# Is the Monty Hall Problem Game Theory?

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Martha Robinson

The Monty Hall Problem is a classic puzzle that has been debated by mathematicians, statisticians, and game theorists for decades. It is named after the host of the popular game show “Let’s Make a Deal,” which aired from 1963 to 1977. In this article, we will explore whether the Monty Hall Problem can be considered a game theory problem.

## What is the Monty Hall Problem?

The premise of the Monty Hall Problem is simple. There are three doors, behind one of which is a valuable prize such as a car.

The other two doors conceal goats or other undesirable items. The contestant chooses one door without knowing what is behind it. After their choice, the host (Monty Hall) opens one of the two remaining doors to reveal a goat.

At this point, Monty offers the contestant a chance to switch their choice from their original door to the other remaining door. The question is: Is it advantageous for the contestant to switch their choice?

## The Solution

The answer might surprise you: Yes, it is advantageous for the contestant to switch their choice! This was famously proven by mathematician Marilyn vos Savant in her “Ask Marilyn” column in Parade magazine in 1990.

The reasoning behind this solution lies in probability theory. Initially, there was a one-third chance that the contestant had chosen the correct door and a two-thirds chance that they had chosen incorrectly. When Monty opens one of the incorrect doors, he essentially eliminates one of those possibilities and leaves only two doors remaining.

By switching their choice, the contestant increases their chances of winning from one-third to two-thirds because they are essentially betting on both remaining doors instead of just one.

## Is it Game Theory?

Now that we understand how to solve the Monty Hall Problem let’s consider whether it falls under game theory.

Game theory is a branch of mathematics that studies decision-making in situations where two or more individuals or groups are competing for a particular outcome. It involves analyzing the strategies and actions of all parties involved to determine the most advantageous course of action.

While the Monty Hall Problem does involve decision-making and strategy, it is not strictly a game theory problem. There is only one player (the contestant) and no opposing player or group.

However, the Monty Hall Problem has been used as an example in game theory courses to illustrate concepts such as Nash equilibrium and dominant strategies. In this context, it can be considered a game theory problem.

## Conclusion

In conclusion, the Monty Hall Problem is an interesting puzzle that has sparked much debate and discussion among mathematicians, statisticians, and game theorists. While it may not strictly fall under game theory, it has been used as an example in game theory courses and can offer insights into decision-making and probability theory.

The key takeaway from this problem is that sometimes our intuition can lead us astray when it comes to probability. By understanding the underlying principles of probability theory, we can make more informed decisions in all areas of life.