A General Incentives-Based Framework for Fairness in Multi-agent Resource Allocation

TL;DR

GIFF presents a learning-free framework for fairness in multi-agent resource allocation by post-processing pre-trained Q-values with a local fairness gain and a counterfactual advantage correction. Operating in a centralized control setting, it proves that the fairness surrogate is a principled lower bound on true fairness improvements and provides monotonicity and slack guarantees, enabling safe deployment. Empirically, GIFF achieves superior fairness-utility trade-offs across ridesharing, homelessness prevention, and job allocation, generalizing to α-fairness and Generalized Gini metrics. The approach is simple to tune (β,δ) and provides auditable performance guarantees, making it practical for socially sensitive, dynamic environments.

Abstract

We introduce the General Incentives-based Framework for Fairness (GIFF), a novel approach for fair multi-agent resource allocation that infers fair decision-making from standard value functions. In resource-constrained settings, agents optimizing for efficiency often create inequitable outcomes. Our approach leverages the action-value (Q-)function to balance efficiency and fairness without requiring additional training. Specifically, our method computes a local fairness gain for each action and introduces a counterfactual advantage correction term to discourage over-allocation to already well-off agents. This approach is formalized within a centralized control setting, where an arbitrator uses the GIFF-modified Q-values to solve an allocation problem. Empirical evaluations across diverse domains, including dynamic ridesharing, homelessness prevention, and a complex job allocation task-demonstrate that our framework consistently outperforms strong baselines and can discover far-sighted, equitable policies. The framework's effectiveness is supported by a theoretical foundation; we prove its fairness surrogate is a principled lower bound on the true fairness improvement and that its trade-off parameter offers monotonic tuning. Our findings establish GIFF as a robust and principled framework for leveraging standard reinforcement learning components to achieve more equitable outcomes in complex multi-agent systems.

Figures (4)

• Figure 1: Comparison of fairness versus system utility. Each line is plotted in order of increasing fairness tradeoff weight $\beta$, starting from the red X ($\beta=0$) Top: Passenger fairness (measured as $-var(\mathbf{Z}_p)$) versus overall service rate. Bottom: Driver fairness (measured as $-var(\mathbf{Z}_d)$) versus overall service rate. The red X indicates the baseline performance (raw Q-values without fairness adjustments).
• Figure 2: Variance vs. Fairness Weight. Top row: GIFF results using $\log\left(1+\frac{\beta}{1-\beta}\right)$. Bottom row: SI results using $\log(1+\beta)$.
• Figure 3: Results for the homelessness dataset. Top: Comparison of the benefit of fairness (BoF) distribution as the price of fairness (PoF) threshold is increased. Bottom: The BoF gap compared to the best method, excluding BoF=0. Each vertical slice corresponds to the distribution over all 38 features.
• Figure 4: Fairness and utility for the Job Allocation environment as functions of $\beta$ and $\delta$.

Theorems & Definitions (14)

• Theorem 1: Local–Gain Lower Bound
• Theorem 2: Monotone Surrogate Fairness
• Corollary 1: Strict Increase at a Switch
• Theorem 3: Local–Gain Lower Bound
• Lemma 1: $\alpha$-fairness: exact additivity
• Lemma 2: Negative variance: nonnegative synergy
• Lemma 3: GGF: joint gain dominates locals
• Lemma 4: Maximin: joint never underestimates locals
• Theorem 4: Monotone increase of the sum of local fairness gains
• Corollary 2: Strict increase at a true switch under uniqueness