Background
Subgame perfect equilibrium (SPE) is a concept crucial in understanding strategic decision-making within sequential games in economics. This refinement of Nash equilibrium ensures that the strategies not only form a Nash equilibrium in the entire game but also in every subgame, thereby eliminating non-credible threats and moves.
Historical Context
Introduced and popularized in the 1960s by Reinhard Selten, subgame perfect equilibrium addressed some of the limitations of Nash equilibrium, particularly in the context of dynamic games (sequential or extensive-form games). Selten’s work in this area, extending Nash’s insights, was influential enough to earn him a Nobel Memorial Prize in Economic Sciences in 1994.
Definitions and Concepts
Subgame Perfect Equilibrium: A set of strategies where the strategy chosen by each player forms a Nash equilibrium in every subgame of the original game. This is achieved typically through a method known as backward induction.
Major Analytical Frameworks
Classical Economics
Classical economics largely focuses on simple, static models of competition and markets where strategic considerations, as detailed in game theory, are often blurred. Therefore, subgame perfect equilibrium does not typically feature prominently in classical models.
Neoclassical Economics
Neoclassical economics incorporates more detailed modeling of market dynamics and strategic interactions among economic agents. Hence, game theoretical concepts, including subgame perfect equilibrium, become more prominent in scenarios like oligopolistic competition and mechanism design.
Keynesian Economics
While primarily concerned with macroeconomic aggregates and government interventions, the microfoundations of Keynesian models can occasionally make use of game-theoretic concepts to describe the interaction among economic agents or policymakers in sequential decisions.
Marxian Economics
Marxian economics does not typically employ game theory extensively. Hence, subgame perfect equilibrium is not a major focus in this tradition.
Institutional Economics
Subgame perfect equilibrium can play a role in institutional economics when considering how institutions evolve through the strategic interactions of virtue players within given rules over time.
Behavioral Economics
Behavioral economics, while centered on deviations from traditional rationality assumptions, can still apply the concept of subgame perfect equilibrium to understand how real human behavior aligns or deviates from subgame-perfect solutions in strategic situations.
Post-Keynesian Economics
Similar to traditional Keynesian but also delving into strategic interactions between sectors or agents in an economy, game theory, including subgame perfect equilibria, adds depth to the analysis, especially in dynamic contexts.
Austrian Economics
Austrian economics, with its focus on individual actions and market processes over time, can apply subgame perfect equilibrium to analyze entrepreneurial decisions and market adaptations.
Development Economics
Development economics employs subgame perfect equilibrium to design mechanism and incentive structures that promote growth and development, analyzing sequential and strategic interactions between various stakeholders.
Monetarism
While Monetarism primarily focuses on the macroeconomic implications of monetary policy, game theory and subgame perfect equilibrium can be relevant in policy formulation and anticipation of responses from other economic agents.
Comparative Analysis
The use of subgame perfect equilibria varies greatly across schools of economics, aligning more closely with those that incorporate heavy emphasis on strategic decision-making, such as neoclassical and behavioral economics, rather than those focused on broader economic aggregates or historical and socio-economic structures.
Case Studies
- Ultimatum Game: Illustrates the concept as it often represents a situation where subgame perfect equilibrium predictions diverge from real human behavior.
- Stackelberg Competition: Demonstrates how firms’ sequential strategic decisions reach SPE, optimizing their Stackelberg equilibrium strategies.
Suggested Books for Further Studies
- “Game Theory: An Introduction” by Steven Tadelis
- “Strategies and Games: Theory And Practice” by Prajit K. Dutta
- “An Introduction to Game Theory” by Martin J. Osborne
Related Terms with Definitions
- Nash Equilibrium: A situation where no player can increase their payoff by unilaterally deviating from their strategy.
- Backward Induction: A method used in dynamic games to find subgame perfect equilibria by analyzing the game from the end and proceeding backward.
- Sequential Game: A game where players make decisions at different points in time.
