We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.

我们研究了离散时间的讨价还价模型，其中包括有限数量的参与者、提议参与者的随机选择、响应者的内生确定集合和顺序以及一组有限的可行替代方案。在无成本延迟的情况下，标准最优条件和递归方程系统可能不足以在平稳策略 (SSPE) 中存在子博弈完美均衡。我们提出了 SSPE 的特征，它对有成本和无成本的延迟都有效。我们解决了无成本延迟下的 SSPE 与成本延迟消失时 SSPE 的限制之间的关系。当延迟代价高昂时，SSPE 总是存在，但在无代价延迟下不一定如此，即使允许混合策略。作为准 SSPE，这令人惊讶，最优条件和递归方程组的解总是存在的。这个问题是由递归方程组的潜在奇异性引起的，这与谈判过程中永久分歧的可能性密切相关。