Pricing optimization and competition under the linear nested stochastic choice model
研究了在消费者行为遵循线性嵌套随机选择模型时，企业如何优化多产品定价，发现调整后的加价在某些条件下为常数，并观察到“亏本销售”效应，进而将定价简化为单变量问题，并构建了寡头竞争下的纳什均衡。
Abstract In this article, we investigate the pricing optimization of firms selling multiple alternatives to the market where consumer purchase behavior follows the linear nested stochastic choice (LNSC) model. As a special case of the nested stochastic choice (NSC) model, LNSC similarly features a two‐step Luce procedure. Considering differentiated price sensitivities in a non‐exact preference function form, the present research specifically shows that, for any product in each nest, the adjusted markup is constant under certain conditions; and the adjusted nest‐level markup is constant among nests under another sufficient condition. The “loss‐leader” effect is observed, which indicates that it may be optimal to price a product with a negative adjusted markup or even a negative margin to attract more attention to the corresponding nest. Based on these results, the pricing optimization can be simplified to a single‐variable problem where the objective function is unimodal. Then, a special case with an exponential preference function is discussed along with its concavity of the total expected profit. The above results are also used to construct the oligopoly multiproduct price competition and characterize the Nash equilibrium. Finally, a series of sensitivity analyses are conducted to reveal the impacts of key parameters on the optimal solutions.