# Regularized Proportional Fairness Mechanism for Resource Allocation Without Money

arXiv: https://arxiv.org/abs/2501.01111 · HTML: https://mlsanity.com/paper/2501.01111/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 2 Jan 2025.

## Builds on (most cited first, 12 of 12)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Optimal Auctions through Deep Learning: Advances in Differentiable Economics](https://mlsanity.com/paper/1706.03459/) (2017)
- [Optimal-er Auctions through Attention](https://mlsanity.com/paper/2202.13110/) (2022)
- [Deep Learning for Two-Sided Matching](https://mlsanity.com/paper/2107.03427/) (2021)
- [Learning Revenue-Maximizing Auctions With Differentiable Matching](https://mlsanity.com/paper/2106.07877/) (2021)
- [Duality and Optimality of Auctions for Uniform Distributions](https://mlsanity.com/paper/1404.2329/) (2014)
- [Nash Social Welfare Approximation for Strategic Agents](https://mlsanity.com/paper/1607.01569/) (2016)
- [An n-to-1 Bidder Reduction for Multi-item Auctions and its Applications](https://mlsanity.com/paper/1406.3278/) (2014)
- [Exploitability Minimization in Games and Beyond](https://mlsanity.com/paper/2210.10207/) (2022)
- [Learning Payment-Free Resource Allocation Mechanisms](https://mlsanity.com/paper/2311.10927/) (2023)
- [Mechanism Design without Money for Fair Allocations](https://mlsanity.com/paper/2112.07255/) (2021)

## Abstract (arXiv)

Mechanism design in resource allocation studies dividing limited resources among self-interested agents whose satisfaction with the allocation depends on privately held utilities. We consider the problem in a payment-free setting, with the aim of maximizing social welfare while enforcing incentive compatibility (IC), i.e., agents cannot inflate allocations by misreporting their utilities. The well-known proportional fairness (PF) mechanism achieves the maximum possible social welfare but incurs an undesirably high exploitability (the maximum unilateral inflation in utility from misreport and a measure of deviation from IC). In fact, it is known that no mechanism can achieve the maximum social welfare and exact incentive compatibility (IC) simultaneously without the use of monetary incentives (Cole et al., 2013). Motivated by this fact, we propose learning an approximate mechanism that desirably trades off the competing objectives. Our main contribution is to design an innovative neural network architecture tailored to the resource allocation problem, which we name Regularized Proportional Fairness Network (RPF-Net). RPF-Net regularizes the output of the PF mechanism by a learned function approximator of the most exploitable allocation, with the aim of reducing the incentive for any agent to misreport. We derive generalization bounds that guarantee the mechanism performance when trained under finite and out-of-distribution samples and experimentally demonstrate the merits of the proposed mechanism compared to the state-of-the-art.