Confidence and Outcome Expectations in Bilateral Negotiations–A Dynamic Model

Abstract

This work proposes and studies a dynamic model of two bargaining parties exchanging ofers over time, considering their confdence about the share of the “pie” they obtain, which translates into expectations regarding the outcome of the bargaining process. The model predicts the sequence of ofers as well as the fnal agreement for given confdence parameters. A mathematical analysis of the model shows the outcome is an Asymmetric Nash Bargaining Solution with exponents determined by the bargainers’ confdence. Moreover, a compensation efect can be found between confdence and risk aversion. This work also considers that confdence levels of bargainers might change during the negotiation, and we conduct a comprehensive simulation study to analyze the efect of such changes. Through Monte-Carlo simulation, we show that a bargainer is better of if its confdence increases, but the advantage is lost if the other party’s confdence increases in a similar way. In that case, concessions are smaller and negotiations last longer. Changing confdenc parameters make the outcome harder to predict, as it will depend more on the fnal confdence than the initial one. The simulations also show that the average size of concessions, and therefore the fnal agreement, depend not only on whether confdence increases or decreases, but also on the change rate, with stronger efects observed when change accelerates towards the end of the process.