Inverse Approach to the Graph Model for Conflict Resolution under Combinatorial Behavior with Two Decision Makers

Conflict occurs when different stakeholders have different value systems for a given issue, and each of them can change the state of the conflict, but together they determine the resulting outcome. Sometimes, the outcomes that are undesired by decision makers (DMs) or third parties may be obtained. The inverse graph model for conflict resolution (GMCR) is presented to help the DMs or third parties reach to an expected equilibrium. However, in some complex conflicts, different DMs would have distinct behavioral patterns (named combinatorial behaviors), which is beyond the existing inverse GMCR studies. This paper aims to extend inverse GMCR to achieve the desired equilibrium under combinatorial behavior by optimizing the preferences. The combinatorial behavior is first introduced, and then combinatorial equilibrium is formally defined. After that, an inverse preference optimization model with two DMs under combinatorial behavior is developed that is solved by the genetic algorithm (GA). Finally, the Iran nuclear dispute is applied to explain how the proposed approach can be employed in practice.