AI 中文总结
本研究在连续时间定价博弈中，针对策略互补性或替代性的不同阶段博弈，提出企业应设计迟缓算法而非最快算法，以在收敛至竞争均衡时获取剩余。
AI 中文摘要
我们在经典的连续时间定价博弈中研究学习算法的策略设计，引入一个元博弈，其中企业为梯度动态选择学习率，将沿整个学习路径累积利润的贴现和作为收益评估。我们发现由阶段博弈激励驱动的根本二分性：若阶段博弈呈现策略替代性，企业明确偏好最快的算法，以快速利用逐步调整的对手；而在策略互补性下，过快的算法会加速对手的竞争反应，破坏过渡利润空间。尽管竞争价格是基础阶段博弈中的严格占优行动，我们证明企业会最优设计迟缓算法，在向竞争均衡的长期收敛过程中提取剩余。
英文摘要
We study the strategic design of learning algorithms in a canonical continuous-time pricing game. We introduce a meta-game in which firms select learning rates for a gradient dynamic, evaluating payoffs as the discounted sum of profits accrued along the entire learning path. We uncover a fundamental dichotomy driven by stage-game incentives: if the stage game exhibits strategic substitutability, firms unambiguously prefer the fastest possible algorithms to rapidly exploit a gradually adjusting opponent. Under strategic complementarity, however, an excessively fast algorithm accelerates the rival's competitive response, destroying transitional profit margins. Even though the competitive price is a strictly dominant action in the underlying stage game, we prove that firms optimally design sluggish algorithms, extracting surplus during a prolonged convergence to the competitive equilibrium.
