Who Gets Cited? A Game-Theoretic Approach to Generative Engine Optimization

Generative search gives publishers an incentive to optimize their sources for visibility, and a source can become more visible by changing how it looks rather than by improving what it says. Existing defenses against generative engine optimization (GEO) are static: publishers can arbitrage them once the policy is set. We introduce Nash-GEO, a game-theoretic method for designing platform policies that reward useful supporting material over presentation manipulation. The platform searches for publisher edits that gain citation exposure under its policy and uses those responses to refine the policy. We prove that a presentation edit offers no citation advantage on any engine if the platform removes it before generation. If such edits cost anything, no publisher benefits from making them, regardless of others' actions. Once citation positions are full, GEO redistributes exposure rather than creating it: even if every publisher optimizes, total exposure cannot increase. Across multiple generative engines, the policy reduces manipulation's advantage over adding supporting material from 4.99% to 0.51% for two search-generated strategies, and to 2.32% when additional strategies are tested. Adding supporting material outperforms presentation editing alone by 7.0%, with an advantage on every engine. These findings show how generative search platforms can shape competition among publishers by rewarding content improvements over presentation manipulation.