忽略对手价格会引发短期串谋假象,长期仍需建模竞争者才能高效定价。
Should Demand Models Incorporate Competitor Prices? Oblivious Learning and Algorithmic Collusion

- 用迭代最小二乘法模拟卖家学习需求,分是否建模对手价格两种策略。
- 盲目忽视对手价格需更激进探索,否则价格会陷入伪均衡并出现短暂串谋现象。
- 当所有卖家都知情时,市场收敛到竞争性最优,是唯一稳定策略组合。
在多个卖家重复定价的平台中,定价算法是否应显式建模对手价格?经典学习理论认为应建模,忽略会导致模型误设和效率损失。然而近期研究指出,故意忽视对手价格可能促进串谋并提升利润。本文在需求未知且含噪声的简化市场中,分析了卖家通过迭代最小二乘法学习需求的动态。若所有卖家均盲目(oblivious)忽略对手价格,则需更激进探索以弥补信息缺失;充分探索下价格收敛至竞争均衡,但探索衰减时会出现连续的伪均衡。分析发现,存在短暂的价格异常波动,导致临时串谋模式,但随学习推进而消失。当存在知情与盲目卖家共存时,知情者严格优于盲目者。从博弈角度,唯一纳什均衡是全知情市场,此时价格高效收敛至竞争性结果。整体表明,串谋模式不可持续,盲目建模无法带来长期收益。因此,在竞争市场中,结合对手信息与充分价格探索仍是可靠策略。
原文摘要 · Abstract (English)
On a platform with many sellers, should a pricing algorithm explicitly model competitors' prices when learning demand? Classical learning arguments suggest an affirmative answer: ignoring competitors induces model misspecification and inefficiency. In contrast, recent work on algorithmic collusion suggests that strategic obliviousness -- deliberately ignoring competitor prices -- may facilitate collusive outcomes and improve profits. We study this modeling choice in a stylized competitive market with unknown noisy demand, in which multiple sellers repeatedly set prices and estimate demand via iterated least squares, and either incorporate competitors' prices into their demand models (informed) or ignore them (oblivious). We first show that, relative to a monopolist, an oblivious seller in a competitive market must explore more aggressively to compensate for the loss of dynamic competitor information. Building on this insight, we characterize market dynamics when all sellers are oblivious and show that prices converge to the competitive outcome under sufficient exploration, while a continuum of pseudo-equilibria arises when exploration decays. Analyzing the resulting price trajectories, we uncover an excursion phenomenon that gives rise to transient collusive patterns that dissipate as learning progresses. In markets with both oblivious and informed sellers, the informed strictly out-earn the oblivious. Read as a strategy game, the modeling choice has a unique Nash equilibrium: the all-informed market, in which prices converge to the competitive outcome efficiently. Overall, our results indicate that collusive patterns are not robust and are not sustained by oblivious modeling; therefore, incorporating competitor information, together with sufficient price exploration, remains a reliable strategy for sellers in competitive markets.
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