中文摘要：

本文主要研究了带预算约束和质量分的关键词广告,在有质量分的情况下,给出了广告主预算的两个临界值,一个是无预算约束的对称纳什均衡报价向量可能成为有预算约束的对称纳什均衡预算的最小值,另一个是任一无预算约束的对称纳什均衡报价向量都是有预算约束的对称纳什均衡预算的最小值。而且广告主预算的两个临界值都与质量分无关。

英文摘要：

This paper mainly studies keyword auction with budget constraints and quality score. In the presence of quality score,we provide two budget minimum. One is under which a bidding vector of symmetric Nash equilibrium without budget constraints maybe is a symmetric Nash equilibrium with budget constraints,the other is under which any bidding vector of symmetric Nash equilibrium without budget constraints must be sustained as a symmetric Nash equilibrium with budget constraints. And the thresholds of budgets have nothing to do with the quality score.