Computing Quantal Response Equilibrium for Sponsored Search Auctions

Sponsored search auctions (SSAs) have attracted much research attention in recent years and different equilibrium concepts have been studied to understand advertisers’ behaviors. However, the assumption that bidders are perfectly rational in these studies is unrealistic in the real world. In this work, we investigate the quantal response equilibrium (QRE) for SSAs. QRE is powerful in characterizing the bounded rationality in the sense that it only assumes that an advertiser chooses a better strategy with a larger probability instead of choosing the best strategy deterministically. We propose a homotopy-based method to compute the QRE of SSAs. We further show that there are many nice properties of the SSAs compared with general normal formal games, which can be used to improve the computational performance. Our experimental results indicate that our algorithm outperforms the basic traversal method.