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

TL;DR

The paper tackles private cake-cutting by extending the strategyproof, envy-free CC_puv algorithm to a privacy-preserving setting. It introduces PP_CC_puv, which secures agents' valuations via Shamir secret sharing and secure multiparty computation, replacing the original dynamic graph with a fixed graph to prevent information leakage while preserving fairness, strategyproofness, and efficiency. The protocol discretizes valuations, partitions the cake into intervals, and performs an oblivious, iterated max-flow allocation, with final allocations revealed under restricted or full visibility. This work delivers perfect privacy under honest-majority assumptions and enables coordinator-free, ad-hoc deployment, offering a foundation for privatizing a broader class of cake-cutting algorithms with practical communication costs on the order of $O(n^2)$.

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.

Figures (2)

• Figure 1: A piecewise uniform valuation with $\ell=2$ intervals.
• Figure 2: An example of a flow graph $G(S',X)$

Theorems & Definitions (5)

• Definition 3.1
• Theorem 5.1
• Theorem 5.2
• Theorem 5.3
• Lemma A.1