How to Apply Multidimensional Graphs in Non-Cooperative Games

Abstract

This paper starts from the doctoral thesis on non-cooperative games by John Forbes Nash and applies a multidimensional coordinate space approach to visualize a full model of non-cooperative games in the same graphical space and time, with infinity equilibrium points, solutions, strong solutions, and sub-solutions. This graphical transformation into multidimensional cooperative games that we call Mega-Disks Networks Mapping (MDN-Mapping). The principles behind this application to Nash are found in Estrada (2015), where MDNMapping is shown to capture a large amount of information from n dimensions in the same graphical space and time. The MDN-Mapping creates the possibility of visualizing large numbers of endogenous and exogenous variables that are distributed, moved, and interconnected in different Nano-Disks (j), Micro-Disks (k), Sub-Disks (L), and General-Disks (m) within the Mega-Disk (MD) and without visual restrictions. This makes it possible to observe how infinity endogenous variables are moving simultaneously with infinity exogenous variables in the same graphical space. At the same time, we can visualize how all these variables interact by visualizing large numbers of asymmetric spiral-shaped figures with n faces that are continuously changing. These asymmetric spiral-shaped figures with n faces experience expansion or contraction, depending on the changes that occur during the movement from any Nano-Disk (j) to the Mega-Disk (MD) or on the mega-arithmetic mean.