Extensive form games

Definition

Extensive form games are a type of game representation that allows for a detailed visualization of players' strategies, decisions, and possible outcomes over time. They are depicted using a tree-like structure, where nodes represent decision points and branches represent the choices available to players. This format is particularly useful in analyzing dynamic interactions, where the order of moves and possible subgames play a crucial role in determining optimal strategies.

5 Must Know Facts For Your Next Test

1. Extensive form games can include elements like chance events, allowing for a more comprehensive representation of uncertainty and randomness in player decisions.
2. The concept of subgames is integral to extensive form games, as it allows players to analyze smaller parts of the game and their corresponding equilibria.
3. A subgame perfect equilibrium is a refinement of Nash equilibrium specifically designed for extensive form games, ensuring that players' strategies are optimal at every possible point in the game.
4. In extensive form games, players may have incomplete information about others' payoffs or strategies, which can significantly affect their decision-making process.
5. The structure of extensive form games can illustrate various scenarios, such as sequential moves and simultaneous moves, providing insights into strategic interactions over time.

Review Questions

• How do extensive form games differ from normal form games in terms of representation and strategic analysis?
  • Extensive form games differ from normal form games primarily in their representation. While normal form games present strategies and payoffs in a matrix format suitable for simultaneous decisions, extensive form games use a tree structure that illustrates sequential decision-making over time. This allows for a clearer understanding of how earlier moves influence later choices, enabling a deeper analysis of strategic interactions, including the examination of subgames and the use of backward induction.
• Discuss the importance of subgame perfect equilibrium in extensive form games and how it applies to real-world decision-making scenarios.
  • Subgame perfect equilibrium is crucial in extensive form games because it ensures that players’ strategies are not only optimal at the outset but also at every point in the game. This concept prevents players from making threats or promises that could be disregarded later on. In real-world decision-making scenarios, such as negotiations or strategic business moves, recognizing subgame perfect equilibria helps individuals anticipate reactions and maintain credibility throughout the interaction, leading to more consistent and reliable outcomes.
• Evaluate how extensive form games can incorporate elements of chance and incomplete information, and discuss their implications for strategy development.
  • Extensive form games can incorporate elements of chance by including chance nodes that represent uncertain outcomes affecting players' decisions. Additionally, they can address incomplete information by allowing players to have varying knowledge about others' payoffs or strategies. These aspects complicate strategy development since players must consider not only their own actions but also the probabilistic outcomes and potential hidden information held by others. This dynamic can lead to more nuanced strategies that account for risk management and adaptive responses to uncertainty during gameplay.

Related terms

Normal form games: A representation of games in which players' strategies and payoffs are summarized in a matrix format, showing the possible outcomes based on simultaneous decisions.

Payoff matrix: A table that describes the payoffs received by each player in a game for every combination of strategies they might choose.

Backward induction: A method used to solve extensive form games by analyzing the game from the end back to the beginning, allowing players to determine optimal strategies at each decision point.