Incumbent Advantage: Brand Bias and Cognitive Manipulation Dynamics in LLM Recommendation Systems A new study reveals that large language models exhibit a strong brand bias, recommending well-known brands 100% of the time when product specifications are identical, but this dominance can be broken by minor rating advantages or authority-style marketing language. The research, conducted across three commercial LLMs using skincare products, also identifies a social dilemma in multi-brand optimization where collective adoption of strategies reduces individual payoffs. These findings highlight the need to study generative engine optimization as both a security risk and an emerging marketing practice. arXiv:2606.17443v1 Announce Type: new Abstract: Large language models LLMs are becoming a major way for consumers to find products, but we do not yet understand how brands compete in this new channel. We study brand dynamics in LLM recommendations using skincare products -- a category where consumers cannot easily judge quality before buying and must rely on brand reputation -- across three commercial LLMs GPT-4o-mini, Claude Sonnet, Gemini 3 Flash , with a robustness check on search goods. In three experiments, we find: 1 a Conditional Monopoly where well-known brands get recommended 100% of the time IAI = 10.0 when all products have the same specifications, but this dominance disappears with less than a +0.1-star rating advantage for a competitor; 2 authority-style marketing language, including fabricated clinical-evidence claims, breaks this monopoly at a Bias Surplus Value equal to +0.17 rating points, with each model responding differently; and 3 a social dilemma in multi-brand GEO competition: when all brands adopt the same optimization strategy, individual payoff falls from +0.802 to +0.007 in our payoff proxy, and non-participating brands receive zero recommendations in our tests. Our results suggest that generative engine optimization GEO should be studied not only as a security risk, but also as an emerging marketing practice that shapes market competition.