🤖 AI Summary
This study addresses the lack of uniqueness, stability, and attainability of competitive equilibria in general equilibrium theory by modeling the economic system as an asymptotically mean-stationary information process composed of agents with finite information capacity. Within an information-theoretic framework, the authors integrate finite-capacity channel models, statistical dependence operators, and multi-parameter joint limit analysis to rigorously embed the classical Walrasian equilibrium—as a zero-entropy limit—within an adaptive setting for the first time. The analysis demonstrates that as the entropy rate approaches zero and channel capacity diverges, the system converges to a rational expectations competitive equilibrium. Moreover, it uncovers positive-entropy dynamic structures in non-equilibrium states that lie beyond the descriptive scope of classical theory, thereby enriching the dynamic foundations of equilibrium analysis.
📝 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.