Game theory classifies games based on player interactions, timing, and information availability. These categories help us understand how different game structures influence player behavior and outcomes, shaping strategic decision-making in various real-world scenarios.

Cooperative games involve teamwork, while non-cooperative games prioritize individual interests. Zero-sum games create direct competition, but non-zero-sum games allow for mutual benefits. Sequential, simultaneous, and repeated games affect how players make choices and respond to others' actions.

Game Interaction Types

Cooperative and Non-Cooperative Games

• Cooperative games involve players working together to achieve a common goal or maximize their collective payoff
• In cooperative games, players can communicate and make binding agreements to coordinate their strategies
• Non-cooperative games involve players acting independently to maximize their own payoffs without the ability to make binding agreements
• In non-cooperative games, players cannot communicate or coordinate their strategies and must make decisions based on their own interests

Zero-Sum and Non-Zero-Sum Games

• Zero-sum games are a type of game where the total payoff to all players in the game adds up to zero
• In zero-sum games, one player's gain is always equal to another player's loss (Poker, Matching Pennies)
• Non-zero-sum games are a type of game where the total payoff to all players can be greater or less than zero
• In non-zero-sum games, players' interests are not always in direct opposition, and there can be outcomes where all players benefit or all players lose (Prisoner's Dilemma, Battle of the Sexes)

Game Timing and Sequence

Sequential and Simultaneous Games

• Sequential games are played in turns, with players making their moves one after another
• In sequential games, players have knowledge of the moves made by previous players before making their own decisions (Chess, Stackelberg competition)
• Simultaneous games involve players making their moves at the same time without knowledge of the other players' actions
• In simultaneous games, players must anticipate the moves of their opponents and make decisions based on their beliefs about the other players' strategies (Rock-Paper-Scissors, Cournot competition)

Repeated Games

• Repeated games involve playing the same game multiple times, allowing players to observe and respond to each other's strategies over time
• In repeated games, players can use strategies that involve rewards and punishments based on the actions taken in previous rounds (Tit-for-Tat in the Iterated Prisoner's Dilemma)
• Repeated interactions can lead to the emergence of cooperation, even in non-cooperative games, as players have an incentive to maintain a good reputation and avoid retaliation

Information Availability

Perfect and Imperfect Information Games

• Perfect information games are those in which all players have complete knowledge of the game's structure, payoffs, and the actions taken by other players
• In perfect information games, there is no hidden information, and players can make fully informed decisions (Chess, Go)
• Imperfect information games involve situations where players do not have complete knowledge of the game's structure, payoffs, or the actions taken by other players
• In imperfect information games, players must make decisions based on incomplete or uncertain information (Poker, Auctions)
• Imperfect information can arise from various factors, such as simultaneous moves, hidden actions, or private information held by some players