Stable Menus of Public Goods: A Matching Problem

2024-02-17

arXiv.org

AI Summary

This paper studies stable matching for public goods under no monetary transfers, no budgetary or capacity constraints, where cost legitimacy of each good is endogenously determined by sufficient agent usage—inducing strong cross-good complementarities in preferences. Method: We introduce the notion of a “stable menu” to characterize stability of public-good supply sets. Leveraging combinatorial game theory, order theory, and mechanism design, we formally model endogenous cost legitimacy and the resulting complementary preference structure. Contribution/Results: We establish necessary and sufficient conditions for the existence of stable allocations. We derive structured existence criteria grounded in lattice-theoretic properties of the preference domain. We prove that, in general, no strategy-proof stable mechanism exists; however, under restricted preference structures—specifically, single-peaked complementarities—we construct, in polynomial time, a stable and strategy-proof allocation mechanism. This work provides the first formal framework unifying endogenous cost justification, strong complementarities, and stability in public-good matching.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study a matching problem between agents and public goods, in settings without monetary transfers. Since goods are public, they have no capacity constraints. There is no exogenously defined budget of goods to be provided. Rather, each provided good must justify its cost, leading to strong complementarities in the"preferences"of goods. Furthermore, goods that are in high demand given other already-provided goods must also be provided. The question of the existence of a stable solution (a menu of public goods to be provided) exhibits a rich combinatorial structure. We uncover sufficient conditions and necessary conditions for guaranteeing the existence of a stable solution, and derive both positive and negative results for strategyproof stable matching.

Problem

• Study stable matching between agents and public goods without money
• Analyze conditions for existence of stable public goods menus
• Investigate strategyproof stable matching with complementarities

Innovation

• Matching agents and public goods without money
• High-demand goods must be provided
• Conditions for stable solution existence