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The Complexity of Exchange

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  • Rob Axtell

    ()
    (Brookings Institution and Santa Fe Institute)

Abstract

Recent results on the computational complexity of Brouwer and Kakutani fixed points is reviewed. It is argued that the non-polynomial complexity of fixed-point algorithms makes Walrasian general equilibrium an unrealistic model of real markets. A radically more decentralized and distributed picture of markets involves repeated bilateral trade between agents in a large population. Such bilateral exchange processes converge to equilibrium allocations that are Pareto optimal and are meaningfully viewed as a kind of massively parallel, distributed computation of Pareto optimal allocations. It is proved that bilateral exchange processes are in P , the class of problems that can be solved in polynomial time. The number of bilateral interactions required to reach equilibrium is proportional to AN^2 , where A is the number of agents and N is the number of commodities.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1999 with number 211.

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Date of creation: 01 Mar 1999
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Handle: RePEc:sce:scecf9:211

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Postal: CEF99, Boston College, Department of Economics, Chestnut Hill MA 02467 USA
Fax: +1-617-552-2308
Web page: http://fmwww.bc.edu/CEF99/
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Cited by:
  1. Magliocca, Nicholas & McConnell, Virginia & Walls, Margaret & Safirova, Elena, 2012. "Zoning on the urban fringe: Results from a new approach to modeling land and housing markets," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 198-210.
  2. Ennio Bilancini & Fabio Petri, 2008. "The Dynamics of General Equilibrium: A Comment on Professor Gintis," Department of Economics University of Siena 538, Department of Economics, University of Siena.
  3. Ghosal, Sayantan & Porter, James, 2010. "Out of Equilibrium Dynamics with Decentralized Exchange Cautious Trading and Convergence to Efficiency," The Warwick Economics Research Paper Series (TWERPS) 928, University of Warwick, Department of Economics.
  4. K. Vela Velupillai, 2006. "Variations on the Theme of Conning in Mathematical Economics," Working Papers 112, National University of Ireland Galway, Department of Economics, revised 2006.
  5. Alan Kirman & Sheri Markose & Simone Giasante & Paolo Pin, 2007. "Marginal contribution, reciprocity and equity in segregated groups: Bounded rationality and self-organization in social networks," Economics Discussion Papers 629, University of Essex, Department of Economics.
  6. Robert Axtell, 2007. "What economic agents do: How cognition and interaction lead to emergence and complexity," The Review of Austrian Economics, Springer, vol. 20(2), pages 105-122, September.
  7. van der Hoog, Sander, 2008. "On the disequilibrium dynamics of sequential monetary economies," Journal of Economic Behavior & Organization, Elsevier, vol. 68(3-4), pages 525-552, December.
  8. Paola Tubaro, 2009. "Agent-based Computational Economics: a Methodological Appraisal," EconomiX Working Papers 2009-42, University of Paris West - Nanterre la Défense, EconomiX.
  9. Dan Ladley & Seth Bullock, 2008. "The Strategic Exploitation of Limited Information and Opportunity in Networked Markets," Computational Economics, Society for Computational Economics, vol. 32(3), pages 295-315, October.
  10. repec:ebl:ecbull:v:2:y:2008:i:3:p:1-7 is not listed on IDEAS
  11. Edoardo Gaffeo & Mauro Gallegati & Umberto Gostoli, 2012. "An agent-based "proof of principle" for Walrasian macroeconomic theory," CEEL Working Papers 1202, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
  12. Chen, Shu-Heng, 2012. "Varieties of agents in agent-based computational economics: A historical and an interdisciplinary perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 1-25.
  13. Koppl, Roger, 2010. "Some epistemological implications of economic complexity," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 859-872, December.
  14. Ghosal, Sayantan & Porter, James, 2013. "Decentralised exchange, out-of-equilibrium dynamics and convergence to efficiency," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 1-21.
  15. Schnizler, Björn & Neumann, Dirk & Veit, Daniel & Napoletano, Mauro & Catalano, Michele & Gallegati, Mauro & Reinicke, Michael & Streitberger, Werner & Eymann, Torsten, 2005. "Environmental analysis for application layer networks," Bayreuth Reports on Information Systems Management 1, University of Bayreuth, Chair of Information Systems Management.

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