Aspects of Game Theory & John Nash

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1 Aspects of Game Theory & John Nash Karina Castro Professor Petersen Math 101 April 6, 2016

2 Aspects of Game Theory & John Nash Math as we know is very important in life because it calculates every little detail in life. There has been people that actually wonder who came up with math and sometimes it can be a good wonder but other times it can be not so good. Math can be easy for some people and not so easy for some but it is something that is very necessary to know because it does affect us in certain ways. It is always a good idea to research when one is wondering about things to stop the wondering. In order to have a very detailed research there needs to be a specific topic on math and in this case the topic will be on the Game Theory. Not only will it be on the game theory but it will also include a person that was involved in it and that person was John Nash. To help with this research on math there are some aspects that would totally help and those are: history, applications, and calculations. To start, history is one main thing that can help us understand a little more on the game theory and on John Nash. The game theory started as a proposed creation of a discipline that would make use of the scientific method to study human conflict and interactions ( Game Theory ). It was invented by two mathematicians who were John von Neumann and Oskar Morgenstern. These two men published a book called The Theory of Games and Economic Behavior in 1944 which, helps explain a little more about how the game theory works. Another

important person involved with the game theory is John Nash. Nash was well known because he expanded the game theory. He actually put life experiences into the game theory.

3 important person involved with the game theory is John Nash. Nash was well known because he expanded the game theory. He actually put life experiences into the game theory. What exactly is game theory? Basically what it is, is coming up with strategies that help within a game. Any game like tic-tac-toe, chess, and poker have a solution in just strategies. It is all on planning the next move because one is able to see what the outcome will be if a certain move is done. It is very interesting to see how simple games had to deal with math because who thinks of it that way when playing a game like tic-tac-toe or chess? According to Chen and Vekhter, not only is the game theory part of playing games but it also applies to other subjects in life. For example, we have biology. Which, it is really interesting how a bird named ziczacs can go in a crocodile s mouth to eat the parasites but yet the crocodile won t eat the bird. The reason for that is because there are benefits, that is called the equilibrium point.

Although science can be a bit hard to be put into the game theory, it does follow some principles of the game theory that is why biology can relate to it.

4 Although science can be a bit hard to be put into the game theory, it does follow some principles of the game theory that is why biology can relate to it. Game theory also plays a big part in Economics because a lot of businesses can relate for the fact that it involves prices. If two companies have the similar products and they both set their products to an equivalent high amount there are still high profits but if one of the companies were to lower the prize a bit more than the other company it would make the people more interested in that product just because it is less expensive causing higher profits as well but for one company. A big reason why this was an important subject to research was because the game theory applies to politics. It is known that politics can be very complicated but how does it involve the game theory? Politics goes based on a lot of decision making and that is when the game theory jumps in because it creates decision that lead to conclusions. Lastly, there is the calculations of the game theory. According to John Nash there where ways to calculate game theory by using scenarios. There was one used and it was the prisoner s

5 dilemma which, involves two men that were involved in a crime. They are given choices, it can go either good or bad. If one confesses it gets less time in jail and the other that does not confess gets more. If they both do not confess they both serve a little amount of time in jail but if they both do confess they both serve a long time in jail. It is hard for them to know if the other partner will confess or not. Scenarios like these were called the Nash equilibrium it is something really interesting (Chang). This was a form of how to calculate the game of theory and it was in such a simple way. A way this can relate to math 101 is by probability. Probability deals with risking chances and outcomes that come from them. Just how there are outcomes to the game of theory when certain calculations are made. Another thing probability has is the fact that it involves games like poker. Every move has to be calculated and there are many chances of losing and winning depending on the cards one gets. What s the probability that one will get good cards? It is not known so one does not know the outcome. Both game and probability theory are quite similar to each other. This research based on math and it subject on game theory was easy to accomplish by looking for its history, applications, and calculations. The game theory started with two mathematicians John von Neumann and Oskar Morgenstern. After them, John Nash came in with how game theory has a lot to do with life experiences. We do not only know that but we also

6 know what game theory applies to like; biology, economics, politics just to name a few. Calculations is also very important and although it might seem hard it really is not thanks to John Nash. He was able to provide different kinds of scenarios that really helps one understand a bit more about game theory. Math works in many interesting ways and ways that help us through life situations.

7 Works Cited Chang, Kenneth. "Explaining a Cornerstone of Game Theory: John Nash s Equilibrium." The New York Times. The New York Times, 24 May Web. 01 Apr < Chen, Janet, and Dan Vekhter. "Applications of Game Theory." Applications of Game Theory. N.p., n.d. Web. 29 Mar < "Game Theory." Von_Neumann. N.p., n.d. Web. 29 Mar <

A Brief Introduction to Game Theory

A Brief Introduction to Game Theory Jesse Crawford Department of Mathematics Tarleton State University April 27, 2011 (Tarleton State University) Brief Intro to Game Theory April 27, 2011 1 / 35 Outline