Auction Mechanisms for Efficient Single-Type Divisible Resource Allocation

Abstract

We study how to efficiently allocate the infinitesimal divisible resource under auction mechanism. In this chapter, we mainly focus on allocating a fixed amount of a single-type resource. A VCG-type auction mechanism is proposed with a two-dimensional bid, which specifies a per unit price and a maximum of the demand. Due to the absence of enough information related to the infinite-dimensional valuations of individual players in a single-bid strategy, it is challenging to implement the efficient Nash equilibrium (NE) in a dynamic way. In this chapter, we introduce a pair of parameters related to players’ valuations, and design a decentralized dynamic process assisted with this pair of values, such that at each iteration, a single player updates its best bid under a constrained set of demand. Under the proposed auction mechanism, we show the incentive compatibility, efficiency, and uniqueness of the NE. Furthermore, our method is guaranteed to converge to the efficient NE, and it presents the enhanced convergence performance compared with those methods proposed in the literature. Case studies are given to demonstrate the results developed in this work.