Game-Theoretic Price Formation in Order Books with Liquidity Costs

Summary

The paper models how an asset’s price forms when it is traded through an order book. It develops two related approaches: a finite many-person game and a mean-field game, with trading costs that reflect limited liquidity. In both frameworks, the authors derive analytical expressions linking the formed price to realized order flow. This provides a way to study how traders’ interactions and liquidity constraints shape prices.

The paper also examines when the finite-player model converges to its mean-field counterpart, identifying conditions for that agreement. It reports a numerical assessment using high-frequency data from ten NASDAQ stocks, one Brazilian stock, and one cryptocurrency traded on Binance. The provided description does not state the specific formulas, assumptions, convergence conditions, or numerical findings. Its evidence is therefore limited here to the stated empirical scope; the models’ practical fit and applicability beyond those markets cannot be assessed from this summary alone.

Key ideas

• The paper studies order-book price formation through finite-player and mean-field game models.
• Limited liquidity is represented as a source of trading costs.
• Analytical expressions connect formed prices to realized order flow.
• The authors identify conditions for finite-game prices to converge to mean-field prices.
• A numerical study uses high-frequency observations from equities and a cryptocurrency.

Tags

# Price formation in financial markets: a game-theoretic perspective


# Price formation in financial markets: a game-theoretic perspective









We propose two novel frameworks to study the price formation of an asset negotiated in an order book. Specifically, we develop a game-theoretic model in many-person games and mean-field games, considering costs stemming from limited liquidity. We derive analytical formulas for the formed 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 with a large experiment using high-frequency data from ten stocks listed in the NASDAQ, a stock listed in B3 in Brazil, and a cryptocurrency listed in Binance.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.