Extensive Form

Published Apr 29, 2024

Definition of Extensive Form

Extensive form is a way of representing games that highlights the sequential aspects of decision-making among players. It is commonly used in game theory, a branch of economics that studies strategic interactions among rational players. The extensive form specifies not only the possible strategies each player can adopt but also the order in which they make decisions, the information each player has when making these decisions, and the outcomes associated with each combination of decisions.

Example

Imagine a game between two companies, Company A and Company B, deciding whether to enter a new market. The decision-making process is sequential: Company A decides first whether to enter or not, and then Company B, knowing Company A’s decision, makes its decision. This situation can be represented in an extensive form diagram, where the nodes represent the points at which decisions are made, branches represent the choices available to the players, and the ends of the branches (also known as terminal nodes) represent the final outcomes based on the decisions made by both players.

In this example, if both companies enter the market, they may have to share profits, resulting in a lower payoff for each compared to the scenario where only one enters and monopolizes the market. However, if neither enters, they both forgo potential profits. The extensive form would show all these possibilities, including the payoffs associated with each outcome.

Why Extensive Form Matters

Extensive form representation is crucial for analyzing strategic situations that involve sequential moves, providing insights that are not apparent in strategic (or normal) form representation. It helps in understanding the strategic benefits of being the first or second mover in a market, the role of information at different stages of the game, and how the structure of the game affects the strategies and payoffs of the players.

Understanding extensive form games is essential for economists and strategists in various fields, including business competition, bargaining, and negotiation, as well as in political or military strategy where decisions are made in a sequence and depend on the observed or anticipated actions of others.

Frequently Asked Questions (FAQ)

How does the concept of information sets play into extensive form games?

In the extensive form, information sets are used to represent what a player knows at the time they make a decision. If multiple points in the game are within the same information set, it means the player cannot distinguish between these points when making their decision, highlighting the role of imperfect information. Information sets are crucial for analyzing games where players make decisions with partial knowledge of others’ actions, affecting strategy formulation significantly.

Can extensive form games be converted into strategic (normal) form games?

Yes, extensive form games can be converted into strategic (or normal) form games, although some information might be lost in this translation. The strategic form summarizes the strategies and payoffs in a matrix form without explicitly showing the order of moves or the information available at each decision point, which can simplify analysis but misses the nuanced understanding of the dynamics that extensive form provides.

What role does backward induction play in solving extensive form games?

Backward induction is a method used to solve extensive form games with perfect information by starting from the end (terminal nodes) and working backward to infer the actions at earlier decision points. It helps in determining the optimal strategy of players by considering the best possible response at each stage, given the decisions of other players in subsequent moves. This technique is particularly useful in sequential games where later actions depend on prior ones.

Understanding extensive form games enriches the analysis of strategic interactions by shedding light on the dynamics of sequential decision-making, the strategic advantages of information, and the implications of timing in competitive environments.