Procurement Auctions via Approximate Submodular Optimization
Abstract
We study the problem of procurement auctions, in which an auctioneer seeks to acquire services from a group of strategic sellers with private costs. The quality of the services is measured through some \emph{submodular} function that is known to the auctioneer. Our goal is to design \emph{computationally efficient} procurement auctions that (approximately) maximize the difference between the quality of the acquired services and the total cost of the sellers, in a way that is incentive compatible (IC) and individual rational (IR) for the sellers, and generates non-negative surplus (NAS) for the auctioneer.
Leveraging recent results from the literature of \emph{non-positive} submodular function maximization, we design computationally efficient frameworks that transform submodular function optimization algorithms to \emph{mechanisms} that are IC and IR for the sellers, NAS for the auctioneer, and \emph{approximation-preserving}. Our frameworks are general and work both in the \emph{offline} setting where the auctioneer can observe the bids and the services of all the sellers simultaneously, and in the \emph{online} setting where the sellers arrive in an adversarial order and the auctioneer has to make an irrevocable decision whether to purchase their service or not. We further investigate whether it is possible to convert state-of-art submodular optimization algorithms into a descending auction. We focurs in the adversarial setting, meaning that the schedule of the descending prices is determined by an advesary. We show that a submodular optimization algorithm satisfying bi-criteria $(\alpha, 1)$-approximation in welfare can be effectively converted to a descending auction in the adversarial setting in if and only if $\alpha \leq \frac 1 2$. Our result highlights the importance of a carefully designed schedule of descending prices to effectively convert a submodular optimization algorithm satisfying bi-criteria $(\alpha, 1)$-approximation in welfare with $\alpha > \frac 1 2$ to a descending auction. We also further establish a connection between descending auctions and online submodular optimization algorithms.
We demonstrate the practical applications of our frameworks by instantiating them with different state-of-the-art submodular optimization algorithms and comparing their welfare performance through empirical experiments on publicly available datasets that consist of thousands of sellers.
Leveraging recent results from the literature of \emph{non-positive} submodular function maximization, we design computationally efficient frameworks that transform submodular function optimization algorithms to \emph{mechanisms} that are IC and IR for the sellers, NAS for the auctioneer, and \emph{approximation-preserving}. Our frameworks are general and work both in the \emph{offline} setting where the auctioneer can observe the bids and the services of all the sellers simultaneously, and in the \emph{online} setting where the sellers arrive in an adversarial order and the auctioneer has to make an irrevocable decision whether to purchase their service or not. We further investigate whether it is possible to convert state-of-art submodular optimization algorithms into a descending auction. We focurs in the adversarial setting, meaning that the schedule of the descending prices is determined by an advesary. We show that a submodular optimization algorithm satisfying bi-criteria $(\alpha, 1)$-approximation in welfare can be effectively converted to a descending auction in the adversarial setting in if and only if $\alpha \leq \frac 1 2$. Our result highlights the importance of a carefully designed schedule of descending prices to effectively convert a submodular optimization algorithm satisfying bi-criteria $(\alpha, 1)$-approximation in welfare with $\alpha > \frac 1 2$ to a descending auction. We also further establish a connection between descending auctions and online submodular optimization algorithms.
We demonstrate the practical applications of our frameworks by instantiating them with different state-of-the-art submodular optimization algorithms and comparing their welfare performance through empirical experiments on publicly available datasets that consist of thousands of sellers.
