Auction Design for ROI-Constrained Buyers

Problem definition: We consider a setting where buyers have constraints on their minimum return on investment (ROI). We seek to investigate the impact of ROI constraints on the bidding behavior of buyers in the widely used second price auctions. We further study the design of an optimal auction that can mitigate the negative consequences of ROI constraints. Academic/Practical Relevance: In online advertising markets, second price auctions are widely used to sell advertising impressions to advertisers. Second price auctions are prevalent because they are truthful when the advertisers (buyers) are quasilinear. However, the quasilinearity assumption and, consequently, truthful bidding break down when buyers are concerned about their ROI. This can lead to significant revenue and welfare loss under second price auctions. Methodology: We use game theory and mechanism design. Results: We present a tractable framework to model and study ROI constraints. Under this model, we characterize the equilibrium bidding strategy of ROI-constrained buyers in second price auctions with a reserve price. We show that buyers whose valuation is close to the reserve price do not participate in second price auctions, and high-valuation buyers participate in the auctions and may shade their bid when their target ROI is large and the market is competitive. We further design optimal auctions when buyers desire a certain target ROI. We show that the optimal auction can take one of the following three forms. In the first form, the ROI of all buyers is exactly equal to their target ROI. In the second form, the optimal mechanism is second price auctions with a reserve and a possible subsidy, and in the third form, while the ROI of low-valuation buyers is their target ROI, high-valuation buyers enjoy a higher ROI. Managerial Implications: Our results show that when buyers are ROI constrained, second price auctions can be significantly inefficient both in terms of revenue and social welfare. This highlights the need to design an optimal auction that acknowledges ROI constraints in order to alleviate their negative impact, improving both revenue and welfare.

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