Algorithmic recommender systems such as Spotify and Netflix affect not only consumer behavior but also producer incentives. Producers seek to create content that will be shown by the recommendation algorithm, which can impact both the diversity and quality of their content. In this work, we investigate the resulting supply-side equilibria in personalized content recommender systems. We model users and content as $D$-dimensional vectors, the recommendation algorithm as showing each user the content with highest dot product, and producers as maximizing the number of users who are recommended their content minus the cost of production. Two key features of our model are that the producer decision space is multi-dimensional and the user base is heterogeneous, which contrasts with classical low-dimensional models. Multi-dimensionality and heterogeneity create the potential for specialization, where different producers create different types of content at equilibrium. Using a duality argument, we derive necessary and sufficient conditions for whether specialization occurs: these conditions depend on the extent to which users are heterogeneous and to which producers can perform well on all dimensions at once without incurring a high cost. Then, we characterize the distribution of content at equilibrium in concrete settings with two populations of users. Lastly, we show that specialization can enable producers to achieve positive profit at equilibrium, which means that specialization can reduce the competitiveness of the marketplace. At a conceptual level, our analysis of supply-side competition takes a step towards elucidating how personalized recommendations shape the marketplace of digital goods, and towards understanding what new phenomena arise in multi-dimensional competitive settings.

翻译：诸如Spotify和Netflix等算法推荐系统不仅影响消费者行为，也影响生产者的激励。生产者力求创作能被推荐算法展示的内容，这会影响其内容的多样性和质量。本文研究了个性化内容推荐系统中由此产生的供给均衡。我们将用户和内容建模为$D$维向量，将推荐算法建模为向每位用户展示点积最高的内容，将生产者建模为最大化被推荐其内容的用户数量减去生产成本。我们模型的两个关键特征是：生产者决策空间是多维的，且用户群体是异质的——这与经典的低维模型形成对比。多维性和异质性为专业化分工创造了可能，即均衡中不同生产者创作不同类型的内容。利用对偶论证，我们推导了专业化分工是否发生的充要条件：这些条件取决于用户的异质程度，以及生产者能否在不承担高昂成本的情况下同时在所有维度上表现良好。随后，我们在两个用户群体的具体情境中刻画了均衡时内容的分布。最后，我们表明专业化分工能使生产者在均衡中实现正利润，这意味着专业化分工可能降低市场的竞争性。在概念层面，我们对供给方竞争的分析迈出了阐明个性化推荐如何塑造数字商品市场的一步，并有助于理解多维竞争环境中出现的新现象。