CORE: Central Regions in Economy and Cooperative Game Theory

Explore the concept of CORE, focusing on its dual definition in economics as central regions and in game theory as a set of feasible allocations. Understand historical context, key events, detailed explanations, models, and its significance.

Historical Context

The term “core” has dual meanings across economics and game theory:

1. Core-Periphery Model: This model was initially introduced by John Friedmann in the 1960s and popularized by economists like Paul Krugman. It provides a framework for understanding economic inequalities between central (core) and outlying (periphery) regions within and across countries.

2. Core in Game Theory: Introduced in the 1950s by economists such as Lloyd Shapley and Martin Shubik, the core in cooperative game theory is a set of allocations where no subset of agents (coalition) can reallocate resources among themselves to make every member of that coalition better off.

Types/Categories

Core-Periphery Model

1. Regional Core: Highly developed urban centers with significant economic activities.
2. Global Core: Developed countries with advanced infrastructure, high GDP, and robust trade networks.

Core in Game Theory

1. Economic Core: Allocations within an economy that cannot be improved upon by any coalition of consumers.
2. Game Theory Core: Allocations in a cooperative game where no coalition can improve the members’ outcomes by reallocating resources.

Key Events

• 1960s: Introduction and development of the Core-Periphery Model by John Friedmann.
• 1953: Shapley and Shubik publish works that formalize the concept of the core in cooperative games.

Detailed Explanations

Core-Periphery Model

The Core-Periphery Model illustrates economic disparity:

• Core Regions: Characterized by high population density, advanced infrastructure, and concentrated economic activities.
• Periphery Regions: Less developed, with sparse populations and poorer communication networks.

Core in Game Theory

In economics, the core refers to:

• Feasible Allocations: Resource distributions that can’t be improved by any coalition.
• Edgeworth Box: Visual representation in a two-agent economy showing the core as Pareto-efficient allocations preferable to the initial endowment.

Mathematical Formulas/Models

Edgeworth Box Model

Consider a two-agent economy with the following representation:

    graph TB
	    start((Initial Endowment))
	    pareto1((Pareto Efficient))
	    pareto2((Pareto Efficient))
	    pareto3((Pareto Efficient))
	
	    start --> pareto1
	    start --> pareto2
	    start --> pareto3

• Core Convergence Theorem: As the number of agents increases, the core converges to competitive equilibria.

Importance and Applicability

• Economic Planning: Identifying core regions helps allocate resources efficiently and develop strategies to reduce regional disparities.
• Game Theory: Ensuring allocations are within the core helps in achieving fair and stable outcomes.

Examples and Considerations

Examples

• Core Regions: New York City, Tokyo, and London are global economic cores.
• Core Allocations: In a market, competitive equilibria usually align with core allocations.

Considerations

• Infrastructure Investments: Building infrastructure in peripheral regions can help reduce economic disparities.
• Coalition Stability: Ensuring allocations are within the core increases stability in cooperative settings.

Related Terms with Definitions

• Pareto Efficiency: An allocation where no individual can be made better off without making someone else worse off.
• Coalition: A group of agents who can collaborate to achieve better outcomes.

Comparisons

• Core vs Periphery: Core regions have more economic activities and better infrastructure than periphery regions.
• Core vs Competitive Equilibria: Core allocations become competitive equilibria as the number of participants increases.

Interesting Facts

• Historical Impact: The core-periphery model has been pivotal in regional development policies worldwide.
• Mathematical Significance: The core concept has deep implications in mathematical economics and optimization.

Inspirational Stories

• Economic Revivals: Countries like South Korea transitioned some peripheral regions into core regions through strategic investments in education and infrastructure.

Famous Quotes

• “In the long run, we are all dead.” — John Maynard Keynes (highlighting the importance of short-term core strategies).

Proverbs and Clichés

• “The rich get richer and the poor get poorer.” (Describes core-periphery disparity)

Expressions, Jargon, and Slang

• “Economic Hub”: Often used to describe core regions.
• “Coalition-proof”: An allocation is stable against any coalition’s efforts to change it.

FAQs

Why are core regions important in economic planning?

Core regions are vital as they drive economic growth and development.

What ensures an allocation is in the core in game theory?

An allocation is in the core if no coalition can make its members better off by reallocating resources among themselves.

References

1. Friedmann, J. (1966). Regional Development Policy: A Case Study of Venezuela.
2. Shapley, L. S., & Shubik, M. (1953). A Method for Evaluating the Distribution of Power in a Committee System.

Summary

The term “CORE” has significant implications both in regional economics and cooperative game theory. Understanding the core-periphery model helps in addressing economic disparities, while core allocations in game theory ensure stable and fair outcomes in cooperative settings. Recognizing the importance of core regions and allocations is essential for effective economic planning and achieving optimal resource distribution.