Game Theory Questions Medium
In game theory, extensive form games are a way to represent and analyze sequential decision-making situations. They are used to model games where players make decisions in a specific order, taking into account the actions and decisions of other players.
The extensive form of a game consists of a game tree, which represents the sequence of actions and decisions that players can take. The tree starts with a single node, called the root, which represents the initial decision point. From the root, branches extend to different nodes, representing the possible actions that players can take at each decision point. These nodes are connected by edges, which indicate the order in which decisions are made.
Each player in the game is represented by a different branch of the tree, and their decisions are represented by the nodes along their branch. The game tree also includes information about the payoffs or outcomes associated with each possible combination of actions taken by the players.
Extensive form games allow for the analysis of strategic interactions, as players can anticipate the actions and decisions of others and choose their own actions accordingly. They provide a framework to study concepts such as equilibrium, optimal strategies, and the concept of backward induction, where players reason backward from the final decision point to determine their optimal actions.
Overall, extensive form games provide a visual representation of sequential decision-making situations in game theory, allowing for the analysis of strategic interactions and the determination of optimal strategies for players.