Multidimensional Budget-Feasible Mechanism Design

2025-08-12

AI Summary

This paper studies multidimensional budget-feasible mechanism design, where multiple strategic agents each hold a subset of items and privately report their costs; the goal is to procure a high-value item set subject to a global budget constraint $B$. Prior work is restricted to single-dimensional settings and lacks benchmarks or approximation guarantees for the multidimensional case. Method: We introduce the first formal multidimensional model, observe that the standard optimal solution $ ext{OPT}$ becomes infeasible in this setting, and propose a new, tractable benchmark $ ext{OPT_Bench}$. Leveraging XOS valuation functions, we design a truthful and budget-feasible mechanism. Contribution/Results: We prove that $ ext{OPT_Bench}$ admits a constant-factor approximation, and our mechanism achieves the first constant approximation ratio for multidimensional budget-feasible procurement—establishing foundational theoretical guarantees for this previously unexplored direction.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

In budget-feasible mechanism design, a buyer wishes to procure a set of items of maximum value from self-interested players. We have a valuation function $v:2^U o mathbb{R}_+$, where $U$ is the set of all items, where $v(S)$ specifies the value obtained from set $S$ of items. The entirety of current work on budget-feasible mechanisms has focused on the single-dimensional setting, wherein each player holds a single item $e$ and incurs a private cost $c_e$ for supplying item $e$. We introduce multidimensional budget feasible mechanism design: the universe $U$ is now partitioned into item-sets ${G_i}$ held by the different players, and each player $i$ incurs a private cost $c_i(S_i)$ for supplying the set $S_isubseteq G_i$ of items. A budget-feasible mechanism is a mechanism that is truthful, and where the total payment made to the players is at most some given budget $B$. The goal is to devise a budget-feasible mechanism that procures a set of items of large value. We obtain the first approximation guarantees for multidimensional budget feasible mechanism design. Our contributions are threefold. First, we prove an impossibility result showing that the standard benchmark used in single-dimensional budget-feasible mechanism design, namely the algorithmic optimum is inadequate in that no budget-feasible mechanism can achieve good approximation relative to this. We identify that the chief underlying issue here is that there could be a monopolist which prevents a budget-feasible mechanism from obtaining good guarantees. Second, we devise an alternate benchmark, $OPT_{Bench}$, that allows for meaningful approximation guarantees, thereby yielding a metric for comparing mechanisms. Third, we devise budget-feasible mechanisms that achieve constant-factor approximation guarantees with respect to this benchmark for XOS valuations.

Problem

• Designing truthful mechanisms for multidimensional budget-feasible procurement
• Overcoming monopolist limitations in multidimensional mechanism design
• Achieving constant-factor approximation for XOS valuations with new benchmark

Innovation

• Multidimensional budget feasible mechanism design
• Alternate benchmark for approximation guarantees
• Constant-factor approximation for XOS valuations