Edgeworth's limit theorem¶
Edgeworth's limit theorem is an economic theorem, named after Francis Ysidro Edgeworth, stating that the core of an economy shrinks to the set of Walrasian equilibria as the number of agents increases to infinity.
Core Idea¶
Edgeworth's limit theorem states that, under specified regularity and replication conditions, the core of a pure-exchange economy converges to its set of Walrasian competitive equilibria as the economy becomes large. The core contains feasible allocations that no coalition can block by redistributing its own endowments so every coalition member is better off. A Walrasian allocation, by contrast, is supported by common prices at which each agent optimizes subject to a budget and aggregate markets clear. The theorem links these cooperative and price-mediated solution concepts.
Scope of Application¶
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Core shrinkage. Replicating consumer types limits allocations that coalitions can block as market size grows.
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Walrasian foundations. Competitive price-taking allocations emerge as the limiting cooperative solution under the theorem's conditions.
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Debreu–Scarf economies. Finite replicas provide the canonical framework for approximate convergence.
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Aumann continuum economies. Atomless agents yield an exact core-equivalence result in the corresponding model.
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Coalition analysis. Endowments, preferences, feasibility, and coalition improvement rules determine blocking power.
Clarity¶
Edgeworth's limit theorem connects two different solution concepts in large replicated exchange economies: allocations unblocked by any coalition and allocations supportable by competitive prices. It does not say every finite economy has a singleton core or that market power vanishes without assumptions on preferences, endowments, and replication. Naming the theorem makes the limit operation and the notion of convergence explicit.
Manages Complexity¶
Edgeworth's limit theorem reduces a large replicated exchange economy to the distance between two allocation sets: the cooperative core and Walrasian equilibria. The analyst tracks consumer types, replication factor, preferences, endowments, feasible coalitions, and supporting prices. As replication grows, coalition-blocking possibilities become dense enough to eliminate allocations far from competitive support. Small-economy bargaining power and large-economy price-taking form branches of one convergence argument.
Abstract Reasoning¶
Limit move. From a sequence of exchange economies whose individual influence vanishes, infer convergence of core allocations toward competitive allocations under the theorem's assumptions. Replica move. Compare enlarged replicas to isolate what changes because the market thickens rather than because preferences or endowments change. Blocking move. Test whether coalitions can improve upon an allocation and relate shrinking blocking power to price-supported outcomes. Assumption move. Check convexity, continuity, and replication conditions before applying the conclusion. Boundary move.
Knowledge Transfer¶
Within the home domain. Edgeworth's limit theorem transfers across general-equilibrium theory, cooperative games, and replica economies where the core of increasingly large exchange economies approaches competitive allocations under specified convexity and regularity assumptions. Blocking coalitions, replication, price support, and convergence retain formal roles. Beyond the home domain (C — theorem). It applies literally to economic models satisfying those hypotheses; parallels to “large groups becoming competitive” elsewhere are analogy. Its boundary is sharp: finite cores need not equal equilibria, nonconvexities or market power can defeat convergence, and the theorem does not establish empirical price-taking from population size alone.
Relationships to Other Abstractions¶
Current abstraction Edgeworth's limit theorem Domain-specific
Parents (1) — more general patterns this builds on
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Edgeworth's limit theorem presupposes Convergence Prime
Edgeworth's limit theorem structurally presupposes Convergence rather than being a subtype of it.
Hierarchy path (1) — routes to 1 parentless root
- Edgeworth's limit theorem → Convergence
Neighborhood in Abstraction Space¶
Edgeworth's limit theorem sits in a moderately populated region (55th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Game-Theoretic Models & Paradoxes (37 abstractions)
Nearest neighbors
- Arrow–Debreu Model — 0.87
- Perfect Competition — 0.86
- Coase Theorem — 0.86
- Pirate game — 0.85
- Mixed Strategy Equilibrium — 0.84
Computed from structural-signature embeddings · 2026-10-08