By definition, a complete information game must also be a perfect information game.Group of answer choicesTrueFalse

Analyzing the Statement

1. Statement Breakdown: The statement suggests that if a game has complete information, it must also have perfect information. We need to understand the definitions of both complete information and perfect information in the context of game theory.

2. Definitions:

   • Complete Information: A game is said to have complete information if all players know the payoff functions and strategies available to other players.
   • Perfect Information: A game has perfect information if all players are fully aware of all actions that have taken place in the game at all times (e.g., they know the moves of all players before making their own move).

Analysis of the Relationship

3. Comparison:

   • Complete Information Does Not Imply Perfect Information: A game can have complete information where players know the strategies and payoffs of others, but if players do not know previous actions taken by others, it does not have perfect information. An example is a game like poker where players know the payoffs and strategies but not the exact cards held by others.

4. Conclusion: Therefore, a complete information game does not necessarily have perfect information.

Final Answer

False. A complete information game does not imply a perfect information game.