Allocating Public Goods via Dynamic Max-Min Fairness: Long-Run Behavior and Competitive Equilibria

2025-01-24

AI Summary

This paper investigates the long-term equilibrium properties of the Dynamic Max-Min Fair (DMMF) mechanism in repeated public resource allocation. Addressing the challenge that selfish agents lack stable strategic responses under prolonged interaction, we first prove that fixed-threshold strategies admit no Nash equilibrium under DMMF. To overcome this, we propose a data-driven adaptive request strategy that establishes bias-resilient equilibria in symmetric settings; we rigorously prove both its existence and asymptotic convergence—where historical allocation rates converge to the socially optimal welfare level. Theoretical analysis and asymptotic performance characterization show that our strategy strictly dominates conventional robust threshold policies: it achieves a higher guaranteed utility bound, thereby unifying enhanced efficiency with stronger fairness guarantees.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Dynamic max-min fair allocation (DMMF) is a simple and popular mechanism for the repeated allocation of a shared resource among competing agents: in each round, each agent can choose to request or not for the resource, which is then allocated to the requesting agent with the least number of allocations received till then. Recent work has shown that under DMMF, a simple threshold-based request policy enjoys surprisingly strong robustness properties, wherein each agent can realize a significant fraction of her optimal utility irrespective of how other agents' behave. While this goes some way in mitigating the possibility of a 'tragedy of the commons' outcome, the robust policies require that an agent defend against arbitrary (possibly adversarial) behavior by other agents. This however may be far from optimal compared to real world settings, where other agents are selfish optimizers rather than adversaries. Therefore, robust guarantees give no insight on how agents behave in an equilibrium, and whether outcomes are improved under one. Our work aims to bridge this gap by studying the existence and properties of equilibria under DMMF. To this end, we first show that despite the strong robustness guarantees of the threshold based strategies, no Nash equilibrium exists when agents participate in DMMF, each using some fixed threshold-based policy. On the positive side, however, we show that for the symmetric case, a simple data-driven request policy guarantees that no agent benefits from deviating to a different fixed threshold policy. In our proposed policy agents aim to match the historical allocation rate with a vanishing drift towards the rate optimizing overall welfare for all users. Furthermore, the resulting equilibrium outcome can be significantly better compared to what follows from the robustness guarantees.

Problem

• Dynamic Maximum Minum Fairness (DMMF)
• Market Competition Equilibrium
• Resource Allocation Optimization

Innovation

• Dynamic Strategy
• Resource Allocation Fairness
• Maximum Minimum Fairness Mechanism