A minority-proof cheap-talk protocol

This paper analyzes the implementation of correlated equilibria that are immune to joint deviations of coalitions by cheap-talk protocols. We construct a universal cheap-talk protocol (a polite protocol that uses only 2-player private channels) that is resistant to deviations of fewer than half the players, and using it, we show that a large set of correlated equilibria can be implemented as Nash equilibria in the extended game with cheap-talk. Furthermore, we demonstrate that in general there is no cheap-talk protocol that is resistant for deviations of half the players.