This paper concerns the mechanism design for online resource allocation in a strategic setting. In this setting, a single supplier allocates capacity-limited resources to requests that arrive in a sequential and arbitrary manner. Each request is associated with an agent who may act selfishly to misreport the requirement and valuation of her request. The supplier charges payment from agents whose requests are satisfied, but incurs a load-dependent supply cost. The goal is to design an incentive compatible online mechanism, which determines not only the resource allocation of each request, but also the payment of each agent, so as to (approximately) maximize the social welfare (i.e., aggregate valuations minus supply cost). We study this problem under the framework of competitive analysis. The major contribution of this paper is the development of a unified approach that achieves the best-possible competitive ratios for setups with different supply costs. Specifically, we show that when there is no supply cost or the supply cost function is linear, our model is essentially a standard 0-1 knapsack problem, for which our approach achieves logarithmic competitive ratios that match the state-of-the-art (which is optimal). For the more challenging setup when the supply cost is strictly-convex, we provide online mechanisms, for the first time, that lead to the optimal competitive ratios as well. To the best of our knowledge, this is the first approach that unifies the characterization of optimal competitive ratios in online resource allocation for different setups including zero, linear and strictly-convex supply costs.

翻译：本文研究战略环境下在线资源分配的机制设计问题。在该环境中，单一供应商将容量有限的资源分配给以顺序且任意方式到达的请求。每个请求关联一个可能出于自私动机而虚报其请求需求和估值的智能体。供应商向请求被满足的智能体收取费用，但需承担负载相关的供应成本。目标在于设计激励相容的在线机制，该机制不仅决定每个请求的资源分配，还确定每个智能体的支付，以（近似）最大化社会福利（即总估值减去供应成本）。我们采用竞争分析框架研究该问题。本文的主要贡献在于开发了一种统一方法，针对不同供应成本设置实现了最优竞争比。具体而言，我们证明：当无供应成本或供应成本函数为线性时，该模型本质上属于标准0-1背包问题，我们的方法实现了与现有最优方法匹配的对数级竞争比；对于供应成本为严格凸函数这一更具挑战性的场景，我们首次提供了能获得最优竞争比的在线机制。据我们所知，这是首个统一刻画零成本、线性成本及严格凸成本等不同设置下在线资源分配最优竞争比的方法。