3. Conflict Models in Graph Form

The basic design of the Graph Model for Conflict Resolution (GMCR) is presented in this chapter, which includes both the logical and matrix formulations of this simple and flexible approach to tackling challenging disputes. The chapter starts by defining the normal and option forms of a game so the reader will fully appreciate their exact connections to GMCR. The Graph Model is then defined in terms of decision makers (DMs), the feasible states or scenarios of the conflict model under study, the movements among states under the control of each particular DM, and the DM’s relative preferences over the states. The transitions among states controlled by each DM are represented by a directed graph in which the vertices represent the states and the arcs the movements between them, explaining some of the GMCR terminology. Because movements in a graph can be recorded using a matrix, the logical ways to express moves, and the relative preferences of states, have equivalent matrix representations. A generic sustainable development conflict and a groundwater contamination dispute are utilized to illustrate the concepts presented in this foundational chapter. The contents of this chapter provide background definitions for additional definitions and theorems developed in Chaps. 4–9.