Two-party bargaining processes based on subjective expectations: a model and a simulation study

This work presents a model for a two-party bargaining process in which multiple offers are exchanged as the negotiation goes on, under a risk of breakdown. Typical game theoretical analyses of such settings assume the breakdown risk is known and the parties are able to calculate an initial offer that is immediately accepted by the other party, ending the negotiation. Aiming to develop a model that is closer to real-life situations, in which parties do exchange many offers in a bargaining process, we consider the parties are unable to compute the far-reaching consequences of their offers, and are guided by their subjective expectations of the outcome of the negotiation. This introduces a new perspective to the analysis of two-party bargaining processes: the confidence of the bargainers in terms of what they hope to achieve by bargaining with each other. The resulting model can be seen as an extension of the Zeuthen-Hicks bargaining model. We show analytically that under the assumption of concave utilities of both parties, the bargaining process converges to the nonsymmetric Nash bargaining solution, where the asymmetry is caused by differences in expectations. This result provides a new interpretation of the parameters of the nonsymmetric Nash bargaining solution, linking them to behavior in the bargaining process. As an additional contribution, we perform a simulation study to examine the role of confidence and to analyze the outcomes for non-concave utility functions.