kaal:claim:6607458-023

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.

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

Wulf A. Kaal, Computative Economics A Framework for Economic Analysis under Computational Abundance (2026), VI.C. Uniqueness and Convergence (Banach), p. 19
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 the composite best-response map to be a contraction under an appropriate metric

conditionsupport: arguedinstitutional-design

• extended_by kaal:claim:6655138-032 Without the reflection-mass invariant, the reflection layer can grow to dominate the first-order surfaces it i...
• extended_by kaal:claim:6655138-029 The composite best-response map is contractive on the population-distribution component of the state space onl...

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