# kaal:claim:6607458-023

**Claim.** Proposition 2: if the composite best-response map is a contraction under an appropriate metric, the recursive equilibrium is unique and iteration of the map from any starting point converges to it, by the Banach fixed-point theorem.

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

**Holds when.**

- requires the composite best-response map to be a contraction under an appropriate metric

**Source quote.**

> Suppose the composite best-response map Ψ is a contraction on the product space of generation functions and domain models under an appropriate metric. Then there exists a unique recursive equilibrium, and the sequence (G_t, M_t) generated by repeated application of Ψ from any starting point

**From.** Wulf A. Kaal, *Computative Economics A Framework for Economic Analysis under Computational Abundance* (2026), VI.C. Uniqueness and Convergence (Banach), page 19

**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.** institutional-design

**Keywords.** uniqueness, convergence, banach-fixed-point, contraction-mapping

**Related claims.**

- extended_by: https://wulfkaal.github.io/claims/6655138-032
- extended_by: https://wulfkaal.github.io/claims/6655138-029

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