Dynamic Equilibrium of Market Making with Price Competition

Jialiang Luo () and Harry Zheng ()
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Jialiang Luo: Imperial College
Harry Zheng: Imperial College

Dynamic Games and Applications, 2021, vol. 11, issue 3, No 6, 556-579

Abstract: 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.

Keywords: Dynamic equilibrium; Market making; Price competition; Nonzero-sum stochastic differential game; Generalized Issac’s condition; 93E20; 90C39 (search for similar items in EconPapers)
JEL-codes: C7 G1 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13235-020-00373-w

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