Zeuthen–Hicks bargaining provides a dynamic model that explains how two parties in a negotiation make concessions to reach the Nash bargaining solution. However, it is not clear whether this process will always reach the global optimum corresponding to the Nash bargaining solution, or could end at a local optimum, or even in disagreement. In this paper, we analyze different types of utility functions, both analytically and in a computational study, to determine under which circumstances convergence to the Nash bargaining solution will be achieved. We show that non-standard preferences, involving, e.g., reference point effects, might indeed lead to multiple local optima of the Nash bargaining objective function and thus failure of the bargaining process. This occurs more often if expectations of parties are mutually incompatible.

中文翻译：

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Zeuthen-Hicks讨价还价中的多个局部最优：对不同偏好模型的分析

Zeuthen-Hicks讨价还价提供了一个动态模型，该模型解释了谈判中的两方如何做出让步以达成Nash讨价还价解决方案。但是，尚不清楚此过程是否将始终达到与Nash讨价还价解决方案相对应的全局最优值，或者是否会以局部最优值结束甚至不一致。在本文中，我们在分析和计算研究中分析了不同类型的效用函数，以确定在哪种情况下可以收敛到Nash讨价还价解决方案。我们表明，涉及例如参考点效应的非标准偏好确实可能导致Nash讨价还价目标函数的多个局部最优，从而导致讨价还价过程失败。如果各方的期望是相互矛盾的，则这种情况会经常发生。