Fair Artificial Currency Incentives in Repeated Weighted Congestion Games: Equity vs. Equality

TL;DR

This paper explores how artificial currency incentives can promote fair resource sharing in repeated weighted congestion games, balancing equity and equality while ensuring system-optimal outcomes.

Contribution

It provides a rigorous mathematical framework for fairness metrics and develops optimal, weight-dependent pricing policies that guarantee convergence to system-optimal, fair resource allocations.

Findings

Achieving perfect equity is always possible at the system-optimal level.

Maximum equality may not always be achievable, depending on system parameters.

Numerical simulations confirm the effectiveness of proposed policies.

Abstract

When users access shared resources in a selfish manner, the resulting societal cost and perceived users' cost is often higher than what would result from a centrally coordinated optimal allocation. While several contributions in mechanism design manage to steer the aggregate users choices to the desired optimum by using monetary tolls, such approaches bear the inherent drawback of discriminating against users with a lower income. More recently, incentive schemes based on artificial currencies have been studied with the goal of achieving a system-optimal resource allocation that is also fair. In this resource-sharing context, this paper focuses on repeated weighted congestion game with two resources, where users contribute to the congestion to different extents that are captured by individual weights. First, we address the broad concept of fairness by providing a rigorous mathematical characterization of the distinct societal metrics of equity and equality, i.e., the concepts of providing equal outcomes and equal opportunities, respectively. Second, we devise weight-dependent and time-invariant optimal pricing policies to maximize equity and equality, and prove convergence of the aggregate user choices to the system-optimum. In our framework it is always possible to achieve system-optimal allocations with perfect equity, while the maximum equality that can be reached may not be perfect, which is also shown via numerical simulations.