Determining bidding strategies in sequential auctions: Quasi-linear utility and budget constraints

A great deal of research is actively being conducted concerning Internet auctions. A method has previously been proposed for obtaining the optimal bidding strategy by using dynamic programming in a sequential auction, which is one form of auction. However, the conventional method assumes that the utility of an agent who is bidding takes a general additive form, and the remaining endowment of money during bidding has to be represented in each of the various states that are taken into consideration in the dynamic programming procedure. As a result, when the initial endowment of money m is large, the number of states that have to be taken into consideration becomes extremely large. In this paper, by assuming that the utility of an agent takes a quasi-linear form, which is a type of additive form, the authors show that the optimal strategy using dynamic programming is obtained since the number of states is reduced to 1/m times the number obtained when the utility takes a general additive form. However, when the agent utility is assumed to take a quasi-linear form, it is impossible to represent budget constraints. Therefore, in this paper, the authors propose a method of quickly obtaining a quasi-optimal strategy when budget constraints exist by modifying the strategy that is obtained when quasi-linear utility is assumed and show the effectiveness of the proposed method through experimental evaluations.