Multiple local optima in Zeuthen–Hicks bargaining: an analysis of different preference models

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.