We show that any correlated equilibrium payoff of two-player repeated games with imperfect monitoring and without discounting can be reached as the Nash equilibrium payoff of the game extended by a universal mechanism of unmediated communication. This result holds regardless the particular concept of equlibrium involved (upper, lower, Banach or uniform equlibrium). The communication mechanism is built up by using commutative one-way functions. These functions are designed with the help of cryptographic tools.
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