We study two-person complete-information bargaining games in a noncooperative setting. The alternating-offers model studied by Rubinsten (1982) is modified so that, after each rejection of an offer, players have to decide on who to propose in the turn. Without an agreement, there is no proposal in the turn and the players try to choose a propose in the next turn. Under this rule, there are multiple equilibria and there can be a prolonged delay. We then show that two kinds of restrictions are needed to gain the unique equilibrium predicted by Rubinstein's original model. The first one is that the players have to propose alternately though the timing can be negotiated. The second one is that players cannot increase their demands over time. Though either of them cannot deter haggling by itself, they are strong enough to sop haggling and to derive the unique bargaining outcome if they are together imposed.
Running title: Less Structured Bargaining.