How to Apply Multidimensional Graphs in Non-Cooperative Games

11 Pages Posted: 27 Nov 2017

See all articles by Mario Arturo Ruiz Estrada

Mario Arturo Ruiz Estrada

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

S. I. Cohen

Erasmus University Rotterdam (EUR) - Department of Economics; University of Dubai

Marcin Staniewski

University of Finance and Management in Warsaw, Poland, Faculty of Management and Finance

Date Written: November 21, 2017

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.

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 and Cohen, Solomon I. and Staniewski, Marcin, How to Apply Multidimensional Graphs in Non-Cooperative Games (November 21, 2017). Available at SSRN: https://ssrn.com/abstract=3075673 or http://dx.doi.org/10.2139/ssrn.3075673

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/

Solomon I. Cohen

Erasmus University Rotterdam (EUR) - Department of Economics ( email )

P.O. Box 1738
Rotterdam, 3000 DR
Netherlands

University of Dubai ( email )

AL MAKTOOM STREET
Dubai, 14143
United Arab Emirates

Marcin Staniewski

University of Finance and Management in Warsaw, Poland, Faculty of Management and Finance ( email )

55 Pawia Street
Warsaw, 01-030
Poland

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