Advances in the graph model for conflict resolution

Abstract

In this thesis we present some advances obtained in the graph model for conflict resolution (GMCR). The first one is a new stability concept, called symmetric sequential stability (SSEQ), which was proposed for conflicts involving n decision makers (DMs) and the relationships between this new concept and the existing concepts in GMCR is analyzed. In addition, an extension of this concept to other preference structures is proposed. The second advance was to propose matrix representations to facilitate the obtaining of stable states according to the stability definitions proposed in the GMCR with probabilistic preferences and also according to the SSEQ notion proposed for such model. The third advance was to modify the GMCR allowing the DMs to have iterated levels of unawareness about the options available to them in a conflict, i.e., we consider that DMs may be unaware of some of their options, or some options of their opponents and, therefore, may have only partial knowledge of the state space of the conflict. Finally, the fourth and final advance of this thesis is to present an alternative definition of the stability concept generalized metarationality for conflicts with n-DMs. Our motivation to propose such an alternative definition lies on the fact that, unlike the definition of generalized metarationality for n-DMs in the literature, our definition coincides with the generalized metarationality for conflicts involving only two DMs. In addition, we have pointed out some problems in results that relate this definition to other solution concepts in the GMCR and analyze which properties are satisfied by the alternative definition that we propose.