various relevance estimates so as to improve overall relevance estimation that guides ranking. Neural-network-based retrieval methods estimate relevance (often probability) by learning document and query representations and/or integrating multiple relevance signals. 28 As feature-based approaches they can be viewed as obeying the PRP. The PRP was shown to be optimal under some assumptions; for example, the independence of document relevance from that of others. 33

Post-ranking dynamics. Careful examination of the PRP, and retrieval methods based on the PRP, reveals a major gap: post-ranking effects are not accounted for; specifically, changes in the corpus documents made by incentivized publishers that respond to the induced ranking so as to improve the ranking of their documents. We focus on publishers (content providers) as those affected by, and affecting, the dynamics. We do not consider the dynamics driven by users of the systems, for example, via clickthrough actions. Later in the article, we discuss the importance, challenges, and potential future directions of accounting simultaneously for publisher and user-driven dynamics.

To highlight the importance of ac-
counting for post-ranking effects on
corpus content consider the following
example. 2 A publisher writes a docu-
ment that contains both common in-
formation and information which is
unique to the document; that is, this
unique information cannot be found
in any other document in the cor-
pus. The publisher, for some reason,
is more interested in her document
being highly ranked for queries that
touch on the non-unique information.
However, the ranking function “penal-
izes” documents having a mixture of
information (that is, not being focused
on the information sought for in these
queries). In terms of the PRP and cur-
rent retrieval paradigms the approach
of the ranking function is justifiable:
one can assume that the user who
posted the query would prefer read-
ing documents that are focused on in-
formation related to the query rather
than having to wade through poten-
tially long documents and distill the
sought information. Now, suppose
that the publisher decides to remove
We discuss some of the fundamen-
tal, and far reaching, modeling and al-
gorithmic implications of the competi-
tive and incentivized settings in which
search engines operate. Specifically, we
examine post-ranking corpus effects
and survey our work on a game-theo-
retic analysis of the strategic behavior
of publishers (content providers) and
on addressing ranking robustness. We
also briefly describe the challenges of
empirical evaluation and analysis in
competitive search settings. Later, we
focus on our theoretical work on the
suboptimality in competitive settings
of the most basic search (ranking) and
recommendation principle and we sur-
vey our work on settings where incen-
tivized parties are ranking algorithms
and prediction algorithms (regression)
that compete with each other.

Search Engines

The main goal of search engines is to rank documents in a corpus by their presumed relevance to the information need expressed by a query posted by a user. There has been a huge body of work on devising relevance estimates for documents. For example, the similarity between term-based vectors representing documents and queries serves as a relevance estimate in the well-known vector space model. 35 Modern relevance ranking functions are learned (trained) using a training set which contains queries and corresponding relevance judgments of documents. 25, 28 These approaches allow to integrate various types of relevance estimates.

The theoretical foundation of virtually all ad hoc retrieval paradigms, classical and modern, is the probability ranking principle (PRP): 33 Documents are ranked by the probability that they are relevant to the query wherein the probability is estimated using all the information available to the search system. The PRP is the direct basis of the probabilistic retrieval approach20 and was shown to underlie the basic language modeling approach. 23 Feature-based learning-to-rank methods can also be viewed as obeying the PRP, even if relevance probability is not directly estimated. That is, these approaches are trained to minimize ranking loss with respect to ground truth ranking and they essentially integrate

We believe
the design
of search and
recommendation
methods must be
revolutionized to
account for the
strategic incentives
of the various
parties that affect
(or are affected by)
the system.