预算约束下广义第二价格关键字拍卖均衡分析

在关键字拍卖中,广告主预算约束是影响投标策略均衡的重要因素。针对广泛应用的广义第二价格机制,分析了预算约束下的关键字拍卖均衡性质。按照广告主的点击估价和预算分布情况,将广告主划分为天然完全赢家、天然部分赢家和天然输家这三种类型,提出了广告主投标临界值与关键值的概念,基于关键字拍卖不断重复进行的特点,分别从长期视角与短期视角建立了静态模型与动态模型,研究结果表明:静态环境下拍卖存在唯一的纯策略纳什均衡;动态环境下当广告主采用最优反应投标策略时拍卖将收敛至唯一的纳什均衡点,并且动态环境下拍卖商收入不低于静态环境下的拍卖收入。数值算例的结果表明在动态环境下不同的初始报价会导致拍卖收敛至不同的均衡点。研究结果为拍卖商提供了拍卖收入预测和拍卖机制优化的决策依据。

Equilibrium Analysis of GSP Keyword Auctions with Budget Constraint

Advertiser's budget constraint is an important factor which affects the bidding strategy equilibrium in keyword auctions. This research analyzes the equilibrium of budgeted keyword auction with the widely used generalized second price mechanism. The advertisers are divided into three types “born full winner” “born partial winner” “born loser” in accordance with the distribution of their click values and budgets, and the concepts “critical bids” and “key bids” are developed. Based on the repeated characteristic of keyword auctions the static model and dynamic model are developed respectively from the long-term view and short-term view. Studies have shown that there is unique pure strategy Nash equilibrium in the static environment and the auction converges to unique Nash equilibrium point in the dynamic environment when the advertisers adopt the best-response strategy, and in the dynamic environment the auctioneer's revenue is higher than that in the static environment. The numerical examples show that in the dynamic environment the auction converges to deferent equilibrium point with different initial bidding vectors. The results provide the auctioneer with a basis for decision making for the revenue forecast and auction mechanism optimization.