What are the assumptions of perfect information in game theory?

In game theory, perfect information refers to a situation where all players have complete and accurate knowledge about the game, including the rules, strategies, and payoffs. The assumptions of perfect information in game theory are as follows:

1. Common knowledge: It is assumed that all players have the same knowledge about the game, including the number of players, their identities, and the available strategies and payoffs. This assumption ensures that there are no information asymmetries among the players.

2. No uncertainty: Perfect information assumes that there is no uncertainty or randomness involved in the game. Players have full knowledge of the past, present, and future actions and outcomes, allowing them to make rational decisions based on this information.

3. No hidden actions: It is assumed that all players can observe and accurately assess the actions taken by other players. There are no hidden or private actions that can affect the outcome of the game. This assumption ensures that players can make informed decisions based on the actions of others.

4. No hidden information: Perfect information assumes that all players have complete knowledge of the strategies and payoffs of the game. There are no hidden or private information that can give any player an advantage over others. This assumption ensures that all players have equal access to information.

5. Rationality: It is assumed that all players are rational decision-makers who aim to maximize their own payoffs. They have the ability to analyze the available information and choose the best strategy accordingly. This assumption ensures that players make optimal decisions based on their knowledge.

These assumptions of perfect information in game theory provide a simplified framework for analyzing strategic interactions among rational players. However, in real-world situations, these assumptions may not hold, and players may have imperfect or incomplete information, leading to more complex and realistic game scenarios.