论文标题
在消费者参考效果下的价格竞赛中无需重新学习
No-regret Learning in Price Competitions under Consumer Reference Effects
论文作者
论文摘要
我们研究了两家公司之间的重复价格竞争的长期市场稳定性，消费者的需求取决于公司发布的价格和消费者的价格期望称为参考价格。根据基于内存的动态，消费者的参考价格随时间而变化，这是所有历史价格的加权平均值。我们专注于公司不了解需求功能以及如何形成参考价格的环境，而是可以访问甲骨文，以衡量消费者对当前张贴价格的响应。我们表明，如果这些公司运行了无重格算法，特别是在线镜像下降（OMD），阶梯尺寸降低，那么市场就会稳定，从某种意义上说，公司的价格和参考价格会融合到稳定的NASH平衡（SNE）。有趣的是，我们还表明，市场可以稳定下来。我们进一步表征了降低和恒定OMD步长的收敛速率。
We study long-run market stability for repeated price competitions between two firms, where consumer demand depends on firms' posted prices and consumers' price expectations called reference prices. Consumers' reference prices vary over time according to a memory-based dynamic, which is a weighted average of all historical prices. We focus on the setting where firms are not aware of demand functions and how reference prices are formed but have access to an oracle that provides a measure of consumers' responsiveness to the current posted prices. We show that if the firms run no-regret algorithms, in particular, online mirror descent(OMD), with decreasing step sizes, the market stabilizes in the sense that firms' prices and reference prices converge to a stable Nash Equilibrium (SNE). Interestingly, we also show that there exist constant step sizesunder which the market stabilizes. We further characterize the rate of convergence to the SNE for both decreasing and constant OMD step sizes.
