On the bargaining set of three-player games
The description and the characterization of the (Aumann-Maschler) bargaining set are known, but its determination is still hard given a generic transferable utility cooperative game. We provide here an exhaustive determination of the bargaining set of any three-player game, balanced or not, superadditive or not.
N-Non-Cooperative Games Under a Dynamic Multidimensional Graphical Prism
This paper explores the concept of multidimensional Nash equilibrium as a prospective solution in a non-cooperative multi-player normal form game. The paper suggests a paradigm shift: a new multidimensional geometric approach to capture all symmetrical and asymmetrical strategic graphical movements in real space and time. The Multidimensional Non-Cooperative Games Graphical Framework (MNCGG-Framework) extends the traditional two-dimensional normal form game into a multidimensional graphical framework that synchronizes the optimal agent interactions with corresponding payoffs in real-time. The paper applies the proposed graphical framework on John Forbes Nash’s six examples on non-cooperative games taken from his doctoral dissertation.
The semireactive bargaining set of a cooperative game
Abstract. The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person rationality, the reduced game property, a weak version of the converse reduced game property with respect to subgrand coalitions, and subgrand stability. Furthermore, it is shown that there is a suitable weakening of subgrand stability, which allows to characterize the prebargaining set. Replacing the reduced game by the imputation saving reduced game and employing individual rationality as an additional axiom yields characterizations of both, the bargaining set and the semireactive bargaining set.