Safe implementation in mixed Nash equilibrium

• Authors: Anand Chopra, Malachy James Gavan and Antonio Penta
• Journal of Mathematical Economics, Vol. 122, Article 103196, February 2026.

Safe Implementation (Gavan and Penta, 2025) combines standard implementation with the requirement that the implementing mechanism is such that, if up to agents deviate from the relevant solution concept, the outcomes that are induced are still ‘acceptable’ at every state of the world. In this paper, we study Safe Implementation of social choice correspondences in mixed Nash equilibrium. We identify a condition, Set-Comonotonicity, which is both necessary and (under mild domain restrictions) almost sufficient for this implementation notion.