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Natural Instability of Equilibrium Prices

Author

Listed:
  • Dmitry Levando

    (National Research University Higher School of Economics, Moscow, Russia)

  • Maxim Sakharov

    (Bauman Mstu, Moscow, Russia)

Abstract

We develop a theory of market fluctuations caused by strategic trade with complete information and without outside shocks. The constructed general equilibrium duopoly is a strategic market game with infinite strategies and multiple mixed strategies equilibria. First order conditions (FOC) of the game are the ill-posed problems (Hadamard, 1909), but every equilibrium mixed strategy can be only approximated. This imposes restrictions on convergence of common beliefs of players about actions of each other, existence of rational expectations and a price discovery property of the market, although the market is informationally efficient (Fama, 1970). We suggest a modification of Tikhonov regularization to construct pseudo-solutions. All endogenous variables of the model are exposed to unremovable instabilities, ‘natural instabilities', specific to parameters of a chosen approximation. Our result is also related to existence of common knowledge, sun-spot equilibrium, and noise trade.

Suggested Citation

  • Dmitry Levando & Maxim Sakharov, 2018. "Natural Instability of Equilibrium Prices," Working Papers 2018:01, Department of Economics, University of Venice "Ca' Foscari".
    • Handle: RePEc:ven:wpaper:2018:01
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    1. Julio Dávila & Piero Gottardi & Atsushi Kajii, 2007. "Local Sunspot Equilibria Reconsidered," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 401-425, June.
    2. Peck, James & Shell, Karl & Spear, Stephen E., 1992. "The market game: existence and structure of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 271-299.
    3. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 301-314.
    4. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    5. Dmitry Levando, 2012. "A Survey Of Strategic Market Games," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 57(194), pages 63-106, July - Se.
    6. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    7. Dilip Abreu & Markus K. Brunnermeier, 2003. "Bubbles and Crashes," Econometrica, Econometric Society, vol. 71(1), pages 173-204, January.
    8. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    9. Van Ness, Bonnie F & Van Ness, Robert A & Pruitt, Stephen W, 2000. "The Impact of the Reduction in Tick Increments in Major U.S. Markets on Spreads, Depth, and Volatility," Review of Quantitative Finance and Accounting, Springer, vol. 15(2), pages 153-167, September.
    10. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    11. Madhavan, Ananth, 2000. "Market microstructure: A survey," Journal of Financial Markets, Elsevier, vol. 3(3), pages 205-258, August.
    12. Satyajith Amaran & Nikolaos V. Sahinidis & Bikram Sharda & Scott J. Bury, 2016. "Simulation optimization: a review of algorithms and applications," Annals of Operations Research, Springer, vol. 240(1), pages 351-380, May.
    13. Robert A. Jarrow & Philip Protter, 2012. "A Dysfunctional Role Of High Frequency Trading In Electronic Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-15.
    14. Jean Jacod & Yingying Li & Xinghua Zheng, 2017. "Statistical Properties of Microstructure Noise," Econometrica, Econometric Society, vol. 85, pages 1133-1174, July.
    15. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    16. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    17. Adam Brandenburger, 2014. "The Language of Game Theory:Putting Epistemics into the Mathematics of Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8844, October.
    18. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    19. Glosten, Lawrence R. & Harris, Lawrence E., 1988. "Estimating the components of the bid/ask spread," Journal of Financial Economics, Elsevier, vol. 21(1), pages 123-142, May.
    20. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
    21. Abreu, Dilip & Brunnermeier, Markus K., 2002. "Synchronization risk and delayed arbitrage," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 341-360.
    22. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
    23. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
    24. Roll, Richard, 1984. "A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market," Journal of Finance, American Finance Association, vol. 39(4), pages 1127-1139, September.
    25. Atsushi Kajii, 1997. "On the Role of Options in Sunspot Equilibria," Econometrica, Econometric Society, vol. 65(4), pages 977-986, July.
    26. Harris, Lawrence, 1990. "Estimation of Stock Price Variances and Serial Covariances from Discrete Observations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(3), pages 291-306, September.
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    Cited by:

    1. A. Larionov V. & E. Salina S. & А. Ларионов В. & Е. Салина С., 2019. "Регулирование и оценка рисков деятельности платежных систем // Regulation and Risk Assessment of Payment Systems," Управленческие науки // Management Science, ФГОБУВО Финансовый университет при Правительстве Российской Федерации // Financial University under The Government of Russian Federation, vol. 9(3), pages 40-55.

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    More about this item

    Keywords

    Strategic market games; ill-posed problems; common knowledge; rational expectations; efficient market; price fluctuations;
    All these keywords.

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D59 - Microeconomics - - General Equilibrium and Disequilibrium - - - Other
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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