Fair Resource Allocation for Demands with Sharp Lower Tail Inequalities

Abstract: We consider a fairness problem in resource allocation where multiple groups demand resources from a common source with the total fixed amount. The general model was introduced by Elzayn et al. [FAT*'19]. We follow Donahue and Kleinberg [FAT*'20] who considered the case when the demand distribution is known. We show that for many common demand distributions that satisfy sharp lower tail inequalities, a natural allocation that provides resources proportional to each group's average demand performs very well. More specifically, this natural allocation is approximately fair and efficient (i.e., it provides near maximum utilization). We also show that, when small amount of unfairness is allowed, the Price of Fairness (PoF), in this case, is close to 1.

• The paper proposes a proportional allocation strategy that fairly distributes resources based on mean demand in sharp lower tail scenarios.
• The paper analyzes fairness and efficiency trade-offs, demonstrating near-optimal resource utilization with minimal efficiency loss.
• The study quantifies the Price of Fairness, showing that a slight compromise in fairness keeps efficiency loss close to 1 in practical settings.

The paper "Fair Resource Allocation for Demands with Sharp Lower Tail Inequalities" addresses the challenge of fair resource distribution in situations where multiple groups request resources from a finite supply. This problem is tackled within the framework established by Elzayn et al. (FAT*'19) and further examined by Donahue and Kleinberg (FAT*'20), focusing on scenarios where the demand distribution is known.

Problem Context

In resource allocation problems, fairness and efficiency are often competing objectives. The authors investigate a specific scenario where demand distributions exhibit sharp lower tail inequalities. Sharp lower tail inequalities describe situations where the probability of demand falling below its mean is not just small but decreases sharply. This characteristic is crucial in ensuring that resources are not consistently under-allocated to certain groups due to unpredictable fluctuations in demand.

Main Contributions

1. Natural Allocation Scheme: The authors propose a natural allocation strategy based on proportional assignment. Resources are allocated in proportion to each group's mean demand. This method assumes prior knowledge of the demand distribution.
2. Fairness and Efficiency Analysis: The paper demonstrates that for common demand distributions possessing sharp lower tail inequalities, the proportional allocation strategy is nearly fair and efficient. Near maximum utilization implies that the overall allocation closely matches the total resource availability with minimal waste or shortfall.
3. Price of Fairness (PoF): The concept of PoF quantifies the cost of maintaining fairness in terms of efficiency. The authors show that by allowing a small degree of unfairness, the PoF remains close to 1. This result implies that the efficiency loss due to fairness considerations is minimal.

Implications and Practical Relevance

• Applicability: The findings suggest that in many practical scenarios with sharp lower tail demand distributions, a simple proportional allocation can achieve both fairness and high efficiency. This insight is valuable for designing resource allocation mechanisms in various domains like bandwidth distribution, budget allocations, and emergency resources management.
• Trade-Offs: Understanding the minimal efficiency loss associated with fair allocations can help policymakers and system designers make informed decisions about the extent to which fairness should be prioritized over efficiency.

Conclusion

The study contributes to the theoretical understanding of fair resource allocation under specific demand distribution conditions. It builds on previous work by demonstrating the practical effectiveness of a straightforward allocation method, providing a strong case for its adoption in real-world scenarios where demand distributions are sharp-tailed.

This research thus bridges an important gap between theoretical fairness models and their applicability in pragmatic settings, offering both a robust analytical framework and actionable insights for fair resource distribution.