Integer Linear Optimization Models for Solving the Preference Manipulation Problem Within the Graph Model for Conflict Resolution

Conflicts occur when decision makers (DMs) have different interests and their actions influence each other’s well-being. The graph model for conflict resolution (GMCR) provides a systematic and flexible method to represent and analyze conflicts. Originally, the GMCR was proposed to determine what the equilibrium scenarios are given how DMs can change the conflict scenarios and how they evaluate these scenarios. However, in some situations, one may want to make a particular scenario an equilibrium. To achieve this goal, some incentives must be given to alter DMs’ preferences over states. The preference manipulation problem (PMP) seeks to find the minimum cost necessary to make a particular state an equilibrium according to some stability criteria. This work presents integer linear programming models to solve the PMP for various stability criteria within the GMCR. In order to achieve our goal, we first propose a representation of the stability criteria as instances of a satisfiability problem, which are then translated as constraints in the optimization models. The proposed models were applied in two conflicts: the Cuban missile conflict and the conflict of values. The proposed models present satisfactory performance in both applications.