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.

翻译：大型语言模型（LLMs）正成为消费者发现产品的主要渠道，但我们尚未理解品牌如何在这一新渠道中竞争。我们以护肤品（消费者在购买前难以判断质量、必须依赖品牌声誉的品类）为研究对象，考察三种商用LLM（GPT-4o-mini、Claude Sonnet、Gemini 3 Flash）中的品牌动态，并通过搜索品进行稳健性检验。在三项实验中，我们发现：（1）条件性垄断——当所有产品规格相同时，知名品牌获得100%推荐率（IAI=10.0），但这种优势在竞争对手获得低于+0.1星级评分优势时消失；（2）权威式营销语言（包括虚构临床证据声明）能以等效于+0.17评分点的偏差剩余价值打破这种垄断，且各模型反应不同；（3）多品牌GEO竞争中的社会困境：当所有品牌采用相同优化策略时，个体收益在我们设定的收益代理指标中从+0.802降至+0.007，未参与品牌在测试中获得零推荐。我们的结果表明，生成式引擎优化（GEO）不仅应作为安全风险，更应作为塑造市场竞争的新兴营销实践加以研究。