Mixed Coalitional Stabilities With Full Participation of Sanctioning Opponents Within the Graph Model for Conflict Resolution

Mixed coalition analysis approaches are developed within the framework of the graph model for conflict resolution (GMCR) for analyzing the heterogeneous multicoalitional opponents having mixed coalitional sanctions, in which some sanctioning coalitions may only invoke coalitional improvements (CIs) while others may go to any reachable states to jointly sanction a focal coalition's CIs. To accomplish this, the concept of a full coalition set is defined in which each participating decision maker (DM) is represented once either as an individual player or part of a coalition. All possible scenarios in which a full coalition set could be formed is called the universal coalition set. When calculating the stability of a specific state for a particular coalition in a given conflict, the remaining DMs form the universal coalition set whose moves have the potential to block any CIs by the focal coalition within four specified solution concepts having full participation of sanctioning opponents. To handle heterogeneous opponents with mixed CIs (MCIs), the mixed coalition analysis approach is proposed, which provides a more general coalition analysis framework than existing coalition analysis approaches. Moreover, the interrelationships among coalitional stabilities and mixed coalitional stabilities with full participation are investigated followed by their corresponding matrix representations which can significantly improve their computational efficiency and make the computer implementation possible. Finally, a case study is investigated to demonstrate how to employ the proposed mixed coalition analysis approaches to address a real-world environmental conflict.