This paper investigates how the sponsored-link auction for multiple positions influence the market structure under a duopoly setting. We utilize a model of position auction with con-sumer search in a duopoly setting and derive the consumer distribution, advertiser bidding, and market equilibrium in this game. We discover that there exists a segmentation equilibri-um, in which a platform consists of high and low quality advertisers and consumers, while the other is composed of medium quality agents. The results regarding the agents' distribu-tion could bring valuable insights for regulatory policies about interactions and cooperation between large digital platforms.
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