 # The Practice Of Probability In Economics: The Game Theory

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IB SL Mathematics Exploration

Topic: The practice of Probability in Economics – The Game Theory

Outlined plan of approach:
1.) What is the Game Theory and how is it used in economics?
a. Define Game theory
b. Illustrate its importance in decision-making.

2.) Introduce the Prisoner’s dilemma as a representation of the game theory.
a. What does the Prisoner’s dilemma prove?
i. Explain that the Prisoner’s dilemma demonstrates the probability of each pair of decisions being made and which decision will more likely be preferable/made by each person. ii. Demonstrate the original prisoner’s dilemma iii. Demonstrate the dilemma of decision making between two businesses in regards to the pricing of their products.
b. Calculate the probability
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Use given probability and conditional probability to explain the likelihood of which decision to make.
b. Calculate the expected value.

Relevant to Mathematics: I know how to find the probability of both independent, combined and mutually exclusive events using their formulas. I also know how to find the probability with given statements and conditional statements. I know how to use tree diagrams to see the possible outcomes of events. For example, if I flip a coin, I know the probability of getting a head is a half or the probability of rolling a four on a six-sided die is 1/6.
I know that probability plays an important role in decision-making and in economies with regards to business predications. The idea of this dilemma and the probability of decisions being made that are either to people’s advantage or not to their advantage, interests me and for that reason, along with my preference for economics, I want to do further research in the mathematics behind the high probability of disadvantageous decisions being made.

Thesis: Even though it is in the two decision-makers (those who are contemplating between which decision they should make for their best interest) advantage to cooperate, there is a high probability that they will not cooperate.
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This issue is slightly more prominent in the business world and economics, where businesses go through this extremely risky decision-making process of deciding their price strategy for specific products and the optimal price level they should impose, to ultimately cooperate or compete against rival companies. The game theory is a mathematical model used in various fields such as math, business and economics, in an attempt to look at the relationships between participants’ decisions and how one participant’s actions depend critically on the actions of the other participant. The game theory allows us to predict the optimal decision for each participant in the given situation and the probability of which decision they will choose. Although there is evidence that this idea of the game theory was perceived before, the Game theory was officially introduced by John von Neumann in 1944, in his book “Theory of Games and Economic Behavior”, in which he mathematically analyzed the solutions and strategies to making the optimal decision for participants in various