Paper 2025/1617

Game-Theoretically Fair Coin Toss with Arbitrary Preferences

Abstract

Fair multi-party coin toss protocols are fundamental to many cryptographic applications. While Cleve's celebrated result (STOC'86) showed that strong fairness is impossible against half-sized coalitions, recent works have explored a relaxed notion of fairness called Cooperative-Strategy-Proofness (CSP-fairness). CSP-fairness ensures that no coalition has an incentive to deviate from the protocol. Previous research has established the feasibility of CSP-fairness against majority-sized coalitions, but these results focused on specific preference structures where each player prefers exactly one outcome out of all possible choices. In contrast, real-world scenarios often involve players with more complicated preference structures, rather than simple binary choices. In this work, we initiate the study of CSP-fair multi-party coin toss protocols that accommodate arbitrary preference profiles, where each player may have an unstructured utility distribution over all possible outcomes. We demonstrate that CSP-fairness is attainable against majority-sized coalitions even under arbitrary preferences. In particular, we give the following results: \begin{itemize} \item We give a reduction from achieving CSP-fairness for arbitrary preference profiles to achieving CSP-fairness for structured split-bet profiles, where each player distributes the same amount of total utility across all outcomes. \item We present two CSP-fair protocols: (1) a \emph{size-based protocol}, which defends against majority-sized coalitions, and (2) a \emph{bets-based protocol}, which defends against coalitions controlling a majority of the total utilities. \item Additionally, we establish an impossibility result for CSP-fair binary coin toss with split-bet preferences, showing that our protocols are nearly optimal. \end{itemize}