Price formation in financial markets: a game-theoretic perspective

TL;DR

This paper introduces two game-theoretic frameworks to analyze asset price formation in order books, deriving formulas and conditions for convergence, and validates findings with high-frequency market data across stocks and cryptocurrencies.

Contribution

It presents novel game-theoretic models for price formation considering liquidity costs and establishes convergence conditions between finite and mean-field models.

Findings

Derived analytical formulas for asset prices based on order flow.

Identified conditions for convergence of finite and mean-field game prices.

Validated models with high-frequency data from stocks and cryptocurrencies.

Abstract

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.