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Consider a retailer using sponsored search marketing together with dynamic pricing. The retailer's bid on a search keyword affects the retailer's rank among the search results. The higher the rank, the higher the customer traffic and the customers' willingness to pay will be. Thus, the question arises: When a retailer bids higher to attract more customers, should the accompanying price also decrease (to strengthen the bid's effect on demand) or increase (to take advantage of higher willingness to pay)? We find that the answer depends on how fast the retailer increases its bid. In particular, as the end of the season approaches, the optimal bid exhibits smooth increases followed by big jumps. The optimal price increases only when the optimal bid increases sharply, including the instances where the bid jumps up. Such big jumps arise, for example, when the customer traffic is an S-shaped function of the retailer's bid. This paper was accepted by Serguei Netessine, operations management.
Ye et al. (Thu,) studied this question.