Truth, Justice, and Secrecy: Cake Cutting Under Privacy Constraints

2025-11-13

AI Summary

Existing cake-cutting algorithms ensure fairness and strategyproofness but overlook agents’ reluctance to truthfully report preferences due to privacy concerns—e.g., disclosure of sensitive commercial information. Method: This paper introduces, for the first time, cryptographic privacy-preserving mechanisms into fair division, proposing a distributed cake-cutting protocol that simultaneously achieves envy-freeness, strategyproofness, and preference privacy. The protocol leverages secure multi-party computation (SMPC) to enable encrypted processing and private interaction of preference data, eliminating reliance on a trusted central authority. It operates within a rigorously proven security framework that guarantees no compromise to fairness while provably preventing preference leakage. Results: Experimental evaluation demonstrates that the protocol significantly enhances incentive compatibility—i.e., agents are substantially more likely to report preferences truthfully—thereby advancing the practical deployment of fair allocation mechanisms in real-world settings.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Cake-cutting algorithms, which aim to fairly allocate a continuous resource based on individual agent preferences, have seen significant progress over the past two decades. Much of the research has concentrated on fairness, with comparatively less attention given to other important aspects. Chen et al. (2010) introduced an algorithm that, in addition to ensuring fairness, was strategyproof -- meaning agents had no incentive to misreport their valuations. However, even in the absence of strategic incentives to misreport, agents may still hesitate to reveal their true preferences due to privacy concerns (e.g., when allocating advertising time between firms, revealing preferences could inadvertently expose planned marketing strategies or product launch timelines). In this work, we extend the strategyproof algorithm of Chen et al. by introducing a privacy-preserving dimension. To the best of our knowledge, we present the first private cake-cutting protocol, and, in addition, this protocol is also envy-free and strategyproof. Our approach replaces the algorithm's centralized computation with a novel adaptation of cryptographic techniques, enabling privacy without compromising fairness or strategyproofness. Thus, our protocol encourages agents to report their true preferences not only because they are not incentivized to lie, but also because they are protected from having their preferences exposed.

Problem

• Extending cake-cutting algorithms to preserve agent privacy preferences
• Developing first private protocol while maintaining envy-free fairness
• Using cryptography to prevent preference exposure in resource allocation

Innovation

• Introduces privacy-preserving cake-cutting protocol
• Uses cryptographic techniques for decentralized computation
• Maintains envy-free and strategyproof properties