Game theory is the logical and scientific study that forms a model of the possible interactions between two or more rational players. Here rational means that each player thinks that others are just as rational and have the same level of knowledge and understanding. In the game theory, players deal with the given set of options in a multi-agent situation, it means the choice of one player affects the choice of the other or opponent players.
Game theory and AI are much related and useful to each other. In AI, the game theory is widely used to enable some of the key capabilities required in the multi-agent environment, in which multiple agents try to interact with each other to achieve a goal.
Different popular games such as Poker, Chess, etc., are the logical games with the specified rules. To play these games online or digitally, such as on Mobile, laptop, etc., one has to create algorithms for such games. And these algorithms are applied with the help of artificial intelligence.