Subgames

Definition

Subgames are segments of a game that can be analyzed independently from the larger game structure. These portions are defined by the remaining choices available to players after a certain point in the game, and they maintain their own strategic elements and decision-making processes. Understanding subgames is crucial for analyzing complex games, particularly when determining strategies and outcomes in the context of subgame perfect equilibrium.

5 Must Know Facts For Your Next Test

1. Subgames are formed when a player has made some decisions, and the remaining choices create a smaller game within the original game.
2. Every subgame must start from a decision node where a player can make a choice, meaning it has to represent a full structure that includes all future moves from that point onward.
3. In order for a strategy profile to be considered subgame perfect, it must be Nash Equilibrium not only for the entire game but also for every subgame.
4. Subgame perfect equilibrium ensures that players make optimal decisions at every stage of the game, which means they can't improve their outcome by deviating from their strategy in any subgame.
5. Analyzing subgames helps in identifying strategic commitments and contingent strategies that influence players' decisions throughout the game.

Review Questions

• How do subgames enhance the analysis of strategic decision-making within extensive form games?
  • Subgames allow players to focus on smaller, manageable parts of a larger game, making it easier to analyze potential strategies and outcomes. By breaking down the extensive form game into subgames, players can evaluate their decisions based on what has already occurred and anticipate future moves. This modular approach helps in understanding how earlier decisions impact later options and assists in finding optimal strategies at each decision point.
• Discuss the relationship between subgames and backward induction in determining subgame perfect equilibria.
  • Backward induction is crucial for solving games by working backward from the end of the game to determine optimal strategies. When analyzing subgames through this method, players assess what decisions would lead to favorable outcomes starting from the last moves of each subgame. This process ensures that strategies are not only optimal for the overall game but also for each individual subgame, reinforcing the concept of subgame perfect equilibrium.
• Evaluate how understanding subgames contributes to identifying strategic commitments among players in dynamic environments.
  • Understanding subgames helps players recognize moments where they can make strategic commitments that may influence future moves. In dynamic environments, where players' actions affect subsequent choices, evaluating subgames allows for planning around potential threats or opportunities that arise later in the game. By identifying these key points within subgames, players can devise contingent strategies that enhance their chances of success and deter opponents from deviating from anticipated paths.

Related terms

Extensive Form Game: A representation of games that shows the sequential nature of players' moves, often depicted in a tree structure with branches representing possible actions.

Nash Equilibrium:

A situation in a game where no player can benefit by unilaterally changing their strategy, given the strategies of all other players remain unchanged.

Backward Induction: A method used to solve extensive form games by analyzing the game from the end and determining optimal strategies by moving backward to the beginning.