Algorithmic Aspects of Strategic Trading

2025-02-11

AI Summary

This paper studies strategic portfolio acquisition among multiple algorithmic traders under both temporary and permanent market impacts, where the core challenges are an exponential strategy space and non-convergent best-response dynamics. Theoretically, we establish—for the first time—that the game is a potential game when only temporary impact is present; however, in the general case with both impact types, best-response dynamics fail to converge, rendering Nash equilibrium computation intractable. To address this, we propose an efficient framework for constructing coarse correlated equilibria (CCE) based on Follow-the-Perturbed-Leader (FTPL), achieving polynomial-time complexity. Algorithmically, we design a scalable best-response solver and conduct numerical experiments revealing the critical role of the temporary-to-permanent impact weight ratio in determining dynamic convergence. Our main contributions are: (i) the first proof of potential-game structure under pure temporary impact; (ii) the first polynomial-time CCE algorithm for this setting; and (iii) a systematic characterization of the relationship between equilibrium computability and market impact structure.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Search and Optimization: Algorithm Configuration

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Algorithmic trading in financial markets
• Complexity of strategic game-theoretic behaviors
• Efficient computation of Coarse Correlated Equilibria

Innovation

• Efficient best response algorithm
• Coarse Correlated Equilibria computation
• Follow the Perturbed Leader implementation