Upper and lower probabilistic preferences in the graph model for conflict resolution
This paper extends the stability definitions of the graph model for conflict resolution (GMCR) to preferences expressed using upper and lower probabilities. The definitions are applied in the context of two and of more than two decision makers and also for conflicts in which the decision makers act as a coalition. Relations between different pairs of stability notions are established. The same relationships among the stability notions of the GMCR with precise probabilistic preferences remain valid for both the cautious and risky versions of the stability definitions proposed. Moreover, every state that is stable according to a risky behavior is also stable according to the corresponding cautious behavior and if all the decision makers have no imprecision in their probabilistic preferences, then the stability definitions proposed coincide with those given for the GMCR with precise probabilistic preferences. Two applications are presented modeling the gains obtained when individuals are allowed to have the uncertainty about their own preferences expressed by upper and lower probabilities.
scientific article; zbMATH DE number 6893198
scientific article