Analysis of the constraint proposal method for two-party negotiations

In the constraint proposal method a mediator locates points at which the two decision makers have joint tangent hyperplanes. We give conditions under which these points are Pareto optimal and we prove that under these conditions the mediator’s problem has a solution, when the number of issues in the negotiation is two or any odd number greater than two. In practice, the mediator adjusts a hyperplane going through a reference point until the decision makers’ most preferred alternatives on the hyperplane coincide. We give local convergence conditions for fixed-point iteration as an adjustment process. We also discuss the relationship of exchange economies and the constraint proposal method, and the possible ways of using the method.