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Quality score (QS) plays a critical role in sponsored search advertising (SSA) auctions, and in practice is closely correlated to the historical click-through rate (CTR) of an advertisement. The CTR-QS correlation may impose great influence on advertisers' positioning strategies of selecting the targeting slots in the sponsored list. In the literature, however, QS is implicitly assumed to be an independent variable and exogenously assigned by Web search engines, so that little theoretical or managerial insights can be offered to help understand the positioning dynamics in SSA auctions with CTR-QS correlation. We strive to bridge this research gap in this paper. Based on a discrete time-dependent optimal control model, which explicitly captures the relationship between the historical CTR and QS, we determine the optimal strategy for revenue-maximizing advertisers' QS-based positioning decisions through a policy-iteration-based numerical approximation method. We also investigate two practically-used heuristic strategies, namely the greedy and farsighted positioning strategies, aiming to examine and help understand advertisers' real-world positioning dynamics. Our analysis indicates that both the optimal and greedy positioning strategies lead advertisers to monotonically increase or decrease their targeting slots over time, which may cause a polarization trend emerging in SSA markets. Meanwhile, the farsighted positioning strategy can accelerate the polarization. Our simulations show that both the greedy and farsighted strategies have good revenue performance. Our findings indicate that advertisers should monotonically adjust their targeting positions to maximize their revenue in CTR-QS correlated SSA auctions. Our findings also highlight the need for Web search engine companies to set a lowered weight for historical CTRs or use position-normalized CTRs in their QS measurements, so as to suppress the polarization trend.
Yuan et al. (Tue,) studied this question.