Subgame

Definition

A subgame is a portion of a larger game that consists of a decision tree starting from a particular node, where the strategies and payoffs are analyzed as if the subgame were an independent game. It allows for examining the strategic interactions and outcomes from a specific point in the larger game's structure. Subgames are crucial for understanding the concept of subgame perfect equilibrium, where strategies must be optimal at every point of the game, not just overall.

5 Must Know Facts For Your Next Test

1. Subgames must contain all possible future decisions that can be made from a particular node, ensuring they retain the structure and payoffs of the original game.
2. In order for a strategy to be considered a subgame perfect equilibrium, it must be an optimal strategy in every subgame of the original game.
3. Not all portions of a game qualify as subgames; to be classified as such, they must start at a decision node and include all subsequent nodes reachable from there.
4. Subgames are essential for analyzing dynamic games where players make decisions sequentially rather than simultaneously.
5. The concept of subgames extends to repeated games, where players face similar decision points across multiple iterations.

Review Questions

• How does identifying subgames help in analyzing players' strategies within a game?
  • Identifying subgames allows analysts to break down complex games into smaller parts, making it easier to evaluate players' strategies at various decision points. This helps in understanding how players will behave under different circumstances and enables the assessment of optimal strategies at each stage. By examining each subgame individually, one can determine whether a player's strategy is robust and effective throughout the entire game.
• Discuss the role of backward induction in finding subgame perfect equilibria and its significance in strategic decision-making.
  • Backward induction is essential in finding subgame perfect equilibria as it involves analyzing the game from its conclusion back to the beginning. By evaluating players' choices at each node starting from the end of the game, one can determine optimal strategies for each player. This process ensures that decisions made earlier are consistent with rational choices throughout all subgames, leading to more stable and predictable outcomes in strategic decision-making.
• Evaluate how understanding subgames can influence economic behavior and strategic interactions in competitive markets.
  • Understanding subgames allows economists and strategists to analyze how firms or individuals make decisions based on anticipated future actions of competitors or other agents. In competitive markets, recognizing the potential future moves of rivals helps businesses formulate strategies that are not only optimal today but also sustainable as market conditions change. This foresight can lead to more informed decision-making and competitive advantages, highlighting the importance of strategic planning in dynamic economic environments.

Related terms

Nash Equilibrium: A situation in a game where no player can benefit by changing their strategy while the other players keep their strategies unchanged.

Extensive Form Game: A representation of a game that shows the order of play, choices available at each decision node, and the payoffs for each outcome, often depicted using a tree diagram.

Backward Induction: A method used to solve extensive form games by analyzing the game from the end backward to determine optimal strategies at each point.