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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\u2013Jacobi nonlinear ordinary differential equations. We prove, do not assume a priori, that the generalized Issac\u2019s 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.<\/jats:p>","DOI":"10.1007\/s13235-020-00373-w","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T15:03:10Z","timestamp":1607612590000},"page":"556-579","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Dynamic Equilibrium of Market Making with Price Competition"],"prefix":"10.1007","volume":"11","author":[{"given":"Jialiang","family":"Luo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harry","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"373_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/14697688.2020.1729396","volume":"20","author":"F Abergel","year":"2020","unstructured":"Abergel F, Hur\u00e9 C, Pham H (2020) Algorithmic trading in a microstructural limit order book model. 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