# Game Theory

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Game Theory is a branch of mathematics used to model the strategic interaction between different players in a context with predefined rules and outcomes. Game Theory can be applied in different ambit of Artificial Intelligence:

- Multi-agent AI systems.
- Imitation and Reinforcement Learning (RL).
- Adversary training in Generative Adversarial Network (GAN)s.

Game Theory can also be used to describe many situations in our daily life and Machine Learning models. Game Theory in Artificial Intelligence | Pier Paolo Ippolito - Towards Data Science

For example, a Classification algorithm such as Support Vector Machine (SVM) can be explained in terms of a two-player game in which one player is challenging the other to find the best hyper-plane giving him the most difficult points to classify. The game will then converge to a solution which will be a trade-off between the strategic abilities of the two players (eg. how well the fist player was challenging the second one to classify difficult data points and how good was the second player to identify the best decision boundary).

## Nash Equilibrium

An example of Nash Equilibrium can be when the Support Vector Machine (SVM) classifier agrees on which hyper-plane to use classify our data.

Nash equilibrium is a concept within game theory where the optimal outcome of a game is where there is no incentive to deviate from their initial strategy. More specifically, the Nash equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his chosen strategy after considering an opponent's choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have multiple Nash equilibria or none at all. Nash Equilibrium | James Chen - Investopedia

## Prisoner’s Dilemma

The prisoner's dilemma is a paradox in decision analysis in which two individuals acting in their own self-interests do not produce the optimal outcome. The typical prisoner's dilemma is set up in such a way that both parties choose to protect themselves at the expense of the other participant. As a result, both participants find themselves in a worse state than if they had cooperated with each other in the decision-making process. The prisoner's dilemma is one of the most well-known concepts in modern game theory. Prisoner's Dilemma | Jim Chappelow - Investopedia