Voluntarily separable repeated Prisoner's Dilemma with reference letters

We consider the voluntarily separable repeated Prisoner's Dilemma model in which players randomly meet and form pairs to repeatedly play Prisoner's Dilemma only by mutual agreement. While the literature has dealt with the case of no information flow across partnerships, we consider the case in which players can issue a "reference letter" to verify at least that the partnership entered the cooperation phase. We show that such reference letters can be voluntarily provided by the partners even at some cost, and that the sheer existence of a letter shortens the trust-building periods and thus improves social efficiency.