Extensive form game

Definition

An extensive form game is a representation of a game that captures the sequence of players' moves, their choices, and the potential outcomes, usually illustrated through a game tree. This format allows for a clear visualization of how decisions unfold over time, including the strategic interactions among players and the possible paths the game can take based on their choices. Extensive form games are particularly useful for analyzing situations where timing and order of moves matter.

5 Must Know Facts For Your Next Test

1. Extensive form games can include both simultaneous and sequential moves, allowing for complex interactions between players.
2. Each node in a game tree represents a decision point where a player chooses among available actions, leading to different branches representing possible future scenarios.
3. Extensive form games can incorporate chance events, represented by chance nodes in the game tree, showing the role of randomness in determining outcomes.
4. Players in extensive form games may have imperfect information about others' past actions, which can affect their decision-making and strategy.
5. The concept of Nash equilibrium can be extended to extensive form games by considering best responses at each decision point in the game tree.

Review Questions

• How do extensive form games differ from normal form games in terms of representation and strategic interaction?
  • Extensive form games differ from normal form games primarily in their representation; they use a game tree to illustrate sequential moves and decision points, while normal form games present strategies in a matrix format. This difference allows extensive form games to capture more complex strategic interactions, including how players respond to others' actions over time. In extensive form, the order of moves is crucial as it influences players' decisions and potential outcomes.
• Discuss the significance of subgames within extensive form games and how they contribute to overall strategy analysis.
  • Subgames are significant in extensive form games because they allow analysts to isolate and study specific segments of the game as independent entities. By examining subgames, players can identify optimal strategies within those smaller contexts that may impact overall strategy in the larger game. Understanding subgames also facilitates backward induction, where players anticipate future moves based on current strategies and make informed decisions at earlier stages.
• Evaluate how backward induction can be applied in extensive form games to derive optimal strategies and predict player behavior.
  • Backward induction is a powerful technique used in extensive form games to derive optimal strategies by starting from the game's final outcomes and working backward through the decision nodes. By analyzing what each player would do at every point if they were rational and aiming to maximize their payoff, one can predict how they would act throughout the entire game. This approach not only helps identify Nash equilibria but also clarifies how timing and order influence strategic choices, enabling players to formulate effective plans based on anticipated responses from opponents.

Related terms

game tree: A graphical representation of an extensive form game that illustrates the sequence of moves, choices available to players at each decision point, and the possible outcomes of the game.

subgame: A part of an extensive form game that can be analyzed as a separate game, starting from any decision node within the larger game tree and including all subsequent moves.

backward induction:

A method used in extensive form games to determine optimal strategies by analyzing the game from its final outcomes back to the initial decisions.