Multidimensional Non-Cooperative Games

10 Pages Posted: 23 Mar 2017 Last revised: 4 Apr 2017

See all articles by Mario Arturo Ruiz Estrada

Mario Arturo Ruiz Estrada

University of Malaya (UM) - Faculty of Economics & Administration (FEA)

Date Written: March 22, 2017

Abstract

This paper tries to applying a new multidimensional graphical approach in the doctoral thesis entitled "Non-Cooperative Games" by Professor John Forbes Nash, Jr. We are using a new multidimensional coordinate space approach to visualize the full model of non-cooperative games in the same graphical space and time under infinity equilibrium points, solutions, strong solutions, and sub-solutions. Additionally, this paper is using the original doctoral thesis from Professor John F. Nash, Jr. that was published in May 1950. This paper is willing to transform this Nobel piece of research from a 2-Dimensional view to a Multidimensional view. This graphical transformation we called "multidimensional cooperative games."

Therefore, this paper applies a new multidimensional coordinate space to transform the visualization of Non-cooperative games from 2-Dimensions to N-Dimensions. This new multidimensional coordinate space is called "The Mega-Disks Networks Mapping (MDN-Mapping)." According to Ruiz Estrada (2015): "The MDN-Mapping captures a large amount of information from n-dimensions in the same graphical space and time. Therefore, the MDN-Mapping creates the possibility to visualize a large number of endogenous and exogenous variables that are distributed, moved, and interconnected in different Nano-Disks (j), Micro-Disks (k), Sub-Disks (L), General-Disks (m) in the Mega-Disk (MD) without any visual restriction respectively. Now, it is possible to observe how infinity endogenous variables are moving together with infinity exogenous variables simultaneously in the same graphical space. At the same time, we can visualize how all these variables interact together through the visualization a large number of asymmetric spiral-shaped figures with n-faces that keeps changing always. This asymmetric spiral-shaped figures with n-faces can experience anytime an expansion or contraction that depend on different changes from any Nano-Disk (j) until arrive to the Mega-Disk (MD) (or the mega-arithmetic mean)."

Keywords: Non-cooperative games, John F. Nash, Barging Problem, Econographicology, Multi-Dimensional graphs and Multi-Dimensional Geometry

JEL Classification: C7, C71, C78

Suggested Citation

Ruiz Estrada, Mario Arturo, Multidimensional Non-Cooperative Games (March 22, 2017). Available at SSRN: https://ssrn.com/abstract=2938945 or http://dx.doi.org/10.2139/ssrn.2938945

Mario Arturo Ruiz Estrada (Contact Author)

University of Malaya (UM) - Faculty of Economics & Administration (FEA) ( email )

Kuala Lumpur, 50603
Malaysia
+60126850293 (Phone)

HOME PAGE: http://ssrc.um.edu.my/

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