Anonymous Contracts

2026-02-12

AI Summary

This study addresses the challenge of designing multi-agent contracts that simultaneously ensure anonymity fairness, effectively incentivize effort, and maximize the principal’s payoff. The authors propose an anonymous contracting mechanism that relies solely on the total number of successes, focusing on uniform anonymous contracts that admit a unique equilibrium to guarantee robustness. Through game-theoretic and mechanism design analysis, they uncover a structural reversal in the approximation of social welfare under limited versus unlimited liability: under limited liability, the mechanism achieves a logarithmic-factor approximation, while under unlimited liability it attains an $O(\log n)$ approximation; notably, when agents exhibit heterogeneous success probabilities, the principal can fully extract social welfare. This work establishes the first theoretical bounds on the optimal approximation achievable by anonymous contracts.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Privacy

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We study a multi-agent contracting problem where agents exert costly effort to achieve individually observable binary outcomes. While the principal can theoretically extract the full social welfare using a discriminatory contract that tailors payments to individual costs, such contracts may be perceived as unfair. In this work, we introduce and analyze anonymous contracts, where payments depend solely on the total number of successes, ensuring identical treatment of agents. We first establish that every anonymous contract admits a pure Nash equilibrium. However, because general anonymous contracts can suffer from multiple equilibria with unbounded gaps in principal utility, we identify uniform anonymous contracts as a desirable subclass. We prove that uniform anonymous contracts guarantee a unique equilibrium, thereby providing robust performance guarantees. In terms of efficiency, we prove that under limited liability, anonymous contracts cannot generally approximate the social welfare better than a factor logarithmic in the spread of agent success probabilities. We show that uniform contracts are sufficient to match this theoretical limit. Finally, we demonstrate that removing limited liability significantly boosts performance: anonymous contracts generally achieve an $O(\log n)$ approximation to the social welfare and, surprisingly, can extract the full welfare whenever agents'success probabilities are distinct. This reveals a structural reversal: widely spread probabilities are the hardest case under limited liability, whereas identical probabilities become the hardest case when limited liability is removed.

Problem

• anonymous contracts
• multi-agent contracting
• fairness
• social welfare
• limited liability

Innovation

• anonymous contracts
• uniform contracts
• limited liability
• social welfare approximation
• multi-agent contracting