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 inequalities that determine the bargaining setM1(i)
It is well-known that the payoffs of the various bargaining sets of a cooperativen-person game are finite unions of closed convex polyhedra. In this paper, the system of inequalities that determines these polyhedra for the bargaining setM1(i) is expressed in explicit form.It turns out that this system also expresses the condition that certain games, derived from the original game and from the potential payoffs, have full-dimensional cores.