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Endogenous equilibria in liquid markets with frictions and boundedly rational agents

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Author Info

  • Paolo Dai Pra

    ()
    (Department of Pure and Applied Mathematics, Università di Padova)

  • Fulvio Fontini

    ()
    ("M. Fanno" Department of Economics and Management, Università di Padova)

  • Elena Sartori

    ()
    (Department of Management, Università Ca' Foscari Venezia)

  • Marco Tolotti

    ()
    (Department of Management, Università Ca' Foscari Venezia)

Abstract

In this paper we propose a simple binary mean field game, where N agents may decide whether to trade or not a share of a risky asset in a liquid market. The asset's returns are endogenously determined taking into account demand and transaction costs. Agents' utility depends on the aggregate demand, which is determined by all agents' observed and forecasted actions. Agents are boundedly rational in the sense that they can go wrong choosing their optimal strategy. The explicit dependence on past actions generates endogenous dynamics of the system. We, firstly, study under a rather general setting (risk attitudes, pricing rules and noises) the aggregate demand for the asset, the emerging returns and the structure of the equilibria of the asymptotic game. It is shown that multiple Nash equilibria may arise. Stability conditions are characterized, in particular boom and crash cycles are detected. Then we precisely analyze properties of equilibria under significant examples, performing comparative statics exercises and showing the stabilizing property of exogenous transaction costs.

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File URL: http://virgo.unive.it/wpideas/storage/2011wp7.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Department of Management, Università Ca' Foscari Venezia in its series Working Papers with number 7.

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Length: 35 pages
Date of creation: Aug 2011
Date of revision:
Handle: RePEc:vnm:wpdman:7

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Related research

Keywords: Endogenous dynamics; Nash equilibria; Bounded rationality; Transaction costs; Mean field games; Random utility;

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  1. Guillaume Rocheteau & Pierre-Olivier Weill, 2011. "Liquidity in frictional asset markets," Working Paper 1105, Federal Reserve Bank of Cleveland.
  2. Alessandro Citanna & John Donaldson & Herakles Polemarchakis & Paolo Siconolfi & Stephen Spear, 2004. "General equilibrium, incomplete markets and sunspots: A symposium in honor of David Cass," Economic Theory, Springer, vol. 24(3), pages 465-468, October.
  3. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute.
  4. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 235-60, April.
  5. Chang, Sheng-Kai, 2007. "A simple asset pricing model with social interactions and heterogeneous beliefs," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1300-1325, April.
  6. repec:att:wimass:9621 is not listed on IDEAS
  7. Paolo Dai Pra & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
  8. Jean-Pierre Nadal & Denis Phan & Mirta Gordon & Jean Vannimenus, 2005. "Multiple equilibria in a monopoly market with heterogeneous agents and externalities," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 557-568.
  9. Thaler, Richard, 1981. "Some empirical evidence on dynamic inconsistency," Economics Letters, Elsevier, vol. 8(3), pages 201-207.
  10. Shleifer, Andrei, 2000. "Inefficient Markets: An Introduction to Behavioral Finance," OUP Catalogue, Oxford University Press, number 9780198292272, September.
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  12. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
  13. Follmer, Hans, 1974. "Random economies with many interacting agents," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 51-62, March.
  14. Roger Guesnerie, 2001. "Assessing Rational Expectations: Sunspot Multiplicity and Economic Fluctuations," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262072076, December.
  15. Blume,L. & Durlauf,S., 2002. "Equilibrium concepts for social interaction models," Working papers 7, Wisconsin Madison - Social Systems.
  16. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(02), pages 170-196, June.
  17. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 573-97, May.
  18. Mirta B. Gordon & Jean-Pierre Nadal & Denis Phan & Viktoriya Semeshenko, 2007. "Discrete Choices under Social Influence: Generic Properties," Working Papers halshs-00135405, HAL.
  19. Rama Cont & Jean-Philippe Bouchaud, 1997. "Herd behavior and aggregate fluctuations in financial markets," Science & Finance (CFM) working paper archive 500028, Science & Finance, Capital Fund Management.
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