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Scale Invariance, Bounded Rationality and Non-Equilibrium Economics

  • Samuel E. Vazquez
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    We study a class of heterogeneous agent-based models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and product transformations. A basic guiding principle is scale invariance, which means that the dynamics of the economy should not depend on the units used to measure the different products. We develop the idea of a "near-equilibrium" expansion which allow us to study the dynamics of fluctuations around economic equilibrium. This is similar to the familiar "perturbation theory" studied in many areas of physics. We study some simple models of both centralized and decentralized markets. We show the relaxation to equilibrium when appropriate. More interestingly, we study a simple model of a decentralized market that shows a spontaneous transition into a monetary phase. We use mean field theory analysis to provide a statistical interpretation of the monetary phase. Furthermore, we show that such phase can be dynamically unstable. Finally, we study some simple centralized financial markets, one of which shows a speculative bubble and a crash.

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    File URL: http://arxiv.org/pdf/0902.3840
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    Paper provided by arXiv.org in its series Papers with number 0902.3840.

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    Date of creation: Feb 2009
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    Handle: RePEc:arx:papers:0902.3840
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    1. George Selgin, 2003. "Adaptive Learning and the Transition to Fiat Money," Economic Journal, Royal Economic Society, vol. 113(484), pages 147-165, January.
    2. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
    3. Fumio Hayashi & Akihiko Matsui, 1994. "A Model of Fiat Money and Barter," NBER Working Papers 4919, National Bureau of Economic Research, Inc.
    4. Guillaume Rocheteau & Randall Wright, 2003. "Money in Search Equilibrium, in Competitive Equilibrium, and in Competitive Search Equilibrium," PIER Working Paper Archive 03-031, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    5. Araujo, Luis & Camargo, Braz, 2006. "Information, learning, and the stability of fiat money," Journal of Monetary Economics, Elsevier, vol. 53(7), pages 1571-1591, October.
    6. Irene Giardina & Jean-Philippe Bouchaud, 2002. "Bubbles, crashes and intermittency in agent based market models," Science & Finance (CFM) working paper archive 500022, Science & Finance, Capital Fund Management.
    7. Wilhite, Allen, 2006. "Economic Activity on Fixed Networks," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 20, pages 1013-1045 Elsevier.
    8. Karl Ludwig Keiber, 2008. "Price discovery in the presence of boundedly rational agents," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 235-249.
    9. J. Doyne Farmer & John Geanakoplos, 2008. "The Virtues and Vices of Equilibrium and the Future of Financial Economics," Cowles Foundation Discussion Papers 1647, Cowles Foundation for Research in Economics, Yale University.
    10. Xue-Zhong He & Youwei Li, 2008. "Heterogeneity, convergence, and autocorrelations," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 59-79.
    11. Jérôme Coulon & Yannick Malevergne, 2010. "Heterogeneous expectations and long range correlation of the volatility of asset returns," Working Papers halshs-00541953, HAL.
    12. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    13. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    14. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 2-14, October.
    15. Terrance Odean, 1999. "Do Investors Trade Too Much?," American Economic Review, American Economic Association, vol. 89(5), pages 1279-1298, December.
    16. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-54, August.
    17. Jones, Robert A, 1976. "The Origin and Development of Media of Exchange," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 757-75, August.
    18. John Conlisk, 1996. "Why Bounded Rationality?," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 669-700, June.
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