This paper studies reputation effects in a dynamic simultaneous-offer bilateral bargaining game in which one player might have some kind of irrational commitment that compels him to insist on some particular bargaining allocation. It is shown that if this player insists on this allocation, then the bargaining game will end within the first few rounds and he can get an expected payoff close to that allocation. More importantly, the upper bound within which the bargaining game ends does not depend on the relative strength of the two players.