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.
Source quote, verbatim
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
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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
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Wulf A. Kaal, Computative Economics A Framework for Economic Analysis under Computational Abundance (2026). SSRN: https://ssrn.com/abstract=6607458
Holds when
requires the composite best-response map to be a contraction under an appropriate metric
Classification
conditionsupport: arguedinstitutional-design
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