  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 two families of ranking functions that do not adhere to
the PRP principle. 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.
