# kaal:claim:6607458-022

**Claim.** 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.

**Type.** condition  **Support.** argued

**Holds when.**

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

**Source quote.**

> 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.

**From.** Wulf A. Kaal, *Computative Economics A Framework for Economic Analysis under Computational Abundance* (2026), VI.B. Existence (Brouwer), page 18

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

**Verify.** sha256 of source PDF `75cca35350378eb8904866d068b5d2f3e1504629e6031457ce6c12152a88e3e8` at https://raw.githubusercontent.com/wulfkaal/Academic-Papers/main/papers/pdf/Kaal%20-%202026%20-%20Computative%20Economics%20A%20Framework%20for%20Economic%20Analysis%20under%20Computational%20Abundance.pdf

**Topics.** economics

**Keywords.** existence-proof, brouwer-fixed-point, recursive-equilibrium, compactness, convexity

**Related claims.**

- extended_by: https://wulfkaal.github.io/claims/6655138-018

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