AI 中文总结
本研究提出基于策略图拓扑的图论指标，可审计强化学习算法的合谋行为，为有限信息下的算法定价系统审计提供了新方法。
AI 中文摘要
检测算法合谋颇具挑战，因为监管机构往往难以获取企业的算法、训练数据及市场信息。我们研究一种中等信息场景，其中审计人员可查询企业的冻结定价策略并构建对应的策略图。借助重复定价博弈中纳什均衡的完整表征，我们识别出与合谋奖惩机制相关的策略图图论特征，包括最大介数、吸引子入度及平均路径长度。随后，我们将这些指标应用于分散式Q学习算法及Calvano等人（2020）提出的Q学习算法所学习到的策略上进行测试。研究发现，尤其是最大介数和吸引子入度，与基于标准利润的合谋指数存在强相关性。重要的是，所提出的指标仅依赖策略图的无标签拓扑结构，既不需要价格历史、需求估计，也不需要竞争和垄断基准。我们的研究结果表明，冻结定价策略的结构包含强化学习算法间合谋的稳健信号，为在有限信息下审计算法定价系统提供了有前景的基础。
英文摘要
Detecting algorithmic collusion is challenging because regulators often have limited access to firms' algorithms, training data, and market information. We study an intermediate-information regime in which an auditor can query firms' frozen pricing policies and construct the induced strategy graph. Using a complete characterization of Nash equilibria in a repeated pricing game, we identify graph-theoretic features of strategy graphs that are associated with collusive reward-and-punishment schemes, including maximum betweenness, attractor in-degree, and average path length. We then test these metrics on policies learned by decentralized Q-learning and the Q-learning algorithm of Calvano et al. (2020). We find that especially the maximum betweenness and attractor in-degree are strongly correlated with the standard profit-based Collusion Index. Importantly, the proposed metrics rely only on the unlabeled topology of strategy graphs and require neither price histories, demand estimates, nor competitive and monopoly benchmarks. Our results suggest that the structure of frozen pricing policies contains robust signals of collusion among reinforcement learning algorithms and provides a promising basis for auditing algorithmic pricing systems under limited information.
Comments18 pages, 2 figures, 8 tables. Preliminary draft; comments welcome. JEL: C73, D43, D83, L13, L40, L41
