提出高效算法求解金融交易中的策略博弈，解决传统方法不收敛问题。
Algorithmic Aspects of Strategic Trading
- 设计快速计算最优响应的算法，应对市场冲击下的复杂策略空间。
- 发现临时冲击下可收敛，但整体设置中最佳响应不收敛。
- 用扰动领袖跟踪法高效求解粗相关均衡，适合实际交易场景模拟。
现代金融市场中的算法交易广泛展现出战略性的、博弈论式的行为，其复杂性难以建模。近期一系列研究（Chriss, 2024b,c,a, 2025）在位置构建交易场景中取得进展：各方需在固定时间内买入或卖出指定数量的股份，同时面对临时性与永久性市场冲击，导致策略空间呈指数级增长。尽管此前研究主要关注均衡策略的存在性与结构特性，本文聚焦该模型的算法层面。我们给出一种高效计算最优响应的算法，并证明：仅存在临时冲击时为潜在博弈，且最佳响应动态可收敛；但在一般情形下，最佳响应动态通常不收敛，目前尚无快速算法用于（纳什）均衡计算。为此，我们引入更广义的粗相关均衡（CCE），并通过扰动领袖跟踪法（FTPL）实现其高效计算。实验验证了模型与结果，显示FTPL在临时与永久冲击权重不同的情况下表现出有趣行为。
原文摘要 · Abstract (English)
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.
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