Notion of Equilibrium in Game Theory Explained

According to professor Dixit, John Nash would be a rich man if he got a dollar for every time someone mentioned Nash’s equilibrium. Professor Dixit elucidates much on game theory and the impacts it has had on situations that human beings encounter on a daily basis. Game theory ventures much into studying decision-making with the outcome of each participant depends on the actions of everyone.

In game theory, when a player is choosing a move or a strategy, he or she must also consider the plans and choices that the others will make. This also happens with the rest because as you think about their choices, they are doing the same about yours hence the thinking cycle goes on.

This shows that indeed thinking about the motives of enemies and being aware of complex patterns do at times resist logical analysis. A lot of aspects of strategies and motivations can be studied and turned into science which is game theory.

Game theory took a head start in the 1920s with the work of John Von Neumann which is found in his book with Oscar Morgenstern. The two did a study on ‘zero-sum’ games looking at the interests of two players. With John Nash, he treated more general and realistic cases of a mixture of rivalry and common interests and any number of participants.

The theory entails a notion of equilibrium whereby complex chain thinking about thinking could unite. According to the method, the motives of all participants would be mutually consistent such that each would be selecting his or her most preferred response to the choices of others. This theory can only be useful if the equilibrium it posits is in existence. To prove the existence of the equilibrium, Nash used mathematical techniques in a general class of games.

Reference

https://www.pbs.org/wgbh/americanexperience/features/nash-game/

 

Game Theory Explained

Game theory is the study of mathematical models of negotiation, conflict and cooperation between individuals, organizations and governments. The study has direct applications in contract theory, economics, sociology and psychology.

Game theory is applied in various areas of study to understand why an individual makes a particular decision and how the decisions made by one individual affect others. The application of game theory concepts and techniques to non-game activities is known as gamification.

The Nash Equilibrium

The theory constructs a notion of “equilibrium,” to which the complex chain of thinking could converge. Nash used novel mathematical techniques to prove the existence of equilibrium in a very general class of games. This paved the way for applications. Biologists have even used the notion of Nash equilibrium to formulate the idea of evolutionary stability.

Game theory research involves studies of the interactions among people or groups of people. Because people make use of an ever-increasing number and variety of technologies to achieve desired ends, game theory can be directly applied in areas of negotiation, such as contract theory and indirectly applied in practical pursuits such as engineering, information technology and computer science.

So-called games can range from simple personal or small group encounters or problems to major confrontations between corporations or superpowers. One of the principal aims of game theory is to determine the optimum strategy for dealing with a given situation or confrontation. This can involve such goals as maximizing one’s gains, maximizing the probability that a specific goal can be reached, minimizing one’s risks or losses, or inflicting the greatest possible damage on adversaries.

Game theory was first devised by John Von Neumann. Later contributions were made by John Nash, A. W. Tucker, and others.

Reference: https://whatis.techtarget.com/definition/game-theory