Optimal Bidding Strategies in Dynamic Auctions with Budget Contstraints

We consider the problem of a bidder with limited budget competing in a series of second-price auctions. A motivating example is that of sponsored search auctions, where advertisers bid in a sequence of repeated generalized second price auctions. To characterize the optimal bidding strategy, we formulate the problem as a discounted Markov Decision Process, and provide explicit solutions when the bidder is involved in a large number of auctions.