Extensive form game

Definition

An extensive form game is a representation of a strategic situation where players make decisions at different points in time, often depicted using a tree-like structure. This format allows for the modeling of sequential moves, showing how players' choices lead to different outcomes and enabling the analysis of strategies over time. It is particularly useful for understanding dynamic interactions among players, taking into account their potential actions and reactions at each stage of the game.

5 Must Know Facts For Your Next Test

1. Extensive form games can represent both cooperative and non-cooperative scenarios, allowing players to communicate and potentially form binding agreements or negotiate strategies.
2. The tree structure of extensive form games includes nodes representing decision points, branches for possible actions, and terminal nodes that indicate final outcomes.
3. Backward induction is a method used to analyze extensive form games by solving the game from the end back to the beginning, determining optimal strategies at each decision point.
4. Extensive form games can incorporate imperfect information through information sets, which group decision nodes together when players cannot distinguish between them.
5. These games are particularly useful in scenarios involving bargaining, negotiations, or any situation where the order of play significantly impacts outcomes.

Review Questions

• How does an extensive form game differ from a normal form game in terms of player decision-making?
  • An extensive form game differs from a normal form game primarily in how decisions are made. In an extensive form game, players make decisions sequentially at various points in time, which allows for the consideration of earlier actions when making later choices. In contrast, a normal form game requires players to make their choices simultaneously without knowledge of others' decisions. This sequential aspect in extensive form games enables the modeling of dynamic interactions and strategic dependencies among players.
• Discuss how backward induction is utilized in extensive form games and its significance in determining optimal strategies.
  • Backward induction is a crucial technique used in extensive form games to determine optimal strategies by analyzing the game's outcomes from the end back to the start. By starting at the final decision points, players can deduce which actions will yield the best payoffs based on subsequent moves. This process continues backward through the decision tree until reaching the initial choice. The significance of backward induction lies in its ability to identify subgame perfect equilibria, ensuring that strategies are rational and consistent across all stages of the game.
• Evaluate how information sets in extensive form games contribute to understanding strategic interactions under imperfect information.
  • Information sets in extensive form games play a critical role in understanding strategic interactions when players have imperfect information about one another's choices or states. They group decision nodes together when a player cannot distinguish between them, leading to potential uncertainty about what actions other players have taken. This grouping affects strategy formulation, as players must consider all possible scenarios within an information set when deciding their next move. Evaluating these information sets helps illustrate how limited knowledge influences decision-making and strategy in complex situations.

Related terms

Normal form game: A representation of a strategic game where players make decisions simultaneously, typically displayed in a matrix format.

Payoff: The outcome or benefit that a player receives as a result of the choices made by all players in the game.

Subgame perfect equilibrium: A refinement of Nash equilibrium applicable in extensive form games, where strategies are optimal at every point in the game.