算法定价系统因忽视竞争者价格，可能推高价格至垄断水平。
Misspecified Estimate-then-Optimize Leads to Supra-Competitive Prices
- 企业用自身销售数据拟合需求模型，忽略对手价格来定价。
- 若初始探索阶段价格相近且同在均衡价一侧，易导致远高于纳什均衡的价格。
- 真实租房市场模拟显示结果稳健，适用于多种复杂场景。
我们研究简单算法定价系统在多企业市场中是否可能系统性地产生类似共谋的价格。考虑企业采用短视的‘估计-优化’规则：反复根据自身价格与销量历史拟合需求模型，并设定使估算利润最大化的价格。该需求模型存在误设，忽略了竞争对手的价格。我们分析了该规则在独立随机价格探索期初始化后的动态行为，通过流极限常微分方程分析，刻画了其收敛至高于纳什均衡的超竞争性价格的条件。结果显示，当企业初始探索价格范围相似且位于纳什价格同侧时，会引发超竞争性价格；在对称探索下，价格甚至可达垄断水平。基于真实多户租赁市场的仿真验证表明，即使在有限周期、异质产品及非线性对数概率需求等脱离理论假设的情形下，超竞争性结果仍稳健出现。
原文摘要 · Abstract (English)
We study whether simple algorithmic pricing systems can systematically produce collusive-like prices in multi-firm markets. We consider firms that price using a myopic estimate-then-optimize rule: each repeatedly fits a demand model to its own price and sales history and sets the price that maximizes estimated profit. This demand model is misspecified, omitting competitors' prices. We analyze the dynamics of this rule when it is initialized by an exploration phase of independent random prices. We characterize when this pipeline converges to supra-competitive prices above the Nash equilibrium, via a fluid-limit ordinary differential equation analysis. We show that supra-competitive prices arise when firms initially explore within similar price ranges on the same side of the Nash price. Moreover, prices can be substantially above the Nash price; we show that prices can reach monopoly levels under symmetric exploration. Simulations calibrated to a real multifamily rental market confirm that supra-competitive outcomes arise robustly beyond our theoretical assumptions, including under finite horizons, heterogeneous products, and nonlinear logit demand.
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