In verifiable secret sharing (VSS), a dealer shares a secret input among several parties, ensuring each share is verifiable. Motivated by its applications in the blockchain space, we focus on a VSS where parties holding shares are not allowed to reconstruct the dealer’s secret (even partially) on their own terms, which we address as privacy-targeted collusion if attempted. In this context, our work investigates mechanisms deterring such collusion in VSS among rational and malicious parties. For this problem, we make both algorithmic and combinatorial contributions: We believe these connections between cryptography, game theory, and discrete mathematics will be of broader interest.