Equilibrium payoffs and proposal ratios in bargaining models
Equilibrium payoffs and proposal ratios in bargaining models
复制标题
讨价还价模型中的均衡收益和提议比率
DOI：
10.1007/s00182-019-00698-w
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发表时间：
2019
影响因子：
0.6
通讯作者：
Shunsuke Hanato
中科院分区：
文献类型：
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作者：
Hagiwara Makoto;Hanato Shunsuke;Shunsuke Hanato;Shunsuke Hanato
我们从每个时期如何决定提议者的过程的角度来分析讨价还价模型，该模型是鲁宾斯坦模型（Econometrica 50（1）：97-109，1982）的推广。在我们的模型中，玩家成为提议者的概率取决于提议者的历史，并且玩家划分了大小为 1 的馅饼。我们推导出子博弈完美均衡 (SPE) 并分析其 SPE 收益与该过程的关系。在双边模型中，有一个独特的SPE。在当时玩家模型中，虽然SPE可能不是唯一的，但存在类似于双边模型中的SPE的马尔可夫完美均衡（MPE）。在折扣因子足够大的情况下，如果成为提议者的机会比例收敛到某个值，则参与者在这些均衡下根据该收敛值的比例来分配蛋糕。这个结果意味着，尽管我们的过程的规律性低于马尔可夫过程，但与使用马尔可夫过程的模型中的结果相同。除了这些结果之外，我们还表明 SPE（或 MPE）收益的极限与由提议者机会比率的收敛值加权的非对称纳什讨价还价解决方案一致。
We analyze a bargaining model which is a generalization of the model of Rubinstein (Econometrica 50(1):97–109, 1982) from the viewpoint of the process of how a proposer is decided in each period. In our model, a player’s probability to be a proposer depends on the history of proposers and players divide a pie of size 1. We derive a subgame perfect equilibrium (SPE) and analyze how its SPE payoffs are related to the process. In the bilateral model, there is a unique SPE. In then-player model, although SPE may not be unique, a Markov perfect equilibrium (MPE) similar to the SPE in the bilateral model exists. In the case where the discount factor is sufficiently large, if the ratio of opportunities to be a proposer converges to some value, players divide the pie according to the ratio of this convergent value under these equilibria. This result implies that although our process has less regularity than a Markov process, the same result as in the model that uses a Markov process holds. In addition to these results, we show that the limit of the SPE (or the MPE) payoffs coincides with the asymmetric Nash bargaining solution weighted by the convergent values of the ratio of the opportunities to be a proposer.