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，此类场景中的广告主拥有广泛且互异的产品目录。在这些拍卖中，单个广告主可以在同一查询中同时获得多个广告位，以推广不同的商品。这带来了一个根本性的复杂性：分配是组合性的，因为广告主同时赢得的是一个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（ROI）约束下优化总价值。我们分析了两种主流的拍卖形式：广义第二价格（GSP）与维克里-克拉克-格罗夫斯（VCG）机制。我们的第一个主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，我们证明了两种机制的无政府状态价格（PoA）紧界均为2。