Dynamic programming model for determining bidding strategies in sequential auctions: quasi-linear utility and budget constraints

Authors:
Hiromitsu Hattori;Makoto Yokoo;Yuko Sakurai;Toramatsu Shintani
Affiliations:
Nagoya Institute of Technology, Nagoya, Japan;NTT Communication Science Laboratories, Kyoto, Japan;NTT Communication Science Laboratories, Kyoto, Japan;Nagoya Institute of Technology, Nagoya, Japan
Venue:
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Year:
2001

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Abstract

In this paper, we develop a new method for finding 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 m becomes large. More specifically, 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 m-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 confirmed the efficacy of this method.