As commerce shifts to digital marketplaces, platforms increasingly monetize traffic through Sponsored Shopping auctions. Unlike classic ``Sponsored Search", where an advertiser typically bids for a single link, these settings involve advertisers with broad catalogs of distinct products. In these auctions, a single advertiser can secure multiple slots simultaneously to promote different items within the same query. This creates a fundamental complexity: the allocation is combinatorial, as advertisers simultaneously win a bundle of slots rather than a single position. We study this setting through the lens of autobidding, where value-maximizing agents employ uniform bidding strategies to optimize total value subject to Return-on-Investment (ROI) constraints. We analyze two prevalent auction formats: Generalized Second-Price (GSP) and Vickrey-Clarke-Groves (VCG). Our first main contribution is establishing the universal existence of an Autobidding Equilibrium for both settings. Second, we prove a tight Price of Anarchy (PoA) of 2 for both mechanisms.

翻译：随着商业活动向数字市场转移，平台越来越多地通过赞助购物拍卖实现流量变现。与传统的"赞助搜索"（通常广告主仅对单一链接出价）不同，这些场景中的广告主拥有品类丰富的差异化产品目录。在此类拍卖中，单个广告主可在同一查询中同时获得多个广告位，以推广不同商品。这产生了根本性的复杂性：分配过程是组合性的，因为广告主同时赢得的是广告位组合而非单一位置。我们通过自动竞价的视角研究这一场景，其中价值最大化的智能体采用统一竞价策略，在投资回报率约束下优化总价值。我们分析了两种主流拍卖形式：广义第二价格拍卖与VCG拍卖。我们的首要贡献是证明了两种场景下自动竞价均衡的普遍存在性。其次，我们证明两种机制都具有紧致的无政府状态价格比为2。