Arjun Pahwa Math Research Paper The Application of the Nash Equilibrium in Game Theory to Microeconomics ! One of the most challenging problems a business owner comes across is the

amount of a certain item he or she should stock and the price at which to sell it. Many factors play into ﬁnding this appropriate price. These include the cost of stocking the item, the projected demand, and what the competition is pricing the same item at. The latter of the three factors is considered to be the most challenging to consider. When attempting to tackle this problem we must consider three factors. First, we must be able to accurately predict the outcome of our decisions. Second, we must be able to accurately predict our competitionʼs decisions. Finally, we must be able to predict the outcome of our competitionʼs decisions. If all of these three requisites can be met our solution will be able to provide us the necessary information needed to price our item. ! The solution to this problem is game theory. Game theory is a branch of

mathematics that is used to predict the actions of an opponent or competitor in a certain “game.” Game theory has many applications including war, macro and microeconomics, and even biology. Game theory is a relatively new concept created by John von Neumann and Oskar Morgenstern in 1944. Over time it has evolved into a very complex ﬁeld of mathematics that has applications in many other ﬁelds. John von Neumannʼs contribution to game theory was speciﬁc to economics. He contributed the minmax theorem in 1928. This theorem stated that in certain zero sum games all players will be able to pick a strategy that will reduce the potential losses for all players. This principle was groundbreaking in all ﬁelds of economics, especially in microeconomics. Oskar

Morgenstern helped John von Neumann with his research. Other major contributors are John Nash, Reinhard Selten, and John Hersanyi. This paper will focus on the contributions of John Nash and...

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