Reputational Cheap-Talk with Limited Records

I study a dynamic cheap-talk game between a long-lived sender and a sequence of short-lived receivers who observe a limited record of the sender’s history of honesty. In the presence of a commitment type, I show that if the prior on this type is zero, the unique equilibrium is babbling. For a positive prior, any equilibrium featuring information transmission follows cyclical dynamics: the rate of honesty increases until the history includes only honest communication, at which point the sender will abuse trust with certainty. I demonstrate that limited records can facilitate more information transmission than full records, which often lead to the permanent cessation of communication. Finally, I consider an extension where receivers observe a binary signal indicating a perfect record over $N$ periods. I show that this structure provides the "best of both worlds," ensuring that some information transmission always persists in equilibrium.