Game theory and John Nash

Game theory is a mathematical framework for science of strategies. Key contributors in this field are mathematicians John von Neumann and John Nash.

Game theory and John NashGame Theory employs mathematics to model strategic interactions among rational players or participants. Many realistic situations are modelled as zero-sum games in which one player gains at the cost of other players or vice versa.

Every game would have players, strategies and payoffs. Types of games are very large in number. Major classes of games are cooperative and non-cooperative games. Game theory has applications in situations when humans, animals or computers make decisions with diverging interests.

Common applications of game theory are in economics, business, diplomacy, military strategies, computer science and social evolution. Payoffs of strategies of a player also depends on strategies of rivals. A typical example is firms competing in the same market.

The “game of chicken” is the most popular example of “conflict model” in game theory. Assume that two drivers are driving strastraight towards each other.

If no one swerves, they will crash and both may lose lives. One who swerves is called chicken or coward. There is a similar model, called “hawk-dove” model. Below is a pictorial view of “game of chicken”.

Nash equilibrium is one of the most important developments in game theory. Nash equilibrium is a stable state of a system of interacting participants or players in which a player can’t gain by changing his/her strategy if other players keep their strategies unchanged.

Nash equilibrium has been employed to analyze complex economic situations, war conditions and arm races. It is proposed here that game theory should be employed to analyze nuclear emergencies, typical of fears in decision makers and public circles.

Decision making in the aftermath of the Fukushima nuclear accident could have been better with the adequate use of game theory.

Consider two companies A and B. Both companies have a choice to advertise or not to advertise their products. Advertising would yield a better payoff. Nash equilibrium will be the case when both companies choose to advertise their products. Complete payoff table is shown below.

John von Neumann and John Nash are major developers of game theory. They and their work are described below very briefly.

John von Neumann (28 Dec 1903 – 08 Feb 1957) was a Hungarian-American mathematical physicist of towering eminence. He invented game theory through his minimax theorem. Minimax theorem is a decision rule for minimizing the possible loss in worst case scenario.

In addition to game theory, his theorem is also used artificial intelligence, decision theory, computer science and statistics. He is considered the last greatest mathematician of the history to date. He got several awards including Medal of Freedom and Enrico Fermi Award. Unfortunately, he died early at the age of 53.

John von Neumann
John Nash (13 June 1928 – 23 May 2015) is an American mathematician who is globally well known for his classic breakthrough contribution to the field of game theory. He struggled hard with his mental illnesses. He died in 2015 in an automobile accident with his wife Alicia. He had a long association with mathematics department of Princeton University.
John Nash and Alicia Nash
Nash was a person of private nature. His life was dramatized by a beautiful film, A Beautiful Mind (2001), in which Nash and Alicia Nash were portrayed by actors Russell Crowe and Jennifer Connelly.
Game theory
Declaration: Information and pictures included here were collected from several in-print and digital sources and are presented here in a coherent manner for a broad scope readership.

By Dr Mukhtar Ahmed Rana

Mukhtar does research on Instrumentation, Physics, and Environmental Science.