It seems to me that it is much more symmetric. In both situations one side guess, due to fundamental uncertainties of human interactions -- each side knows their subjective costs/benefits, but not costs/benefits of the other side.

For 'guesser protocol', the initiatior guess whether the ask is appropriate (say initiator_known _benefit > responder_guessed_cost), while in 'asker protocol', the task of guessing is shifted to responder, as the responder has to guess whether the reject is appropriate (say responder_known_cost > initiator_guessed_benefit).