Upper and lower probabilistic preferences in the graph model for conflict resolution

Abstract

We propose a model where decision makers may express their preferences among the possible conflict scenarios using upper and lower probabilities in the graph model for conflict resolution (GMCR). In this new model, we propose eight stability definitions (solution concepts) that are generalizations of the four stability concepts commonly used in the GMCR model, namely: cautious α-Nash stability, risky α-Nash stability, cautious (α,β)-metarationality, risky (α,β)-metarationality, cautious (α,β)-symmetric metarationality, risky (α,β)-symmetric metarationality, cautious (α,β,γ)-sequential stability and risky (α,β,γ)-sequential stability. We present these definitions for conflicts with two or more decision makers and also for conflicts in which the decision makers act as a coalition and analyze the relationship between them. We present two applications and perform the stability analysis using the proposed model to illustrate the gains obtained when individuals are allowed to have the uncertainty about their own preferences expressed by upper and lower probabilities.