The Foundation of Game Theory: John Von Neumann

The results of this study infiltrate John von Neumann's life mainly in mathematics and economics studies. He can lay the foundation of game theory. It is a valuable model for business and fiscal decision making. He also made an important contribution to mathematics and physics world through self-replicating automata and participation in the notorious Manhattan Project. This research also points out the importance of critical thinking and innovation in society and discusses various ways in which John von Neumann embodies the spirit of this thought.

Before John von Neumann published his thesis "strategic game theory" in 1928, game theory did not exist as a truly unique field. Von Neumann 's original proof uses Brouwer' s fixed point theorem for continuous mapping to a compact convex set. This will be a standard way of game theory and mathematical economics. Following his paper was the 1944 book "Game and Economic Behavior Theory" co-authored with Oscar Morgan Stern. The second edition of the book provides an axiom utility theory to reconvert Daniel Bernoulli's old utility theory (money) into an independent field. Von Neumann's work in game theory peaked in the book of 1944. This basic task involves finding a consistent solution for two zero sum games.

One of the earliest work on game theory is the book "game theory and economic behavior" published by John von Neumann and Oskar Morgenstern in 1944 and is considered the origin of the field of game theory. Their work is the first application of mathematical models to the effects of economics and human behavior. Another important work in game theory is based on the work of John Forbes Nash, former work of von Neumann and Morganstein. His first work in a non-cooperative game entitled "Balance Point of N-Man Game" (1950), the subsequent work until 1953 was formalized and called "Nash equilibrium" . Bell Economic Award

According to a report, when young John Nash proved the basic theorem of a non-zero sum game and came to von Neumann, von Neumann said, "But this is trivial." So today is like this. Nevertheless, Nash has completed what other people have, and his contribution to the field of game theory can certainly rival von Neumann. Finally, you can notice that n-tuple S is in space. This is a simple product with vertices (each player has its own simplex). The dimension of this space is d 1 + d 2 + ... + d n. Where di represents the simplex dimension of player i. However, this space is the same as the ball of d 1 + d 2 + ... + d n, it is clear that Brouwer's fixed point theorem applies. Therefore, T has at least one fixed point S, which proves to be a balance point.