Multiple Equilibrium

Background

The concept of multiple equilibrium refers to situations within an economic model where more than one equilibrium solution exists. The equilibrium of a system depicts the state where supply equals demand or where actions within game theory result in stable outcomes.

Historical Context

The concept of equilibrium has been a foundational aspect of economic study since the works of Adam Smith. In the 20th century, the advent of game theory and advances in mathematical economics refined the understanding of equilibrium, paving the way for the analysis of multiple equilibria in various economic contexts.

Definitions and Concepts

Multiple Equilibrium: The presence of more than one solution to a set of equilibrium equations within an economic model. These solutions can either be distinct and localized (locally unique equilibria) or part of a continuum of solutions.
Locally Unique Equilibria: Specific equilibrium points which exist separately, often occurring in odd numbers.
Nash Equilibrium: A set of strategies in a game where no player has anything to gain by changing their own strategy unilaterally. In the context of multiple equilibrium, the computation of Nash equilibria becomes crucial.

Major Analytical Frameworks

Classical Economics

Traditionally, classical economics assumes a single equilibrium driven by free market mechanisms. The idea of multiple equilibria challenges this perspective, suggesting that markets may settle at different points based on initial conditions or external shocks.

Neoclassical Economics

Neoclassical frameworks incorporate mathematical models revealing scenarios where multiple equilibria arise, especially in markets with increasing returns to scale or where agents have limited information.

Keynesian Economics

In Keynesian interpretations, multiple equilibria can result from hysteresis or demand-driven cycles. Economic output can stabilize at various levels due to varying expectations and fiscal policies.

Marxian Economics

From a Marxian standpoint, equilibria emerging from capitalist cycles could vary based on class struggle and economic exploitation, pointing to systemic imbalances.

Institutional Economics

Institutions can impact the pathways leading to multiple equilibria, where legal frameworks, norms, and policies shape economic outcomes distinctly in different contexts.

Behavioral Economics

Highlighting psychological and social factors, behavioral economics explores how bounded rationality and other cognitive biases can lead to multiple equilibrium scenarios.

Post-Keynesian Economics

Focusing on demand-driven growth, post-Keynesian theories argue that investment cycles and financial market conditions can produce varying equilibria in economies.

Austrian Economics

Emphasizes the role of entrepreneurial discovery and market processes, suggesting that multiple equilibria could reflect different expressions of consumer preferences and technological innovations.

Development Economics

Here, multiple equilibria highlight the possible growth trajectories for developing nations influenced by externalities, capital trapping, and path dependency.

Monetarism

Monetarist views, especially concerning monetary policy’s influence, acknowledge multiple equilibria in price levels and growth rates due to varying levels of money supply and velocity.

Comparative Analysis

Analyzing multiple equilibrium across different economic schools of thought reveals diverse implications and policy prescriptions. For instance, Keynesian approaches might suggest intervention to shift equilibria, while neoclassical thought supports frameworks emphasizing market-led adjustments.

Case Studies

Game Theory Example: In strategic games, real-world application often identifies multiple Nash equilibria, whereby two firms could both set prices high or engage in a price war, depending on initial strategic moves.
Market Examples: Financial markets can present multiple equilibrium scenarios through phenomena like arbitrage and speculative attacks, as observed in currency crises and stock markets.

Suggested Books for Further Studies

“Game Theory” by Drew Fudenberg and Jean Tirole
“Microeconomic Theory” by Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green
“Equilibrium in Economics” by Denton Morrison
“Increasing Returns and Path Dependence in the Economy” by W. Brian Arthur

Nash Equilibrium: A situation in a game where no player can benefit by unilaterally changing their strategy, given other players’ strategies.
Pure Strategy Equilibrium: A strategic choice in game theory where a player’s strategy entails a specific action with certainty.
Mixed Strategy Equilibrium: A scenario in game theory where players randomly choose among strategies according to specific probabilities.
Path Dependence: The idea that decisions and outcomes are shaped by historical trajectories and initial conditions.