While page views are often sold instantly through real-time auctions when users visit websites, they can also be sold in advance via guaranteed contracts. In this paper, we present a dynamic programming model to study how an online publisher should optimally allocate and price page views between guaranteed and spot markets. The problem is challenging because the allocation and pricing of guaranteed contracts affect advertisers' purchase between the two markets, and the terminal value of the model is endogenously determined by the updated dual force of supply and demand in auctions. We take the advertisers' purchasing behaviour into consideration, i.e., risk aversion and stochastic demand arrivals, and present a scalable and efficient algorithm for the optimal solution. The model is also empirically validated with a commercial dataset. The experimental results show that selling page views via both guaranteed contracts and auctions can increase the publisher's expected total revenue, and the optimal pricing and allocation strategies are robust to different market and advertiser types.
Our research in this paper concerns both pricing and allocation so the optimal solution includes and reflects their interaction effects. Our problem setup is similar to @cite_0 . However, both the model and the analysis are significantly different from theirs in three important aspects. First, we consider stochastic demand for buying guaranteed contracts. We use a Poisson process to model the arrival of advertisers and allow unfulfilled demand to be backlogged. While @cite_0 assumes the demand for advertising in the future period can be shifted in advance by using a deterministic exponential decay function, the unfulfilled demand in their setting is not explicitly considered at later time points. Second, we devise an optimal pricing and allocation solution to maximise the publisher s expected total revenue, by extending an algorithm for the Knapsack problem. Different from @cite_0 where the optimal solution is linearly searched, our solution is a greedy algorithm, and is relatively scalable and efficient. Third, we further analyse the model's robustness by incorporating supply and demand uncertainty and customising optimal pricing and allocation for different advertiser segments.
@cite_0
2069696398
There are two major ways of selling impressions in display advertising. They are either sold in spot through auction mechanisms or in advance via guaranteed contracts. The former has achieved a significant automation via real-time bidding (RTB); however, the latter is still mainly done over the counter through direct sales. This paper proposes a mathematical model that allocates and prices the future impressions between real-time auctions and guaranteed contracts. Under conventional economic assumptions, our model shows that the two ways can be seamless combined programmatically and the publisher's revenue can be maximized via price discrimination and optimal allocation. We consider advertisers are risk-averse, and they would be willing to purchase guaranteed impressions if the total costs are less than their private values. We also consider that an advertiser's purchase behavior can be affected by both the guaranteed price and the time interval between the purchase time and the impression delivery date. Our solution suggests an optimal percentage of future impressions to sell in advance and provides an explicit formula to calculate at what prices to sell. We find that the optimal guaranteed prices are dynamic and are non-decreasing over time. We evaluate our method with RTB datasets and find that the model adopts different strategies in allocation and pricing according to the level of competition. From the experiments we find that, in a less competitive market, lower prices of the guaranteed contracts will encourage the purchase in advance and the revenue gain is mainly contributed by the increased competition in future RTB. In a highly competitive market, advertisers are more willing to purchase the guaranteed contracts and thus higher prices are expected. The revenue gain is largely contributed by the guaranteed selling.