Setting:
The setting of the film took place in Princeton University in Princeton, New Jersey, in 1950 and in the Massachusetts Institute of Technology in Cambridge from 1951 to 1959. Main Characters:
John Nash The schizophrenic who later got a Nobel Prize for his mathematical prowess. Alicia Nash The student of Nash who later becomes his wife and helps him overcome his illness. Parcher The Defense Department agent who was also imagined by Nash Charles Nash's roommate whom he also imagined.

Main Problems:
There is a lack of social interaction with his classmates. Nash also has the inability of accepting defeat. He also has the tendencies to have a world of his own, and he also brings to life imaginary friends or people in his illusion of being one who has the responsibility of keeping the world safe. Conclusion:

Nash is a paranoid schizophrenic. His college roommate Charles, his roommate's niece, and the Defense Department agent were all imagined. Nash is hospitalized, and undergoes intense experimental treatment with mixed results. In his later years, he's able to control his illness and goes on to win a Nobel Prize for his economic theories. Description of Behavior:

Nash could function socially in the outside world, but he became engrossed in his science to the point where he became distracted. His abnormality was clear in the movie where he is shown to talk to illusionary individuals. Clearly, to some, his behavior was not adaptive, but to a fellow scientist in the same field, perhaps they could relate to the method in which John Nash received his inspiration. Evidence of Disorder:

The film shows John Nash throwing furniture out his window, and clandestine trips to an imaginary drop off point for his decoded messages. The movie also leads one to believe that Nash felt people were out to harm him. Signs:

Nash is having delusions that he is the key to world safety during the Cold War, and he is also having the illusions that a government agent...

...In the short span of ten years, John Forbes Nash, Jr. published an astounding fourteen papers relating to such diverse mathematical subjects as game theory, differential equations, parabolic equations, and fluid dynamics. Although Nash is best known for his works in game theory, for which he received the Nobel Prize in economics in 1994, his other mathematical works do deserve investigation. Many argue however, that Nash's theories relating to non-cooperative games are much less significant than those applicable to other mathematical subjects.
In 1950, Nash published Equilibrium points in n-person games. Previous works (by von Newmann and Morganstern) state in non-cooperative games, all results achieve a zero sum. In other words, the theory of von Newmann and Morganstern states that in every non-cooperative game there is a winner and a loser. Nash's theory adds to the previous theory of von Newmann and Morganstern by stating that there does not always need to be a winner and a loser. In fact, it states that in a game each side will attempt to win to the best of his ability. The other player will know this and will attempt to counter the strategy of the other player. Eventually, an equilibrium point (also known as a Nash Equilibrium) will occur in the game, where each player neither wins nor loses.
For example, pretend that there are two car dealers in a small town. Together, they have a monopoly on...

...John Forbes Nash Jr. (born June 13, 1928) is a mathematician who worked in game theory and differential geometry. He shared the 1994 Nobel Prize for economics with two other game theorists, Reinhard Selten and John Harsanyi.
After a promising start to his mathematical career, Nash began to suffer from schizophrenia around his 30th year, an illness from which he has only recovered some 25 years later.
JohnNash was born in Bluefield, West Virginia as son of JohnNash Sr. and Virginia Martin. His father was an electrotechnician; his mother a language teacher. As a young boy he spent much time reading books and experimenting in his room, which he had converted into a laboratory.
From June 1945-June 1948 Nash studied at the Carnegie Institute of Technology in Pittsburgh, intending to become a technical engineer like his father. Instead, he developed a deep love for mathematics and a lifelong interest in subjects such as number theory, Diophantine equations, quantum mechanics and relativity theory. He loved solving problems.
At Carnegie he became interested in the 'negotiation problem', which John von Neumann had left unsolved in his book The Theory of Games and Economic Behavior (1928). He participated in the game theory group there.
From Pittsburgh he went to Princeton University where he worked on his equilibrium theory....

...John Forbes Nash Jr.
Introduction
John Forbes Nash Jr. was born on June 13th of 1928. He has greatly impacted
today’s society with his works in game theory, differential geometry, and partial
differential equations. His theories are used in many aspects of our lives today
such as in economics, computing, evolutionary biology, artificial intelligence,
accounting, politics and in military theory. Within his lifetime Nash has received several
prestigious awards. In 1978 he was awarded the John Von Neumann Theory Prize. In
1994 he and his coworkers Reinhard Selton and John Harsanyi were awarded the Nobel
Memorial Prize in Economic Sciences and he was also awarded the Abel Prize in 2015
for his work on non linear partial differential equations.
John Forbes Nash Jr. was born in Bluefield, West Virginia in 1928 to his father
John Forbes Nash, an electrical engineer for the Appalachian Electric Power Company,
and his mother Margaret Virginia Martin, known as “Virginia”, who was a school
teacher. Nash has one younger sister named Martha. Nash had a very advanced,
education filled childhood learning to read and play piano before the age of three. He
...

...beautiful mind is a great way to describe JohnNash because he was a brilliant person who suffered and fought through Schizophrenia. Nash was born on June 13, 1928, in Bluefield, West Virginia. His father was an electrical engineer for the Appalachian Electric Power Company. His mother, name was Virginia Martin and she had been a schoolteacher before she married. Nash had a younger sister, Martha, born November 16, 1930.Nash attended kindergarten and public school. Nash's parents worked hard to create a challenging learning program for their son's education, and arranged for him to take advanced mathematics courses at a local community college during his final year of high school. Nash attended Carnegie Mellon University with a full scholarship, and the George Westinghouse, which was a scientific/mathematic competition that helped students earn scholarship money. He initially majored in Chemical Engineering. He switched to Chemistry, and eventually to Mathematics. After graduating in 1948 with Bachelor of Science and Master of Science degrees in mathematics, he received a scholarship to Princeton University where he pursued his graduate studies in Mathematics. At Princeton he worked on his equilibrium theory. JohnNash had a bright future ahead of him at Princeton but he did go through some devastating problem which created obstacles, like his mental illness,...

...logic and biology. In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute Nash equilibrium.
1.1 John Forbes Nash Jr.
John Forbes Nash, Jr. is an American mathematician who was born on June 13, 1928. His works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. John Forbes Nash Jr. Nash attended Carnegie Institute of Technology with a full scholarship, the George Westinghouse Scholarship and initially majored in Chemical Engineering. He switched to Chemistry, and eventually to Mathematics. After graduating in 1948 with bachelor of science and master of science degrees in mathematics, he accepted a scholarship to Princeton...

...Nash Equilibrium and Dominant Strategies
Nash Equilibrium is a term used in game theory to describe an equilibrium where each player's strategy is optimal given the strategies of all other players. A Nash Equilibrium exists when there is no unilateral profitable deviation from any of the players involved. In other words, no player in the game would take a different action as long as every other player remains the same. Nash Equilibria are self-enforcing; when players are at a Nash Equilibrium they have no desire to move because they will be worse off.
Necessary Conditions
The following game doesn't have payoffs defined:
L
R
T
a,b
c,d
B
e,f
g,h
In order for (T,L) to be an equilibrium in dominant strategies (which is also a Nash Equilibrium), the following must be true:
a > e
c > g
b > d
f > h
In order for (T,L) to be a Nash Equilibrium, only the following must be true:
a > or = e
b > or = d
Prisoners' Dilemma (Again)
If every player in a game plays his dominant pure strategy (assuming every player has a dominant pure strategy), then the outcome will be a Nash equilibrium. The Prisoners' Dilemma is an excellent example of this. It was reviewed in the introduction, but is worth reviewing again. Here's the game (remember that in the Prisoners' Dilemma, the numbers represent years in prison):
Jack
C
NC
Tom
C
-10,-10
0,-20
NC...

...Security Dilemma the Collective Action Problem and the Nash Equilibrium.
Criticism of the United Nations highlight the lack of power it has and its reliance on superpowers for legitimacy. The use by states of the UN is conditional on whether it serves state self-interest and whether the value of participating outweighs the cost (Abbott and Snidal 2005: 27). This brings into question why states would allow the UN to impose International laws and Norms that erode state sovereignty and how this increases international peace and security. It is seemingly irrational that despite the issue of national sovereignty and individual grievances states are extremely hesitant to leave the United Nations (Diehl 2005:4). The importance of the UN in international peace and security can be explained by the dominance of the ‘security dilemma’ and the connection between realism, rational choice theory and the Nash equilibrium.
The security dilemma is the international predicament that can best be categorized as aiming to reduce the uncertainty of an anarchistic world order (Booth and Wheeler 2009:132). The uncertainty of states actions has led some realist theorists to attempt to find the optimum strategy for mitigating external threats and thus secure its own interests.There are two levels to the security dilemma; the dilemma of interpretation which is attempting to discover what other nations are doing behind closed doors, and the dilemma of response; how...