There are two major ways of selling impressions in display advertising. Theyare either sold in spot through auction mechanisms or in advance via guaranteedcontracts. The former has achieved a significant automation via real-timebidding (RTB); however, the latter is still mainly done over the counterthrough direct sales. This paper proposes a mathematical model that allocatesand prices the future impressions between real-time auctions and guaranteedcontracts. Under conventional economic assumptions, our model shows that thetwo ways can be seamless combined programmatically and the publisher's revenuecan be maximized via price discrimination and optimal allocation. We consideradvertisers are risk-averse, and they would be willing to purchase guaranteedimpressions if the total costs are less than their private values. We alsoconsider that an advertiser's purchase behavior can be affected by both theguaranteed price and the time interval between the purchase time and theimpression delivery date. Our solution suggests an optimal percentage of futureimpressions to sell in advance and provides an explicit formula to calculate atwhat prices to sell. We find that the optimal guaranteed prices are dynamic andare non-decreasing over time. We evaluate our method with RTB datasets and findthat the model adopts different strategies in allocation and pricing accordingto the level of competition. From the experiments we find that, in a lesscompetitive market, lower prices of the guaranteed contracts will encourage thepurchase in advance and the revenue gain is mainly contributed by the increasedcompetition in future RTB. In a highly competitive market, advertisers are morewilling to purchase the guaranteed contracts and thus higher prices areexpected. The revenue gain is largely contributed by the guaranteed selling.
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