehlhorn, K.: A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part I. LNCS, vol. 7965, pp. 425–436. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. [DPSV08]
    Devanur, N.R., Papadimitriou, C.H., Saberi, A., Vazirani, V.V.: Market equilibrium via a primal–dual algorithm for a convex program. J. ACM 55(5), 22:1–22:18 (2008)Google Scholar
  5. [EG58]
    Eisenberg, E., Gale, D.: Consensus of Subjective Probabilities: the Pari-mutuel Method. Defense Technical Information Center (1958)Google Scholar
  6. [Fis91]
    Fisher, I.: Mathematical Investigations in the Theory of Value and Prices. PhD thesis, Yale University (1891)Google Scholar
  7. [Jai07]
    Jain, K.: A polynomial time algorithm for computing an Arrow-Debreu market equilibrium for linear utilities. SIAM J. Comput. 37(1), 303–318 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  8. [NRTV07]
    Nisan, N., Roughgarden, T., Tardos, É., Vazirani, V.V. (eds.): Algorithmic Game Theory. Cambridge University Press (2007)Google Scholar
  9. [Orl10]
    Orlin, J.B.: Improved algorithms for computing Fisher’s market clearing prices. In: Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, pp. 291–300. ACM, New York (2010)Google Scholar
  10. [Wal74]
    Walrus, L.: Elements of Pure Economics, or the theory of social wealth (1874)Google Scholar
  11. [Ye07]
    Ye, Y.: A path to the Arrow-Debreu competitive market equilibrium. Math. Program. 111(1), 315–348 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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