Search and recommendation ecosystems exhibit competition among content creators. This competition has been tackled in a variety of game-theoretic frameworks. Content creators generate documents with the aim of being recommended by a content ranker for various information needs. In order for the ecosystem, modeled as a content ranking game, to be effective and maximize user welfare, it should guarantee stability, where stability is associated with the existence of pure Nash equilibrium in the corresponding game. Moreover, if the contents' ranking algorithm possesses a game in which any best-response learning dynamics of the content creators converge to equilibrium of high welfare, the system is considered highly attractive. However, as classical content ranking algorithms, employed by search and recommendation systems, rank documents by their distance to information needs, it has been shown that they fail to provide such stability properties. As a result, novel content ranking algorithms have been devised. In this work, we offer an alternative approach: corpus enrichment with a small set of fixed dummy documents. It turns out that, with the right design, such enrichment can lead to pure Nash equilibrium and even to the convergence of any best-response dynamics to a high welfare result, where we still employ the classical/current content ranking approach. We show two such corpus enrichment techniques with tight bounds on the number of documents needed to obtain the desired results. Interestingly, our study is a novel extension of Borel's Colonel Blotto game.

翻译：搜索与推荐生态系统呈现出内容创作者之间的竞争态势。这一竞争已在多种博弈论框架下得到探讨。内容创作者生成文档，旨在被内容排序器针对不同信息需求所推荐。为使建模为内容排序博弈的生态系统有效运行并最大化用户福祉，系统应保证稳定性，此稳定性与对应博弈中纯纳什均衡的存在性相关联。此外，若内容排序算法所对应的博弈中，内容创作者的任何最优响应学习动态均能收敛至高福祉均衡，则该系统被视为极具吸引力。然而，由于搜索与推荐系统采用的经典内容排序算法依据文档与信息需求的距离进行排序，已有研究表明此类算法无法提供上述稳定性。因此，新型内容排序算法应运而生。本工作提出一种替代方案：通过引入少量固定虚拟文档进行语料库增强。结果表明，通过恰当设计，此类增强能够促成纯纳什均衡，甚至使任何最优响应动态收敛至高福祉结果，同时我们仍沿用经典/现行的内容排序方法。我们提出两种语料库增强技术，并就实现目标所需文档数量给出紧确界。值得注意的是，本研究是对博雷尔上校博弈（Borel's Colonel Blotto game）的创新性拓展。