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

TL;DR

This paper introduces a dynamic programming approach for optimal bidding in sequential auctions that leverages quasi-linear utility to improve computational efficiency and includes a method for semi-optimal bidding under budget constraints.

Contribution

It presents a novel problem formalization using quasi-linear utility to reduce computation time and a new method for semi-optimal bidding with budget constraints.

Findings

Over an m-fold speed-up in computation time achieved.

Effective semi-optimal bidding strategy under budget constraints developed.

Experimental results confirm the efficiency and efficacy of the proposed methods.

Abstract

In this paper, we develop a new method for finding an optimal biddingstrategy in sequential auctions, using a dynamic programming technique. Theexisting method assumes that the utility of a user is represented in anadditive form. Thus, the remaining endowment of money must be explicitlyrepresented in each state, and the calculation of the optimal biddingstrategy becomes time-consuming when the initial endowment of money mbecomes large.In this paper, we develop a new problem formalization that avoids explicitlyrepresenting the remaining endowment, by assuming the utility of a user canbe represented in a quasi-linear form, and representing the payment as astate-transition cost. Experimental evaluations show that we can obtainmore than an m-fold speed-up in the computation time. Furthermore, we havedeveloped a method for obtaining a semi-optimal bidding strategy underbudget constraints, and have experimentally confirmed the efficacy of thismethod.