We study a game-theoretic information retrieval model in which strategic publishers aim to maximize their chances of being ranked first by the search engine while maintaining the integrity of their original documents. We show that the commonly used Probability Ranking Principle (PRP) ranking scheme results in an unstable environment where games often fail to reach pure Nash equilibrium. We propose the Relative Ranking Principle (RRP) as an alternative ranking principle and introduce two families of ranking functions that are instances of the RRP. We provide both theoretical and empirical evidence that these methods lead to a stable search ecosystem, by providing positive results on the learning dynamics convergence. We also define the publishers' and users' welfare, demonstrate a possible publisher-user trade-off, and provide means for a search system designer to control it. Finally, we show how instability harms long-term users' welfare.

翻译：我们研究了一个博弈论信息检索模型，其中策略性发布者旨在最大化其被搜索引擎排名第一的概率，同时保持原始文档的完整性。我们证明，常用的概率排序原则（PRP）排名方案会导致不稳定环境，其中博弈往往无法达到纯纳什均衡。我们提出相对排序原则（RRP）作为替代排序原则，并引入两类符合RRP的排名函数。通过理论和实证证据表明，这些方法通过学习动态收敛的正向结果，能够带来稳定的搜索生态系统。我们还定义了发布者与用户的福利，展示了可能存在的发布者-用户权衡，并为搜索系统设计者提供了控制这一权衡的手段。最后，我们揭示了不稳定性如何损害长期用户福利。