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Infinite Horizon Nash Equilibrium Models of a Limit Order Book

Author

Listed:
  • Alberto Bressan

    (Penn State University)

  • Hongxu Wei

    (Penn State University)

Abstract

The paper analyzes some models of a Limit Order Book, determined as a Nash equilibrium among a large number of traders, in infinite time horizon. We study how the size and shape of the LOB are related to the expected profit rate of traders posting limit orders, and to the random distribution of incoming external buy or sell orders. Formulas are derived which show how the volatility of the stock, and the presence of better informed external agents, determine (i) an increase in the bid-ask spread and (ii) a liquidity reduction, i.e. a decrease in the total amount of stocks posted for purchase or for sale. We also analyze models including “fast” and “slow” traders, that can react more or less quickly to changes in the fundamental value of the stock.

Suggested Citation

  • Alberto Bressan & Hongxu Wei, 2025. "Infinite Horizon Nash Equilibrium Models of a Limit Order Book," Dynamic Games and Applications, Springer, vol. 15(3), pages 847-871, July.
    • Handle: RePEc:spr:dyngam:v:15:y:2025:i:3:d:10.1007_s13235-024-00583-6
    DOI: 10.1007/s13235-024-00583-6
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    References listed on IDEAS

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    1. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    2. Kerry Back & Shmuel Baruch, 2004. "Information in Securities Markets: Kyle Meets Glosten and Milgrom," Econometrica, Econometric Society, vol. 72(2), pages 433-465, March.
    3. Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. II: Continuous-time case," Papers 1110.3229, arXiv.org, revised Sep 2015.
    4. Peter Bank & Dmitry Kramkov, 2015. "A model for a large investor trading at market indifference prices. I: Single-period case," Finance and Stochastics, Springer, vol. 19(2), pages 449-472, April.
    5. Kerry Back & Shmuel Baruch, 2013. "Strategic Liquidity Provision in Limit Order Markets," Econometrica, Econometric Society, vol. 81(1), pages 363-392, January.
    6. Alberto Bressan & Deling Wei, 2014. "A Bidding Game with Heterogeneous Players," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 1018-1048, December.
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