Multi-Agent Non-Discriminatory Contracts

TL;DR

The paper addresses how to balance fairness in payments with the principal's utility in a multi-agent, hidden-action setting with a monotone submodular reward. It introduces the price of non-discrimination (PoND) and its relaxed variant PoND(\beta), establishing near-tight asymptotic bounds: PoND scales as $O(\log n)$ with the number of agents, while a lower bound of $\Omega(\dfrac{\log n}{\log\log n})$ shows this gap is inherent. By allowing $\beta$-non-discrimination with $\beta=n^\delta$, the authors derive constant-factor PoND(\beta) bounds across regimes of $\delta$, and provide a complete two-agent characterization $\mathsf{PoND}(\beta)=1+\dfrac{1}{\sqrt{\beta+1}}$. These results yield a practical framework for selecting discrimination levels in settings like standardized contracting and worker cooperatives, highlighting the trade-off between fairness and principal revenue and offering guidance for design under fairness constraints.

Abstract

We study multi-agent contracts, in which a principal delegates a task to multiple agents and incentivizes them to exert effort. Prior research has mostly focused on maximizing the principal's utility, often resulting in highly disparate payments among agents. Such disparities among agents may be undesirable in practice, for example, in standardized public contracting or worker cooperatives where fairness concerns are essential. Motivated by these considerations, our objective is to quantify the tradeoff between maximizing the principal's utility and equalizing payments among agents, which we call the price of non-discrimination. Our first result is an almost tight bound on the price of non-discrimination, which scales logarithmically with the number of agents. This bound can be improved to a constant by allowing some relaxation of the non-discrimination requirement. We then provide a comprehensive characterization of the tradeoff between the level of non-discrimination and the loss in the optimal utility.

Figures (2)

• Figure 1: Our partition of group $G_1,...,G_k$ in Lemma \ref{['nd_ub']}. Each group is double the size of the previous one, except for the last group. The optimal payment of group $k$ stands for the standardized payment when incentivizing that single group only.
• Figure 2: Illustration of our example in Lemma \ref{['bnd_epslb']}. The blue part ($A$) gets the same payment as in the optimal unconstrained contract, while agents in green part ($B$) receive a uniform payment, which equals the highest payment to agents in $A$ divided by ${n^\delta}$.

Theorems & Definitions (19)

• Definition 1
• Theorem 1
• Lemma 2
• proof
• Lemma 3
• proof
• Conjecture 4
• Remark 1
• Theorem 5
• Lemma 6