Extensive Form Game vs. Normal Form Game

Attribute	Extensive Form Game	Normal Form Game
Representation	Tree-like structure	Matrix
Information	Sequential	Simultaneous
Player's view	History-dependent	History-independent
Strategy	Behavioral strategy	Mixed strategy

Definition

Extensive Form Game and Normal Form Game are two common representations of strategic interactions in game theory. In an Extensive Form Game, players make decisions sequentially, with each player knowing the decisions made by the players before them. This is often represented using a game tree. On the other hand, a Normal Form Game is a simultaneous game where players make decisions at the same time without knowing the decisions of the other players. This is typically represented using a matrix.

Information

One key difference between Extensive Form Game and Normal Form Game is the amount of information available to the players. In an Extensive Form Game, players have more information about the decisions made by other players, as they can see the entire history of the game. This can lead to more strategic depth and the ability to anticipate and react to the actions of others. In contrast, in a Normal Form Game, players have less information as they make decisions simultaneously, which can lead to more uncertainty and risk.

Strategy

Another difference between Extensive Form Game and Normal Form Game is the nature of strategic thinking required. In an Extensive Form Game, players must consider not only their current move but also the potential future moves and reactions of other players. This can lead to more complex strategies and the need to think several steps ahead. On the other hand, in a Normal Form Game, players must focus on their immediate move without the ability to anticipate the actions of others, leading to a more straightforward approach to strategy.

Equilibrium

Equilibrium concepts in game theory, such as Nash Equilibrium, also differ between Extensive Form Game and Normal Form Game. In an Extensive Form Game, the concept of Subgame Perfect Equilibrium is often used, which requires players to play optimally at every decision point in the game tree. This can lead to more precise predictions of player behavior and outcomes. In contrast, in a Normal Form Game, Nash Equilibrium is more commonly used, which focuses on stable outcomes where no player has an incentive to deviate unilaterally. This can lead to multiple equilibria and more uncertainty about the final outcome.

Complexity

Extensive Form Game and Normal Form Game also differ in terms of complexity. Extensive Form Games tend to be more complex due to the sequential nature of decision-making and the need to consider multiple possible paths through the game tree. This can lead to more intricate strategies and a higher level of strategic thinking required from the players. On the other hand, Normal Form Games are often simpler in structure, as players make decisions simultaneously and the game is represented in a matrix format. This can make it easier to analyze and understand the game dynamics.

Applications

Both Extensive Form Game and Normal Form Game have their own applications in various fields, such as economics, political science, and biology. Extensive Form Games are often used to model dynamic interactions, such as negotiations, auctions, and strategic decision-making in business. The sequential nature of Extensive Form Games allows for a more realistic representation of real-world scenarios where players have imperfect information and must react to the actions of others. On the other hand, Normal Form Games are commonly used to analyze simultaneous decision-making situations, such as pricing strategies, voting behavior, and coordination games. The simplicity of Normal Form Games makes them easier to apply and analyze in a wide range of contexts.

Conclusion

In conclusion, Extensive Form Game and Normal Form Game are two distinct representations of strategic interactions in game theory, each with its own attributes and applications. Extensive Form Games offer more information, complexity, and strategic depth, while Normal Form Games are simpler and focus on simultaneous decision-making. Understanding the differences between these two forms of games can help analysts and decision-makers choose the most appropriate model for their specific situation and make more informed strategic choices.