Online Combinatorial Allocation with Interdependent Values

2025-07-31

AI Summary

This paper studies the online combinatorial allocation problem under interdependent values: agents’ valuations for item bundles depend on all participants’ private signals, and agents arrive in a random order (the secretary model). We introduce the first extension of interdependent value models to combinatorial secretary settings, proposing a $2e$-approximate online algorithm for submodular and XOS valuation functions. Furthermore, we design a truthful $4e$-competitive mechanism for online bipartite matching. Our approach integrates techniques from online algorithm design, stochastic arrival modeling, mechanism design, and complementary slackness analysis to jointly address the dual challenges of signal interdependence and combinatorial structure. Remarkably, our mechanisms achieve theoretical performance guarantees comparable to those attainable in the independent-value setting—thereby advancing the online and combinatorial frontiers of interdependent value mechanism design.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study online combinatorial allocation problems in the secretary setting, under interdependent values. In the interdependent model, introduced by Milgrom and Weber (1982), each agent possesses a private signal that captures her information about an item for sale, and the value of every agent depends on the signals held by all agents. Mauras, Mohan, and Reiffenhäuser (2024) were the first to study interdependent values in online settings, providing constant-approximation guarantees for secretary settings, where agents arrive online along with their signals and values, and the goal is to select the agent with the highest value. In this work, we extend this framework to {em combinatorial} secretary problems, where agents have interdependent valuations over {em bundles} of items, introducing additional challenges due to both combinatorial structure and interdependence. We provide $2e$-competitive algorithms for a broad class of valuation functions, including submodular and XOS functions, matching the approximation guarantees in the single-choice secretary setting. Furthermore, our results cover the same range of valuation classes for which constant-factor algorithms exist in classical (non-interdependent) secretary settings, while incurring only an additional factor of $2$ due to interdependence. Finally, we extend our study to strategic settings, and provide a $4e$-competitive truthful mechanism for online bipartite matching with interdependent valuations, again meeting the frontier of what is known, even without interdependence.

Problem

• Extend interdependent values to combinatorial secretary problems
• Provide competitive algorithms for submodular and XOS valuations
• Develop truthful mechanisms for interdependent bipartite matching

Innovation

• Extends combinatorial secretary problems with interdependent valuations
• Provides 2e-competitive algorithms for submodular and XOS functions
• Offers 4e-competitive truthful mechanism for bipartite matching