Explain the concept of common knowledge in game theory.

Common knowledge in game theory refers to information that is known by all players in a game.

In game theory, common knowledge is a crucial concept that helps to determine the outcome of a game. It refers to information that is known by all players in a game, and that they know is known by all other players. This means that each player knows that every other player knows the information, and so on.

For example, in a game of poker, the fact that each player has two cards is common knowledge, as is the fact that the game involves betting and bluffing. However, the specific cards held by each player are not common knowledge, as they are only known by the individual player.

Common knowledge can have a significant impact on the strategies that players adopt in a game. If a piece of information is common knowledge, then it is likely to influence the behaviour of all players in the game. This can lead to the emergence of certain equilibria, where all players adopt strategies that are mutually beneficial.

Overall, common knowledge is an important concept in game theory that helps to determine the outcome of a game. By understanding what information is common knowledge, players can make more informed decisions about the strategies they adopt, and increase their chances of success.