Strict Fairness at What Cost? Envy-Free Contracts with Subsidies

Abstract

We study algorithmic fair contract design, where a principal designs task-level contracts and fairly delegates a set of tasks to a set of agents. Prior work reveals a fairness-revenue dilemma: exact envy-free (EF) contracts may have an unbounded price of fairness (PoF), while approximate notions avoid this unboundedness only by weakening strict fairness. To address this dilemma, we propose a novel scheme, called {\it Envy-free Contracts with Subsidies} (EFS), in which the principal may additionally offer agent-specific subsidies to restore strict fairness. Our main technical result is a tight characterization of the price of fairness for EFS contracts. In sharp contrast to EF contracts, whose PoF can be unbounded, we show that the PoF of EFS contracts is $n^{n+O(1)}$, where $n$ is the number of agents. Moreover, EFS contracts can outperform EF contracts by an arbitrarily large factor in terms of the principal's revenue. Finally, we present the complexity landscape: computing optimal EFS contracts is NP-hard in general, whereas a polynomial-time algorithm exists when the number of tasks is constant.

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