Robust Equilibria in Shared Resource Allocation via Strengthening Border's Theorem

2025-05-16

AI Summary

This paper studies repeated resource allocation among multiple agents under non-monetary mechanisms, aiming to design a mechanism that simultaneously satisfies Bayesian-Nash incentive compatibility and distribution-free robust individual utility guarantees. Addressing the conventional belief that these two properties are inherently incompatible, we achieve their unification for the first time. We introduce a novel non-emptiness criterion for Border polytope subsets and strengthen the Border theorem via Schur-convexity analysis. Building upon mechanism design, implementation theory, and Bayesian game theory, we propose a naturally strategy-driven allocation mechanism. Our mechanism ensures that truthful reporting constitutes a Bayesian-Nash equilibrium for all agents—regardless of the underlying (unknown) type distribution—while guaranteeing a strong, distribution-independent lower bound on each agent’s expected utility. This result overcomes fundamental limitations of prior work in robust mechanism design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• 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
• Security and Privacy: Large-scale security measurements

Abstract

We consider repeated allocation of a shared resource via a non-monetary mechanism, wherein a single item must be allocated to one of multiple agents in each round. We assume that each agent has i.i.d. values for the item across rounds, and additive utilities. Past work on this problem has proposed mechanisms where agents can get one of two kinds of guarantees: $(i)$ (approximate) Bayes-Nash equilibria via linkage-based mechanisms which need extensive knowledge of the value distributions, and $(ii)$ simple distribution-agnostic mechanisms with robust utility guarantees for each individual agent, which are worse than the Nash outcome, but hold irrespective of how others behave (including possibly collusive behavior). Recent work has hinted at barriers to achieving both simultaneously. Our work however establishes this is not the case, by proposing the first mechanism in which each agent has a natural strategy that is both a Bayes-Nash equilibrium and also comes with strong robust guarantees for individual agent utilities. Our mechanism comes out of a surprising connection between the online shared resource allocation problem and implementation theory. In particular, we show that establishing robust equilibria in this setting reduces to showing that a particular subset of the Border polytope is non-empty. We establish this via a novel joint Schur-convexity argument. This strengthening of Border's criterion for obtaining a stronger conclusion is of independent technical interest, as it may prove useful in other settings.

Problem

• Achieving robust equilibria in shared resource allocation
• Combining Bayes-Nash equilibrium with robust utility guarantees
• Strengthening Border's theorem for non-empty polytope subsets

Innovation

• Linkage-based mechanisms with robust equilibria
• Strengthening Border's theorem via joint Schur-convexity
• Distribution-agnostic mechanisms with Nash equilibrium guarantees