The steady rise of e-commerce marketplaces underscores the need to study a market structure that captures the key features of this setting. To this end, we consider a price-quantity Stackelberg duopoly in which the leader is the marketplace operator and the follower is an independent seller. The objective of the marketplace operator is to maximize a weighted sum of profit and a term capturing positive customer experience, whereas the independent seller solely seeks to maximize their own profit. Furthermore, the independent seller is required to share a fraction of their revenue with the marketplace operator for the privilege of selling on the platform. We derive the subgame-perfect Nash equilibrium of this game and find that the equilibrium strategies depend on the assumed rationing rule. We then consider practical implications for marketplace operators. Finally, we show that, under intensity rationing, consumer surplus and total welfare in the duopoly marketplace is always at least as high as under an independent seller monopoly, demonstrating that it is socially beneficial for the operator to join the market as a seller.

翻译：电子商务市场的稳步增长凸显了研究一种能够捕捉该环境关键特征的市场结构的必要性。为此，我们考虑一个价格-数量斯塔克尔伯格双寡头模型，其中领导者是平台运营商，跟随者是一个独立卖家。平台运营商的目标是最大化利润与一个捕捉积极客户体验的项的加权和，而独立卖家则仅寻求最大化自身利润。此外，独立卖家被要求将其收入的一部分分享给平台运营商，以换取在平台上销售的特权。我们推导了该博弈的子博弈完美纳什均衡，并发现均衡策略取决于所假设的配给规则。随后，我们考虑了其对平台运营商的现实意义。最后，我们证明，在强度配给规则下，双寡头市场中的消费者剩余和总福利始终不低于独立卖家垄断下的水平，这表明运营商作为卖家加入市场对社会是有益的。