  I study a repeated game in which a patient player (e.g., a seller) wants to
win the trust of some myopic opponents (e.g., buyers) but can strictly benefit
from betraying them. Her benefit from betrayal is strictly positive and is her
persistent private information. I characterize every type of patient player's
highest equilibrium payoff. Her persistent private information affects this
payoff only through the lowest benefit in the support of her opponents' prior
belief. I also show that in every equilibrium which is optimal for the patient
player, her on-path behavior is nonstationary, and her long-run action
frequencies are pinned down for all except two types. Conceptually, my
payoff-type approach incorporates a realistic concern that no type of
reputation-building player is immune to reneging temptations. Compared to
commitment-type models, the incentive constraints for all types of patient
player lead to a sharp characterization of her highest attainable payoff and
novel predictions on her behaviors.
