Generative AI (GenAI) search systems are transforming how users access information. Unlike ranking-based search systems, where users observe a ranked list of documents, GenAI search systems, given a user's question, generate an answer, often accompanied by external sources (e.g., in the form of citations). Content creators (publishers) seeking to increase exposure might behave strategically and compete with other creators for users' attention. While publishers in ranking-based systems might strategically modify their content to improve its ranking, the incentives in generative systems take on a new form. Publishers may now gain exposure through generated responses and attributions to those responses. We introduce a novel game-theoretic model of the emerging GenAI ecosystem in which publishers compete for attribution-based exposure. We study the learning dynamics of strategic content creators under better-response dynamics. We associate the convergence of learning dynamics to equilibrium with ecosystem stability. Employing the notion of potential games, we study the stability of GenAI ecosystems under several known content selection mechanisms. We demonstrate the instability of mechanisms representing real-world modern systems and characterize a mechanism that induces a stable ecosystem. We conduct extensive simulations to analyze the stability and welfare of GenAI ecosystems under various mechanisms. The simulations support our theoretical findings and reveal an interplay among stability, publisher welfare, and user welfare. In particular, stable mechanisms do not necessarily maximize welfare, demonstrating an important trade-off for platform designers. We then introduce a study illustrating that the proper selection of the GenAI mechanism enables the manifestation of desired trade-offs between publisher welfare and the different sources of user welfare.

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