We study how an advertiser changes his/her bid prices in sponsored search, by modeling his/her rationality. Predicting the bid changes of advertisers with respect to their campaign performances is a key capability of search engines, since it can be used to improve the offline evaluation of new advertising technologies and the forecast of future revenue of the search engine. Previous work on advertiser behavior modeling heavily relies on the assumption of perfect advertiser rationality; however, in most cases, this assumption does not hold in practice. Advertisers may be unwilling, incapable, and/or constrained to achieve their best response. In this paper, we explicitly model these limitations in the rationality of advertisers, and build a probabilistic advertiser behavior model from the perspective of a search engine. We then use the expected payoff to define the objective function for an advertiser to optimize given his/her limited rationality. By solving the optimization problem with Monte Carlo, we get a prediction of mixed bid strategy for each advertiser in the next period of time. We examine the effectiveness of our model both directly using real historical bids and indirectly using revenue prediction and click number prediction. Our experimental results based on the sponsored search logs from a commercial search engine show that the proposed model can provide a more accurate prediction of advertiser bid behaviors than several baseline methods.