We consider a novel pricing and advertising framework, where a seller not only sets product price but also designs flexible 'advertising schemes' to influence customers' valuation of the product. We impose no structural restriction on the seller's feasible advertising strategies and allow her to advertise the product by disclosing or concealing any information. Following the literature in information design, this fully flexible advertising can be modeled as the seller being able to choose any information policy that signals the product quality/characteristic to the customers. Customers observe the advertising signal and infer a Bayesian belief over the products. We aim to investigate two questions in this work: (1) What is the value of advertising? To what extent can advertising enhance a seller's revenue? (2) Without any apriori knowledge of the customers' demand function, how can a seller adaptively learn and optimize both pricing and advertising strategies using past purchase responses? To study the first question, we introduce and study the value of advertising - a revenue gap between using advertising vs not advertising, and we provide a crisp tight characterization for this notion for a broad family of problems. For the second question, we study the seller's dynamic pricing and advertising problem with demand uncertainty. Our main result for this question is a computationally efficient online algorithm that achieves an optimal $O(T^{2/3}(m\log T)^{1/3})$ regret rate when the valuation function is linear in the product quality. Here $m$ is the cardinality of the discrete product quality domain and $T$ is the time horizon. This result requires some mild regularity assumptions on the valuation function, but no Lipschitz or smoothness assumption on the customers' demand function. We also obtain several improved results for the widely considered special case of additive valuations.

翻译：本文提出了一种新颖的定价与广告框架，其中卖方不仅设定产品价格，还通过设计灵活的"广告方案"来影响顾客对产品的估值。我们对卖方可行的广告策略不施加结构性限制，允许其通过披露或隐藏任意信息进行产品宣传。遵循信息设计领域的文献，这种完全灵活的广告可建模为卖方能够选择任意信息策略，向顾客传递关于产品质量/特征的信号。顾客观察到广告信号后，会基于贝叶斯推断形成对产品的信念。本研究旨在探讨两个核心问题：(1) 广告的价值何在？广告能在多大程度上提升卖方收益？(2) 在缺乏顾客需求函数先验知识的情况下，卖方如何利用历史购买反馈自适应地学习并优化定价与广告策略？针对第一个问题，我们引入并研究了广告价值——即使用广告与不使用广告之间的收益差距，并对广泛问题类别给出了精确的紧致刻画。针对第二个问题，我们研究了需求不确定条件下卖方的动态定价与广告决策。对此问题的主要贡献是提出了一种计算高效的在线算法，当估值函数关于产品质量呈线性关系时，该算法可实现最优的$O(T^{2/3}(m\log T)^{1/3})$遗憾率。其中$m$表示离散产品质量域的基数，$T$为时间跨度。该结果仅需对估值函数施加温和的正则性假设，且不要求顾客需求函数满足利普希茨条件或光滑性假设。针对广泛研究的加法估值特例，我们还得到了若干改进结果。