Extensive form representation

Definition

Extensive form representation is a way to model strategic interactions in games using a tree structure that displays the sequential nature of players' decisions over time. This method allows for a clear visualization of the choices available to each player at different points in the game, as well as the outcomes resulting from those choices. It is particularly useful in analyzing dynamic games where timing and order of moves are critical.

5 Must Know Facts For Your Next Test

1. In extensive form representation, nodes represent decision points, branches represent choices, and terminal nodes represent outcomes.
2. This representation can include information sets that show what a player knows when making a decision, especially in games with imperfect information.
3. Extensive form games can illustrate both cooperative and non-cooperative scenarios among players.
4. The use of extensive form representation allows for a better understanding of strategic moves like threats and promises over time.
5. Key concepts like dominant strategies and Nash equilibria can be explored within the context of extensive form games, aiding in predicting player behavior.

Review Questions

• How does extensive form representation enhance our understanding of strategic interactions compared to normal form representation?
  • Extensive form representation enhances our understanding of strategic interactions by providing a detailed view of the sequence of moves and decisions made by players over time. Unlike normal form representation, which summarizes strategies and payoffs in a matrix format, extensive form clearly illustrates the timing and order of actions, allowing for analysis of dynamic scenarios. This helps identify critical moments in gameplay where players may alter their strategies based on previous actions or anticipated future moves.
• Discuss how backward induction is used in extensive form representation to determine optimal strategies.
  • Backward induction is a technique applied in extensive form representation that involves analyzing the game from its end back to the beginning. By starting at the final outcomes and determining the best choices that lead to those outcomes, players can identify optimal strategies at each decision point. This method helps predict player behavior by ensuring that players make decisions that are rational given their knowledge of future possible moves and payoffs.
• Evaluate the role of information sets in extensive form representation and how they affect player strategy in dynamic games.
  • Information sets play a crucial role in extensive form representation as they depict what players know at various points during the game. In situations where players have imperfect information about previous moves or strategies chosen by others, these sets group decision nodes into clusters that represent similar knowledge. This impacts player strategy significantly, as players must make decisions based not only on their own actions but also on their beliefs about opponents' actions. Understanding these information sets is essential for predicting outcomes and analyzing strategic behavior in dynamic games.

Related terms

Normal Form Representation: A matrix representation of a game that displays players' strategies and their corresponding payoffs without indicating the order of play.

Subgame Perfect Equilibrium:

A refinement of Nash Equilibrium applicable in dynamic games, where players' strategies constitute a Nash Equilibrium in every subgame.

Backward Induction: A method used in extensive form games to determine optimal strategies by analyzing the game from the end back to the beginning.