Achieving Irrational Correlated Equilibria without Mediator

This paper investigates the implementation and performance of a decentralized information transmission mechanism in game with complete or incomplete games. We propose a mechanism that realizes irrational correlated equilibria or irrational communication equilibria through a finite rounds of cheap talk without mediator. Designed for games with at least five players, the core procedure involves three players decomposing and encrypting the equilibrium, while two other players securely randomize and deliver the encrypted recommended strategies to designated players. Our results demonstrate that all irrational correlated equilibria or irrational communication equilibria can be achieved through this mechanism, which is both strategically robust and practically implementable.