The study of the strategic interactions of rational decision makers falls within the field of game theory in mathematics and economics. It is used to examine circumstances when an individual's choices and the decisions of others have an impact on the outcome. Game theory revolves on the idea of equilibrium, when players choose their best course of action while taking other players' ideas into consideration.

Now let's apply game theory to the "Prisoner's Dilemma":

The Prisoner's Dilemma Alice and Bob, two of the culprits, are taken into custody and questioned individually. Three choices are available to them:

Both stay quiet and get a little punishment.

One escapes free after betraying, but the quiet one suffers severe consequences.

Everybody betrays the other, and there's a moderate punishment for it.

In this case, betraying the other person would be a legitimate course of action for each individual working in self-interest and ignorant of the other's decision. As a consequence, their joint outcome is worse than it would have been if they had cooperated (both get a little penalty).

In the professional domain, game theory is used in computer science, political science, psychology, economics, and other areas to simulate and assess similar strategic interactions.

Machine learning: Game theory is particularly useful in feature selection (i.e., choosing a subset of important traits to use in model development) when it comes to machine learning applications. The value of a feature is evaluated in terms of how much it adds to the predictive power of the model.

Feature Interaction: Understanding how features interact may be aided by game theory. Certain variables may affect the outcome differently when seen in combination than when examined alone.

Features are ranked according to how big of an impact they have on the outcome of the prediction. This is similar to figuring out the "strategy" that each feature uses to improve the model's overall performance.

Redundancy Reduction: By recognizing the connections and significance, we may eliminate unnecessary or redundant elements from the model, making it simpler and more effective.

When correlations between variables are not immediately apparent, this application is especially helpful with complex datasets. In order to analyze these interactions and create machine learning models that are more effective and efficient, game theory provides a solid foundation.

Dear Doctor

"Game theory is the study of strategic interactions among rational agents who can cooperate or compete with each other. AI systems often face such situations, whether they are negotiating, coordinating, or competing with humans or other AI agents."

To reiterate what was so clearly and succinctly stated by Dr. Hantoosh, Game Theory is indeed the design and study of (mathematical) models of strategic interactions among rational agents, where by "rational agent" we mean any entity that always tries to perform the best possible action based on its goals, preferences and knowledge. It is important in AI because it provides a framework for designing and analyzing intelligent systems that interact with other agents, such as humans, robots, or software.

Besides the obvious application in multi-agent systems, where multiple AI agents cooperate or compete with each other to achieve a common or individual goal as was mentioned in the previous answer, some other quite common examples of the use of Game Theory in AI are adversarial training in generative adversarial networks (GANs), where two neural networks compete with each other to generate realistic images or data, and Reinforcement learning, where an AI agent learns from observing or interacting with other agents (such as a human expert or a game opponent).