Online Resource Allocation via Static Bundle Pricing

2025-12-18

AI Summary

This paper studies online resource allocation with complementary valuations: buyers arrive sequentially, each demanding a bundle of items, and their valuations are drawn from a known distribution. Standard item pricing fails to capture complementarities, while existing bundle-pricing mechanisms suffer from poor generalizability and reliance on restrictive structural assumptions. To address this, we propose the first unified static anonymous bundle-pricing framework, establishing the first general theoretical foundation applicable to diverse complementary settings—including combinatorial auctions and graph routing. Our competitive ratio improves exponentially with resource capacity and reveals a deep connection to qualitative independent partitioning in extremal combinatorics. For $d$-single-minded buyers, we achieve an $O(d^{1/B})$ competitive ratio; for general single-minded and graph-routing settings, we obtain $O(m^{1/(B+1)})$, where $B$ is the minimum bundle size and $m$ the number of resources. We further provide tight information-theoretic lower bounds, resolving a long-standing theoretical gap in this domain.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Combinatorial Optimization
• Machine Learning: Online Learning & Bandits

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Online Resource Allocation addresses the problem of efficiently allocating limited resources to buyers with incomplete knowledge of future requests. In our setting, buyers arrive sequentially demanding a set of items, each with a value drawn from a known distribution. We study environments where buyers' valuations exhibit complementarities. In such settings, standard item-pricing mechanisms fail to leverage item multiplicities, while existing static bundle-pricing mechanisms rely on problem-specific arguments that do not generalize. We develop a unified technique for online resource allocation with complementarities for three domains: (i) single-minded combinatorial auctions with maximum bundle size $d$, (ii) general single-minded combinatorial auctions, and (iii) a graph-based routing model in which buyers request to route a unit of flow from a source node $s$ to a target node $t$ in a capacitated graph. Our approach yields static and anonymous bundle-pricing mechanisms whose performance improves exponentially with item capacities. For the $d$-single-minded setting with minimum item capacity $B$, we obtain an $O(d^{1/B})$-competitive mechanism, recovering the known $O(d)$ bound for unit capacities ($B=1$) and achieving exponentially better guarantees as capacities grow. For general single-minded combinatorial auctions and the graph-routing model, we obtain $O(m^{1/(B+1)})$-competitive mechanisms, where $m$ is the number of items. We complement these results with information-theoretic lower bounds. We show that no online algorithm can achieve a competitive ratio better than $Ω((m/ln m)^{1/(B+2)})$ in the general single-minded setting and $Ω((d/ln d)^{1/(B+1)})$ in the $d$-single-minded setting. In doing so, we reveal a deep connection to the extremal combinatorics problem of determining the maximum number of qualitatively independent partitions of a ground set.

Problem

• Develop static bundle pricing for online resource allocation with complementarities.
• Address inefficiencies in item-pricing for sequential buyer arrivals with valuations.
• Provide competitive mechanisms for combinatorial auctions and graph-based routing models.

Innovation

• Static anonymous bundle pricing for complementarities
• Exponential performance improvement with item capacities
• Unified technique for three combinatorial auction domains