Extensive form representation

Definition

Extensive form representation is a way to depict games in game theory that shows the sequential nature of decisions made by players over time. This representation uses a tree-like structure where nodes represent decision points, branches indicate possible actions, and terminal nodes show outcomes based on those actions. It highlights the order of moves and the potential strategies available to players, making it particularly useful for analyzing dynamic strategic interactions.

5 Must Know Facts For Your Next Test

1. The extensive form representation allows for clear visualization of the order of play and the strategies available at each decision point.
2. It can incorporate various types of games, including those with simultaneous moves, although it's primarily designed for sequential games.
3. Players can use backward induction in extensive form games to determine optimal strategies by analyzing future moves and payoffs.
4. Extensive form representations can illustrate imperfect information scenarios through the use of information sets, grouping decision nodes that are indistinguishable to players.
5. This representation is crucial for studying dynamic games like bargaining, auctions, or any context where timing and order of decisions matter.

Review Questions

• How does extensive form representation differ from normal form representation in the context of analyzing strategic interactions?
  • Extensive form representation differs from normal form representation primarily in its depiction of the sequential nature of decisions. While normal form uses a matrix to represent simultaneous choices and payoffs, extensive form presents a tree structure that illustrates the order in which players make their decisions. This distinction allows for a deeper understanding of dynamic interactions, as it captures how earlier choices influence later options and outcomes.
• In what ways can backward induction be applied to extensive form representations to identify optimal strategies?
  • Backward induction involves analyzing an extensive form game starting from the end outcomes and working backwards to determine optimal strategies at each decision node. By evaluating which actions lead to favorable outcomes for players at terminal nodes, one can deduce the best possible move at earlier stages. This method is effective in games where players anticipate future moves, allowing them to make informed decisions based on potential consequences.
• Evaluate how extensive form representations can be utilized to analyze complex games involving imperfect information and uncertainty among players.
  • Extensive form representations are essential for analyzing complex games with imperfect information as they allow for the inclusion of information sets that group decision nodes indistinguishable to players. This feature helps model situations where players may not know the actions taken by others or may have limited information about their opponents' strategies. By representing these uncertainties within the tree structure, analysts can explore how incomplete knowledge affects decision-making and strategy formulation, ultimately providing insights into behavior in strategic environments.

Related terms

Normal form representation: A matrix-based representation of a game that outlines the strategies and payoffs for each player, focusing on simultaneous decision-making.

Nash Equilibrium:

A situation in a game where no player can benefit from changing their strategy while the other players keep theirs unchanged, indicating stable outcomes.

Subgame Perfect Equilibrium:

An extension of Nash Equilibrium applicable in extensive games, where players' strategies constitute a Nash Equilibrium in every subgame.