kaal:claim:6607458-022

Proposition 1: if the spaces of generation functions and domain models are nonempty, compact, and convex, and the individual optimization and model-update operators are continuous, then a recursive equilibrium exists by the Brouwer fixed-point theorem.

Proposition 1 (Existence). Let the space of generation functions G_i and domain models M_i admit topologies under which they are nonempty, compact, and convex. Suppose the individual optimization operator and the model-update operator are both continuous. Then a recursive equilibrium exists.

Wulf A. Kaal, Computative Economics A Framework for Economic Analysis under Computational Abundance (2026), VI.B. Existence (Brouwer), p. 18
https://ssrn.com/abstract=6607458 · source PDF

Wulf A. Kaal, Computative Economics A Framework for Economic Analysis under Computational Abundance (2026). SSRN: https://ssrn.com/abstract=6607458

• requires nonempty, compact, convex topologies on generation functions and domain models
• requires continuity of the optimization and model-update operators

conditionsupport: arguedeconomics

• extended_by kaal:claim:6655138-018 Recursive equilibrium under Computative Economics is not static equilibrium but equilibrium over the dynamics ...

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