Fair Games Against an All-Powerful Adversary

Pedro Branco, Pratik Soni, Sri Aravinda Krishnan Thyagarajan +1 more

Secure coin-tossing is typically modeled as an input-less functionality, where parties with no private inputs jointly generate a fair coin. In the dishonest majority setting, however, a strongly fair coin-tossing protocol is impossible. To circumvent this barrier, recent work has adopted the weaker notion of game-theoretic fairness, where adversaries are rational parties with preferences for specific outcomes, seeking to bias the coin in their favor. Yet these preferences may encode secret information, making prior protocols that assume preferences are public, fundamentally incompatible with privacy. We initiate a comprehensive study of privacy-preserving game-theoretically fair coin-tossing, where the preferences of honest parties remain private. We propose a simulation-based security framework and a new ideal functionality that reconciles both preference-privacy and game-theoretic fairness. A key ingredient is a certifying authority that authenticates each party’s preference and publishes only aggregate statistics, preventing misreporting while hiding parties' preferences. The functionality guarantees that every honest party receives an output: either a uniform coin; or, if an adversary deviates, a coin that does not increase the adversarial coalition's expected utility. Within this framework, we construct a protocol realizing our ideal functionality under standard cryptographic assumptions that works for both binary and general m -sided coin-tossing. Our binary scheme matches the corruption threshold of Wu-Asharov-Shi (EUROCRYPT '22); our multi-sided scheme builds on Thyagarajan-Wu-Soni (CRYPTO '24) with a corruption guarantee depending on the coalition's preference counts. Technically, our protocols combine authenticated preferences with an anonymous communication layer that decouples identities from preference-dependent actions, together with a deviation-penalty mechanism that enforces game-theoretic fairness. Our work is the first to reconcile game-theoretic fairness with preference privacy, offering new definitional tools and efficient protocols for rational multi-party computation in dishonest majority settings.

Rafail Ostrovsky, Ramarathnam Venkatesan, Moti M. Yung

Carmit Hazay, Yehuda Lindell

Ri‐Hua Zheng, Yang Xiao, Ye‐Hong Chen +2 more

We propose a framework for quantizing randomized quantum games in which entanglement is examined as a tunable fairness resource without relying on fine-tuned strategy parameters. As a case study of the Monty Hall problem, we show that initial entanglement between host and player registers neutralizes classical asymmetry at the distribution level, driving win-probability distributions under different strategic conditions to converge. Implemented on IBM’s Eagle processors via four-qubit encodings, our experiments span a continuum of entanglement strengths and employ extensive randomized trials over broad strategy ensembles. Although the mean no-switch probability remains fixed at its classical value, stronger entanglement progressively suppresses distributional signatures of asymmetric play, yielding increasingly uniform outcome statistics across adversarial conditions. Within the pure-state setting studied here, these findings provide evidence for an experimentally accessible route to quantify entanglement-enabled fairness in quantum games and suggest relevance to quantum information settings involving strategic decision-making under asymmetry.

Carmit Hazay, Yehuda Lindell

Zhonghong Sun

Reputation is commonly used in game theory for mutual cooperation. Assuming that parties value their reputation as well as their payoffs just like people in the real world, this paper considers reputation assumptions when defining the utilities. The new utility consists of two parts: the reputation part and payoff part. The parties are redefined according to the new utility definition. Besides, to represent a more realistic adversary model, a new adversary named semi-rational party is proposed. The semi-rational parties behave like the combination of rational and covert parties. At last, a rational two-party secure computation protocol is constructed. The proof of fairness in the presence of the semi-rational party is stressed in this paper.