Optimal equilibrium bidding strategies for budget constrained bidders in sponsored search auctions

Budget optimization (selecting an optimal set of keywords to bid for, given a limited amount of budget) and bid optimization (determining optimal bids for the selected keywords) in the face of an unpredictable keyword traffic is a challenging problem facing advertisers in sponsored search auctions. Another key requirement in sponsored search auctions is stability of the bid profile, which is usually characterized through the notion of locally envy‐free equilibrium. A variety of budget optimization and bid optimization ideas have been proposed in the literature; the bid profiles suggested by them have varying stability properties. In this paper, our objective is to come up with a bidding strategy for advertisers that is optimal for the budget optimization as well as the bid optimization problems and also guarantees convergence to a locally envy‐free equilibrium. Our approach works with a linear program for the budget optimization problem whose optimal solution is a greedy strategy, which we call the OPT strategy. The OPT strategy yields a bid profile that maximizes the return on investment for the advertisers and ensures convergence of the bid profiles to a locally envy‐free equilibrium in the asynchronous case as well as in a restricted synchronous case. We also suggest an improved strategy called the MAX strategy which produces equal or higher advertiser utilities compared to the OPT strategy while enjoying identical equilibrium convergence properties as OPT.