X Quantal Response Equilibrium for Sponsored Search Auctions: Computation and Inference

Sponsored search auctions have attracted much research attention in recent years and different equilibrium concepts have been studied to understand advertisers’ bidding strategies. 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) solution concept for sponsored search auctions, in which advertisers choose strategies based on their relative expected utilities. 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 assuming that the advertiser chooses the best strategy deterministically. We first propose a homotopy-based method, which is potential to be globally convergent, to compute QRE for sponsored search auctions. We show that this method is effective in finding a QRE. Then we fit the model into the datasets from a commercial search engine and develop an estimator to infer the values of advertisers and click-through rates of their advertisements. Our experiments on several search phrases indicate that the model works quite well for certain queries and the values we estimated are consistent with the basic property of sponsored search auctions.