kaal:claim:6655138-029

The composite best-response map is contractive on the population-distribution component of the state space only when the agent population exceeds a threshold set by per-surface stake parameters; below that threshold the architecture may admit multiple equilibria, and above it convergence is guaranteed.

Source quote, verbatim

The composite map Ψ is contractive on the population-distribution component of the state space when the agent population exceeds a threshold determined by per-surface stake parameters. Below the threshold, the architecture may admit multiple equilibria; above the threshold, convergence is guaranteed.

From

Wulf A. Kaal, Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems (2026), VII.D Architectural conditions for fixed-point existence, AC4, p. 21
https://ssrn.com/abstract=6655138 · source PDF

Cite as

Wulf A. Kaal, Possibility Loops An Operational Architecture for Computative Economics in Agent Coordination Systems (2026). SSRN: https://ssrn.com/abstract=6655138

Holds when

agent populations above the stake-parameter-determined threshold

Classification

conditionsupport: arguedinstitutional-design

Related claims

extends kaal:claim:6607458-023 Proposition 2: if the composite best-response map is a contraction under an appropriate metric, the recursive ...

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