Application of Nash Equilibrium in Macroeconomics

1775 Words Mar 26th, 2012 8 Pages
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.
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The second number corresponds to the outcome for the second player.

our opponent and act accordingly. This is known as solving the game. A dominant strategy is a strategy that will reward one player more than any other player regardless of any other playerʼs actions. To find the dominant strategy you must eliminate layers on the Strategic Form diagram. The following tables will be used to describe how to identify the dominant strategy for each player.

Table 2.2: The table above follows the same rules as Table 2.1

Player 1

Top Middle Down

Left 45 35 25

Player 2 Center 16 25 20

Right 56 54 70

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For Player 2, right is dominated by center. This is because all of the outcomes in

the right column for Player 2 are worse than all of the outcomes in the center column. Because the right column is out of the picture, the middle row dominates the down row for Player 1. With this we are left with a 2 x 2 table shown bellow.

Player 2 Player 1 Top Middle Left 45 35 Center 16 25

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In this table it is easy to see that the dominant choice for Player 1 is middle and

for Player 2 the dominant choice is center. ! The next way of solving games is through the identification of Nash equilibrium.

This method has its advantages over finding the dominant strategy in many scenarios. For example, if Strategy 1 dominates Strategy 2 then using the dominant strategy
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