13/10/2024
United Nations: Nash equilibrium (2024)
By Leon Lester
Sculpture
Cotton, Paper, Metal and Ink
This Artwork is to celebrate the mathematical reasoning of the co-operative body that is the United Nations, created to stop tit-for-tat warring and senseless spending on arms rather than homelessness, health or the environment. The Nash equilibrium is named after its inventor, John Nash, an American mathematician. It is considered one of the most important concepts of game theory because it is based around timelessness or infinity. It attempts to determine mathematically and logically the actions that participants of a game should take to secure the best outcomes for themselves over infinity or the very long-run like the length of the entire Kali Yuga.
The reason why Nash equilibrium is considered such an important concept of game theory relates to its applicability. The Nash equilibrium can be incorporated into a wide range of disciplines, from economics to social sciences to the arms race being a waste a money like all war based on human differences, for example Arabs vs Jews and Christians or Maoists vs Buddhists.
If a game has a unique Nash equilibrium and is played among players under certain conditions, then the NE strategy set will be adopted. Sufficient conditions to guarantee that the Nash equilibrium is played are:
The players all will do their utmost to maximize their expected payoff as described by the game.
The players are flawless in ex*****on.
The players have sufficient intelligence to deduce the solution.
The players know the planned equilibrium strategy of all of the other players.
The players believe that a deviation in their own strategy will not cause deviations by any other players.
There is common knowledge that all players meet these conditions, including this one. So, not only must each player know the other players meet the conditions, but also they must know that they all know that they meet them, and know that they know that they know that they meet them, and so on.
