Interrelationships of Non-cooperative, Classical and Pareto coalitional stability definitions

Theorems are established on the interrelationships among non-cooperative, classical and Pareto coalitional stability definitions within the framework of the graph model for conflict resolution. The classical coalition stability concepts are first redefined and then, based on the concept of Pareto coalition improvement, new definitions are proposed for Pareto coalition Nash, Pareto coalition general metarational, Pareto coalition symmetric metarational, and Pareto coalition sequential stability. Relations among Pareto coalition stability definitions, earlier coalition stability definitions, and non-cooperative analogues are explained. The practical applicability of these stability definitions is illustrated through their application to a real-world conflict, a 2014 offshore oil exploration dispute in the South China Sea. The equilibrium results confirm the theoretical validity of the new definitions, and show that valuable insights that can be garnered using the Pareto coalition stability approach.