How to Bargain: An Interval Approach

In many real-life situations, we need to bargain. What is the best bargaining strategy? If you are already in a negotiating process, your previous offer was a, the seller’s last offer was a > a, what next offer a should you make? A usual commonsense recommendation is to “split the difference”, i.e., to offer a = (a+a)/2, or, more generally, to offer a linear combination a = k · a+ (1− k) · a (for some parameter k ∈ (0, 1)). The bargaining problem falls under the scope of the theory of cooperative games. In cooperative games, there are many reasonable solution concepts. Some of these solution concepts – like Nash’s bargaining solution that recommends maximizing the product of utility gains – lead to offers that linearly depend on a and a; other concepts lead to non-linear dependence. From the practical viewpoint, it is desirable to come up with a recommendation that would not depend on a specific selection of the solution concept – and on specific difficult-to-verify assumptions about the utility function etc. In this paper, we deliver such a recommendation: specifically, we show that under reasonable assumption, we should always select an offer that linearly depends on a and a.