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

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.