第二价格广告拍卖中的收益最大化问题
On Revenue Maximization in Second-Price Ad Auctions
摘要：
最近的论文解决的算法问题，分配广告空间的关键字在赞助搜索拍卖假设定价是通过一个第一价格拍卖，这并不现实的模型，在实践中使用的广义第二价格（GSP）拍卖。为了更真实地模拟这些拍卖的目标，我们引入了第二价格广告拍卖问题，其中投标人的付款由GSP机制决定。我们表明，第二价格的广告拍卖问题的复杂性是完全不同的，比更多的研究第一价格的广告拍卖问题。首先，与第一价格变体不同，对于第一价格变体，已知小的恒定因子近似，将第二价格广告拍卖问题近似为任何非平凡因子是NP难的。其次，这种差异甚至延伸到0-1的特殊情况，我们称之为第二价格匹配问题（2PM）。特别地，离线2PM是APX困难的，并且对于在线2PM，不存在实现非平凡竞争比的确定性算法，也不存在实现优于2的竞争比的随机算法。这与第一价格模型中的类似特殊情况的结果形成对比，标准二分匹配问题，其在多项式时间内可解，并且具有确定性和随机在线算法，从而实现更好的竞争比。在积极的一面，我们提供了一个2-近似离线2PM和5.083竞争随机算法在线2PM。后者的结果利用一个新的推广的经典结果的性能的“排名”算法在线二分匹配。
英文摘要：
Most recent papers addressing the algorithmic problem of allocating advertisement space for keywords in sponsored search auctions assume that pricing is done via a first-price auction, which does not realistically model the Generalized Second Price (GSP) auction used in practice. Towards the goal of more realistically modeling these auctions, we introduce the Second-Price Ad Auctions problem, in which bidders' payments are determined by the GSP mechanism. We show that the complexity of the Second-Price Ad Auctions problem is quite different than that of the more studied First-Price Ad Auctions problem. First, unlike the first-price variant, for which small constant-factor approximations are known, it is NP-hard to approximate the Second-Price Ad Auctions problem to any non-trivial factor. Second, this discrepancy extends even to the 0-1 special case that we call the Second-Price Matching problem (2PM). In particular, offline 2PM is APX-hard, and for online 2PM there is no deterministic algorithm achieving a non-trivial competitive ratio and no randomized algorithm achieving a competitive ratio better than 2. This stands in contrast to the results for the analogous special case in the first-price model, the standard bipartite matching problem, which is solvable in polynomial time and which has deterministic and randomized online algorithms achieving better competitive ratios. On the positive side, we provide a 2-approximation for offline 2PM and a 5.083-competitive randomized algorithm for online 2PM. The latter result makes use of a new generalization of a classic result on the performance of the "Ranking" algorithm for online bipartite matching.
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