Background
In the study of game theory, which examines the strategic interaction between rational decision-makers, the concept of a subgame plays a crucial role. A subgame is a subset of a larger sequential game. The subgame begins at a particular node in the game’s decision tree, where every player has full knowledge of all previous actions taken by other players. Understanding subgames is fundamental to applying game theoretic models in both economic and various other settings.
Historical Context
The idea of subgames first gained prominence in economic theories and operations research, notably through the work of John Nash and others who contributed widely to the development of game theory in the mid-20th century. Selten’s refinement of the Nash Equilibrium into Subgame Perfect Equilibrium brought significant focus onto the analysis of subgames, providing a systematic way to consider strategies as games play out sequentially.
Definitions and Concepts
- Subgame: A subset or part of a sequential game starting from a node (decision point) where players are fully aware of all preceding actions.
- Sequential Game: A type of game where players make decisions one after another, with each decision potentially observable by the other players.
- Perfect Information Game: A subcategory of sequential games where every player knows all the actions that have proceeded at every point of the game.
Major Analytical Frameworks
Classical Economics
Classical economics does not directly address subgames, as it primarily focuses on broader market dynamics rather than strategic decision-making processes typical in game theory.
Neoclassical Economics
While typically not focused on strategic interaction, some neoclassical models incorporate game theoretic concepts, including subgames, to better predict outcomes in oligopolistic markets and bargaining situations.
Keynesian Economic
Keynesian economics deals more with macroeconomic aggregates and does not specifically address subgames or game theory.
Marxian Economics
Marxian economics is generally centered on class struggles and resource distribution and does not incorporate strategic decision-making frameworks like subgames.
Institutional Economics
Explores complex interactions within institutions that could, at times, be modeled using layered, interconnected subgames.
Behavioral Economics
Behavioral economics occasionally uses game theory concepts such as subgames to understand real-life deviations from theoretically predicted rational behavior.
Post-Keynesian Economics
This emerges beyond discussing subgames directly yet supports the use of game theory for modeling complex economic dynamics.
Austrian Economics
Austrian economics focuses more on individual decision-making processes and subjectivity, seldom employing formal game theory methodologies like subgames.
Development Economics
Game theory, including subgame analysis, can be applied to understand strategic decisions in areas such as negotiations, policy implementations, and microcredit games in development contexts.
Monetarism
Primarily concerned with broader economic indicators rather than microscopic strategic analysis typical in subgame theory.
Comparative Analysis
Subgames are particularly analyzed within sequential decisions and negotiations. Their correct identification and understanding can often fall between strategic planning, recursive decision-making principles, and observable outcomes decided by players. By examining subgames, economists and theorists can predict moves and counter-moves, refining mutual expectations based on the game’s pathway which benefits applications in markets or strategy comparisons.
Case Studies
- Repeated Prisoner’s Dilemma: Analysis of subgames to determine trust and repeated interactions.
- Bargaining and Negotiation Models where the strategies involve sequential offers.
- Market Entry Games assessing the strategies for firms entering competitive markets with pre-established players.
Suggested Books for Further Studies
- “Game Theory” by Drew Fudenberg and Jean Tirole
- “An Introduction to Game Theory” by Martin J. Osborne
- “Games and Information: An Introduction to Game Theory” by Eric Rasmusen
Related Terms with Definitions
- Nash Equilibrium: A situation in a strategic game where no player can benefit by changing their strategy while the other players keep theirs unchanged.
- Subgame Perfect Equilibrium (SPE): A refinement of Nash Equilibrium applied within each subgame of the original game.
- Perfect Information: A condition where all players know the moves previously made by all other players in the game.
- Sequential Game: A game where players take turns making decisions over time, often allowing for the development of subgames.
By understanding the concept of subgames, one is better positioned to analyze and predict strategic interactions in various economic and non-economic environments.
