Generating Pareto‐optimal boundary points in multiparty negotiations using constraint proposal method

Abstract

In this paper a constraint proposal method is developed for computing Pareto-optimal solutions in multiparty negotiations over continuous issues. Constraint proposal methods have been previously studied in a case where the decision set is unconstrained. Here we extend the method to situations with a constrained decision set. In the method the computation of the Pareto-optimal solutions is decentralized so that the DMs do not have to know each others' value functions. During the procedure they have to indicate their optimal solutions on different sets of linear constraints. When the optimal solutions coincide, the common optimum is a candidate for a Pareto-optimal point. The constraint proposal method can be used to generate either one Pareto-optimal solution dominating the status quo solution or several Pareto-optimal solutions. In latter case a distributive negotiation among the efficient points can be carried out afterwards.

Analysis of the constraint proposal method for two-party negotiations

“…It is also a property that does not hold for the multi-party generalization of the method considered by Heiskanen et al (2001) and Heiskanen (2001). Hence, most of the results of this paper cannot be generalized to a multi-party setting with the same techniques as used in this paper.…”

“…The meaning of this results is that all the Pareto points can be obtained by taking reference points from the line connecting the decision makers' global optima. Related results are also given by Heiskanen (2001) for strictly pseudoconcave utility functions. 1 Theorem 1.…”

“…To ease the notation we neglect all these additional constraints. See Heiskanen (2001) for the use of the constraint proposal method in negotiations with additional constraints.…”

“…Hence, Theorem 1 gives a more general result for two-party negotiations than the results ofHeiskanen (2001).…”

Modeling Multi-attribute Negotiations in the Navy Detailing Process

“…For the mediator's problem, we apply the idea of Ehtamo's constraint proposal method to find Pareto-optimal solutions [15] [16]. So, the procedure in each turn to find out a Pareto-optimal solution can be described as following:…”