I consider a bargaining game in which only one player can make proposals and the space of proposals is finite. Thus, the game is like a situation where: (i) a CEO suggests a possible hire, who must be okayed by a board of directors, or (ii) the US president nominates a potential judge, who must be okayed by the Senate. My main result is an algorithm that finds the unique subgame-perfect equilibrium. The number of steps in the algorithm is on the order of $n$, the number of possibilities (e.g., applicants to a job) that the bargainers may consider. By contrast, if one uses backwards induction to solve the game, then the number of steps is on the order of $n!$. A corollary of the main result, similar to some results of previous bargaining models, is that the wait costs of only one player, the non-proposer, is relevant to the outcome. The wait costs of the proposer are irrelevant, provided that they are positive. Applied to the nomination process specified by the US Constitution, the corollary suggests that only the Senate's wait costs are relevant to the outcome—the president's wait costs are irrelevant. As I argue, this result may explain a little-noticed regularity of American politics. This is that the Senate seems to have much influence in the selection of lower-court judges but relatively little influence in the selection of Supreme Court justices.

中文翻译：

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对一组有限的替代方案进行单方面讨价还价

我考虑一个讨价还价游戏，其中只有一个玩家可以提出建议，并且建议的空间是有限的。因此，游戏就像这样一种情况：(i) CEO 建议一个可能的聘用人，他必须得到董事会的同意，或者 (ii) 美国总统提名一个潜在的法官，他必须得到参议院的同意。我的主要结果是一种找到独特的子博弈完美均衡的算法。算法中的步数为$n$，讨价还价者可能考虑的可能性（例如，求职者）的数量。相比之下，如果使用逆向归纳法来解决博弈，那么步数大约为$n！$. 主要结果的一个推论，类似于之前讨价还价模型的一些结果，是只有一个参与者（非提议者）的等待成本与结果相关。提议者的等待成本是无关紧要的，只要它们是正的。应用于美国宪法规定的提名程序，推论表明只有参议院的等待成本与结果相关——总统的等待成本无关紧要。正如我所说，这个结果可能解释了美国政治的一个鲜为人知的规律。这就是参议院似乎对下级法官的选择影响很大，而对最高法院法官的选择影响相对较小。