### Summary

Game Theory is a mathematical tool used to study situations where multiple stakeholders interact. In AI, it plays a crucial role in defining algorithms for multi-agent systems and strategic decision-making.

### ELI5

Imagine you and your friend are contestants on a TV show. Both of you are given two options: to compete or to cooperate. What do you choose? The decision becomes complex as it not only depends on what you want but also on what your friend might choose. Game Theory is a way of figuring out the best decisions in these types of situations.

### In-depth explanation

Game Theory, originated in economics, has become pivotal in multiple fields including computer science, and particularly AI. Essentially it’s concerned with strategic interaction among rational entities, referred to as players or agents.

A game in game theoretical sense comprises of several ingredients: players, actions, and payoffs. Players are decision makers or agents. Actions refer to decisions that players can make. Payoffs indicate outcomes associated with combinations of actions made by all players.

The purpose of a game theoretic analysis is to predict outcomes given the rationality of agents, or to design mechanisms to stimulate certain desirable outcomes. This is achieved by understanding and employing different solution concepts such as pure strategies, mixed strategies, Nash equilibriums, social optima, dominant and dominated strategies.

AI leverages Game Theory in a number of contexts, prominent among them are multi-agent systems and reinforcement learning. Multi-agent systems involve numerous AI agents interacting within a particular environment. Designing rational behavior or predicting outcomes in multi-agent systems often requires knowledge of game theory.

In reinforcement learning, agents learn to make decisions by interacting with their environment and witnessing outcomes of their actions. Game Theory is used to model situations where multiple learning agents interact, designing rewards and punishments, and to derive theoretical guarantees on learning algorithms.

### Related terms

Multi-Agent System, Reinforcement Learning (RL),, Nash Equilibrium, Dominant Strategy, Dominated Strategy, Pure Strategy, Mixed Strategy, Social Optima