"Voluntarily Separable Prisoner's Dilemma with Reference Letters"

We consider voluntarily separable repeated Prisoner's Dilemma in which a pair of players meet randomly and repeatedly play Prisoner's Dilemma only by mutual agreement. Fujiwara-Greve and Okuno-Fujiwara (2007) consider the case that once a partnership is dissolved there is no information flow to other partnerships. We consider the case that players can issue a reference letter to the partner if they entered cooperation periods, but the content of a letter is not verifiable. We show that the sheer existence of a letter shortens the trust-building periods of new matches and thus improves efficiency in equilibrium.