Confidence and Outcome Expectations in Bilateral Negotiations–A Dynamic Model

Abstract

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