Berge Solution Concepts in the Graph Model for Conflict Resolution

In this work, we generalize Berge solution concepts in the graph model for conflict resolution for conflicts with 2 or more decision makers (DMs). These concepts are useful to the analysis of interactions among DMs with altruistic behaviors. Berge behavior can be observed in conflicts where DMs act altruistically expecting others to reciprocate so that in the end it is in their own self-interests to behave in this way. The Berge stabilities presented are inspired on commonly used stability notions in the GMCR, such as: generalized metarationality, symmetric metarationality, sequential and symmetric sequential stabilities for conflicts with 2 or more DMs. We investigate the relation among these proposed concepts and also between such concepts and the standard ones. We also establish a relationship between Berge stability and coalition Nash stability of a modified conflict. The chicken and stag hunt games are used as examples to illustrate applications of the Berge stabilities in conflicts. In particular, we show that in the stag hunt game and in a modified version of it, Berge stabilities may be used to select a more desired Nash equilibria.