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arxiv: 2606.28295 · v1 · pith:HVHZCNCEnew · submitted 2026-06-26 · 💰 econ.TH

Equilibrium as a Limit: The Competitive Canon Nested in an Adaptive, Information-Theoretic Economy

Avishek Bhandari This is my paper

Pith reviewed 2026-06-29 01:33 UTC · model grok-4.3

classification 💰 econ.TH
keywords competitive equilibriumWalrasian equilibriuminformation theoryadaptive economyentropy rategeneral equilibriumrational expectations
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The pith

The Walrasian equilibrium arises precisely as a limit point in an adaptive economy modeled as an information source with finite-capacity agents.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models the economy as an asymptotically mean stationary information source with agents acting as finite-capacity information channels. It shows that the standard competitive equilibrium of general equilibrium theory is recovered exactly when three parameter limits are taken along a scaling path and two fixed-point conditions are met. In this limit the entropy rate reaches zero, agent channel capacity diverges, and selection becomes infinitely sharp, causing the system to cease coevolving and satisfy the axioms of the competitive canon. Away from the limit the model is a strict generalization that carries positive entropy and a dependence structure not expressible in the equilibrium primitive. This provides a result-by-result correspondence with existence theorems, indeterminacy results, and recovery of regular economies.

Core claim

The competitive, rational expectations equilibrium is recovered exactly as a joint limit taken along an explicit scaling path in the adaptive order. Three parameter limits and two fixed-point conditions deliver it: the entropy rate falls to zero, agent channel capacity diverges, selection intensity grows infinitely sharp, adaptive learning reaches its expectationally stable rest point, and the recovered structure ceases to coevolve. At that corner the limiting object satisfies the axioms of the canon and its rest state is a Walrasian equilibrium.

What carries the argument

An asymptotically mean stationary information source carrying a partially identified operator of statistical dependence, with agents as finite-capacity information channels, under three parameter limits and two fixed-point conditions.

If this is right

  • The limiting object satisfies the axioms of general equilibrium theory.
  • The rest state is a Walrasian equilibrium.
  • The model provides a correspondence with existence, Sonnenschein-Mantel-Debreu indeterminacy, and regular economies recovery.
  • Away from the limit, the adaptive economy carries a positive entropy rate and a recovered dependence structure that the equilibrium primitive cannot express.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real economies might exhibit positive entropy rates, implying they are always in the generalized adaptive regime rather than at equilibrium.
  • Policy interventions could be analyzed by their effect on the scaling parameters that approach the equilibrium limit.
  • Stability questions in general equilibrium might be re-examined through the lens of the fixed-point conditions in the information-theoretic model.

Load-bearing premise

The economy is an asymptotically mean stationary information source populated by agents that are finite-capacity information channels.

What would settle it

An explicit construction showing that the three parameter limits and fixed-point conditions fail to produce a structure satisfying the Walrasian excess demand axioms.

Figures

Figures reproduced from arXiv: 2606.28295 by Avishek Bhandari.

Figure 1
Figure 1. Figure 1: An observationally equivalent pair. The operators [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
read the original abstract

The competitive equilibrium of general equilibrium theory exists as a fixed point and is, by the theorys own results on aggregate excess demand, in general silent on whether that fixed point is unique, stable, or attained. This paper takes the economy to be not a configuration to be solved for but a process to be recovered, an asymptotically mean stationary information source carrying a partially identified operator of statistical dependence, populated by agents that are finite-capacity information channels. Within this adaptive order the competitive, rational expectations equilibrium is recovered exactly, as a joint limit taken along an explicit scaling path. Three parameter limits and two fixed-point conditions deliver it, the entropy rate falls to zero, agent channel capacity diverges, selection intensity grows infinitely sharp, adaptive learning reaches its expectationally stable rest point, and the recovered structure ceases to coevolve. At that corner the limiting object satisfies the axioms of the canon and its rest state is a Walrasian equilibrium, away from it the adaptive economy is a strict generalisation, carrying a positive entropy rate and a recovered dependence structure that the equilibrium primitive cannot express. We give the nesting as a theorem, establish the result by result correspondence with existence, with the Sonnenschein Mantel Debreu indeterminacy, and with the regular economies recovery, and characterise exactly what the equilibrium limit erases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. The paper claims that Walrasian competitive equilibrium is recovered exactly as a joint limit of an adaptive information-theoretic economy, modeled as an asymptotically mean stationary information source populated by finite-capacity agent channels. The limit is taken along an explicit scaling path defined by three parameter limits and two fixed-point conditions; under these the entropy rate reaches zero, channel capacity diverges, selection intensity becomes infinitely sharp, adaptive learning attains its expectationally stable rest point, and coevolution ceases. The limiting object satisfies the standard GE axioms, with explicit correspondences to existence, Sonnenschein-Mantel-Debreu indeterminacy, and regular economies; away from the limit the model is a strict generalization carrying positive entropy rate and a dependence structure not expressible in the equilibrium primitive.

Significance. If the nesting theorem and its derivations hold, the work supplies an explicit embedding of the competitive canon inside a broader adaptive framework together with a precise characterization of the information erased by the limit. The result-by-result mapping to existence, SMD, and regularity results, combined with the parameter-free scaling path, would constitute a substantive contribution to the foundations of general equilibrium theory.

minor comments (1)
  1. [Abstract] Abstract: 'theorys own results' should read 'theory's own results'.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful summary of the manuscript and the positive assessment of its potential contribution. The recommendation for minor revision is noted.

Circularity Check

0 steps flagged

No significant circularity; explicit limit nesting from general adaptive model to canonical equilibrium.

full rationale

The paper defines an asymptotically mean stationary information source populated by finite-capacity channels as the primitive economy, then recovers Walrasian equilibrium exactly as the joint limit along three parameter scalings and two fixed-point conditions (entropy rate to zero, channel capacity to infinity, selection intensity to infinity, learning to rest point, coevolution ceases). The general case retains positive entropy and recovered dependence structure that the equilibrium primitive cannot express, establishing a strict generalization with explicit result-by-result correspondence to existence, SMD indeterminacy, and regular economies. No equations or steps in the abstract or description reduce the target equilibrium to a fitted input, self-definition, or self-citation chain; the derivation is a standard mathematical nesting theorem from broader process to special case and is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

Extracted solely from the abstract; full paper may contain additional parameters or axioms. The model introduces several new modeling primitives whose independent support is not shown.

axioms (2)
  • domain assumption The economy is an asymptotically mean stationary information source carrying a partially identified operator of statistical dependence.
    Stated as the foundational modeling choice in the abstract.
  • domain assumption Agents are finite-capacity information channels.
    Core modeling assumption used to define the adaptive order.
invented entities (2)
  • entropy rate of the economy no independent evidence
    purpose: Quantifies ongoing information flow and disorder; set to zero in the equilibrium limit.
    Introduced as a state variable that must reach zero for the limit to hold.
  • selection intensity no independent evidence
    purpose: Sharpness parameter that becomes infinite in the limit.
    New parameter controlling how sharply adaptation selects outcomes.

pith-pipeline@v0.9.1-grok · 5761 in / 1579 out tokens · 32475 ms · 2026-06-29T01:33:11.854264+00:00 · methodology

discussion (0)

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Reference graph

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