A Game Theoretic Analysis of the Adversarial Retrieval Setting

The main goal of search engines is ad hoc retrieval: ranking documents in a corpus by their relevance to the information need expressed by a query. The Probability Ranking Principle (PRP) — ranking the documents by their relevance probabilities — is the theoretical foundation of most existing ad hoc document retrieval methods. A key observation that motivates our work is that the PRP does not account for potential post-ranking effects; specifically, changes to documents that result from a given ranking. Yet, in adversarial retrieval settings such as the Web, authors may consistently try to promote their documents in rankings by changing them. We prove that, indeed, the PRP can be sub-optimal in adversarial retrieval settings. We do so by presenting a novel game theoretic analysis of the adversarial setting. The analysis is performed for different types of documents (single-topic and multi-topic) and is based on different assumptions about the writing qualities of documents’ authors. We show that in some cases, introducing randomization into the document ranking function yields an overall user utility that transcends that of applying the PRP.