Algorithmic Aspects of Strategic Trading

TL;DR

This paper explores the algorithmic challenges in strategic trading models with market impact, providing efficient algorithms for best responses and CCE computation, and analyzing their behavior through experiments.

Contribution

It introduces efficient algorithms for computing best responses and Coarse Correlated Equilibria in strategic trading models with market impact.

Findings

Best response algorithms are efficient for certain settings.

Best response dynamics may not converge in general.

FTPL effectively computes CCE and exhibits interesting behaviors.

Abstract

Algorithmic trading in modern financial markets is widely acknowledged to exhibit strategic, game-theoretic behaviors whose complexity can be difficult to model. A recent series of papers (Chriss, 2024b,c,a, 2025) has made progress in the setting of trading for position building. Here parties wish to buy or sell a fixed number of shares in a fixed time period in the presence of both temporary and permanent market impact, resulting in exponentially large strategy spaces. While these papers primarily consider the existence and structural properties of equilibrium strategies, in this work we focus on the algorithmic aspects of the proposed model. We give an efficient algorithm for computing best responses, and show that while the temporary impact only setting yields a potential game, best response dynamics do not generally converge for the general setting, for which no fast algorithm for (Nash) equilibrium computation is known. This leads us to consider the broader notion of Coarse Correlated Equilibria (CCE), which we show can be computed efficiently via an implementation of Follow the Perturbed Leader (FTPL). We illustrate the model and our results with an experimental investigation, where FTPL exhibits interesting behavior in different regimes of the relative weighting between temporary and permanent market impact.