We conduct an investigation on the formal cause of the price of an asset which is negotiated in an order book. In particular, we propose game-theoretic models in many-person games, as well as in infinite games, considering costs stemming from limited liquidity. We derive closed-form formulas for the price in terms of the realized order flow. We also identify appropriate conditions that ensure the convergence of the price we find in the finite population game to that of its mean-field counterpart. We numerically assess our results using high-frequency data from the Brazilian market.
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David Evangelista has a Ph.D. degree in Applied Mathematics from KAUST - King Abdullah University of Science and Technology, master's degree from IMPA - Instituto Nacional de Mathemática Pura e Aplicada (2014), and a degree in mathematics from UFSCar - Universidade Federal de São Carlos (2011). He obtained an award for best article presented by a young researcher by the International Society of Dynamic Games during the 18th International Symposium on Dynamic Games and Applications in July 2018 in Grenoble, France for the article: On the existence of solutions for stationary mean-field games with congestion. He has experience in the area of partial differential equations, mean-field games, and optimal control. His main research interests are in the following areas: mean-field games and optimal control with applications to finance, quantitative finance, and market microstructure.