Interrelationships among noncooperative and coalition stability concepts

Abstract

Insightful theorems are established on interrelationships among coalition and noncooperative stability concepts defined within the paradigm of the Graph Model for Conflict Resolution. More specifically, the newly defined coalition stability definitions that are considered are coalition Nash stability (CNash), coalition general metarationality (CGMR), coalition symmetric metarationality (CSMR) and coalition sequential stability (CSEQ), along with their earlier-defined noncooperative versions. A range of interesting new theorems are derived to establish connections among these coalition stability concepts as well as between noncooperative and coalition stability definitions. Applications with respect to the games of Prisoner’s Dilemma and Chicken, as well as a groundwater contamination dispute, demonstrate how the various stability definitions can be applied in practice and confirm the validity of some of the theorems as well as point out, by example, certain types of relationships which cannot hold.

Keywords

Chicken / coalitions / environmental conflict / Graph Model for Conflict Resolution / noncooperative behaviour / Prisoner’s Dilemma / stability relationships

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