A Dynamic Programming Model for Determining Bidding Strategies in Sequential Auctions: Quasi-linear Utility and Budget Constraints

In this paper, we develop a new method for Þnding the optimal bidding strategy in sequential auctions, using a dynamic programming technique. The existing method assumes that the utility of a user is represented in an additive form. From this assumption, the remaining endowment of money must be explicitly represented in each state, and the calculation of the optimal bidding strategy becomes time-consuming when the initial endowment of money becomes large. More speciÞcally, we develop a new problem formalization whereby the utility of a user can be represented in a quasi-linear form. By assuming a quasi-linear utility, the payment can be represented as a state-transition cost. Accordingly, we can avoid explicitly representing the remaining endowment of money. Experimental evaluations show that we can obtain more than an fold speed-up in the computation time. Furthermore, we have developed a method for obtaining a semi-optimal bidding strategy under budget constraints, and have experimentally conÞrmed the efÞcacy of this method.