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Dynamic Equilibrium of Market Making with Price Competition

Author

Listed:
  • Jialiang Luo

    (Imperial College)

  • Harry Zheng

    (Imperial College)

Abstract

In this paper, we discuss the dynamic equilibrium of market making with price competition and incomplete information. The arrival of market sell/buy orders follows a pure jump process with intensity depending on bid/ask spreads among market makers and having a looping countermonotonic structure. We solve the problem with the nonzero-sum stochastic differential game approach and characterize the equilibrium value function with a coupled system of Hamilton–Jacobi nonlinear ordinary differential equations. We prove, do not assume a priori, that the generalized Issac’s condition is satisfied, which ensures the existence and uniqueness of Nash equilibrium. We also perform some numerical tests that show our model produces tighter bid/ask spreads than those derived using a benchmark model without price competition, which indicates the market liquidity would be enhanced in the presence of price competition of market makers.

Suggested Citation

  • Jialiang Luo & Harry Zheng, 2021. "Dynamic Equilibrium of Market Making with Price Competition," Dynamic Games and Applications, Springer, vol. 11(3), pages 556-579, September.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:3:d:10.1007_s13235-020-00373-w
    DOI: 10.1007/s13235-020-00373-w
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    References listed on IDEAS

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    Cited by:

    1. Yuheng Zheng & Zihan Ding, 2024. "Reinforcement Learning in High-frequency Market Making," Papers 2407.21025, arXiv.org, revised Aug 2024.
    2. Robert Boyce & Martin Herdegen & Leandro S'anchez-Betancourt, 2024. "Market Making with Exogenous Competition," Papers 2407.17393, arXiv.org.

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    More about this item

    Keywords

    Dynamic equilibrium; Market making; Price competition; Nonzero-sum stochastic differential game; Generalized Issac’s condition;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • G1 - Financial Economics - - General Financial Markets

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