We study a game-theoretic model of information retrieval, 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 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 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, and demonstrate a possible publisher-user trade-off, which highlights the complexity of determining which ranking function should be selected by the search engine designer.

翻译：我们研究了一个信息检索的博弈论模型，其中战略发布者旨在最大化其被搜索引擎排名第一的机会，同时保持原始文档的完整性。我们证明了常用的PRP排序方案会导致不稳定环境，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，并引入了两个符合RRP的排序函数。我们提供了理论和实证证据，表明这些方法通过展示学习动态收敛的积极结果，能够构建稳定的搜索生态系统。我们还定义了发布者和用户的福祉，并揭示了可能的发布者-用户权衡，这凸显了搜索引擎设计者选择排序函数的复杂性。