Extensive Form Games and Backward Induction Extensive form games are a class of games where players have complete information about the entire game state at...
Extensive form games are a class of games where players have complete information about the entire game state at the start of the game. This allows players to reason about the entire possible path of the game and choose the best course of action.
One way to analyze extensive form games is through the lens of backward induction. This involves breaking down the game into simpler subgames that can be solved independently. The solution to the original game can then be found by applying a systematic procedure to the subgames.
Key characteristics of extensive form games:
Players have complete information about the game state at the start of the game.
Players can reason about the entire possible path of the game.
There are a finite number of possible actions that each player can take.
The game is typically represented using a game tree, where each node represents a possible game state and each edge represents a possible action.
Examples of extensive form games:
Tic-tac-toe: Each player has complete information about the entire board state.
Chess: White has complete information, while Black has complete information in certain special positions.
Poker: Each player has complete information about their hand and the other players' hands.
Backward induction:
Backward induction is a systematic procedure for solving extensive form games. It involves breaking down the game into simpler subgames and finding a solution to each subgame independently. The solution to the original game can then be found by applying a systematic procedure to the subgames.
Benefits of using backward induction:
It provides a systematic way to solve complex extensive form games.
It allows players to reason about the entire game state at the start of the game.
It can be applied to solve games with a finite number of actions.
Limitations of backward induction:
It can be computationally expensive for games with a large number of players or actions.
It can be difficult to choose the right subgames to decompose the game into.
It can be sensitive to the order in which the subgames are solved