Implicit Evaluation Under Minimal Information: Price Formation in Hierarchical Component Selection
This work provides a theoretical foundation for decentralized evaluation in hierarchical systems without explicit communication channels, which is relevant for multi-agent systems and organizational design.
The paper introduces a proportional-redistribution mechanism for hierarchical component selection under minimal information, where each node updates weights based on observed outcomes and the sign of weight change serves as an implicit evaluation signal. The mechanism is proven to preserve market integrity, has closed-form equilibria for N=2 and explicit affine equilibria under equi-ratio conditions, and is validated on synthetic hierarchies up to 32,768 leaves and three natural-hierarchy datasets.
We study hierarchical component selection under severe information constraints. Component quality is not directly observable, each selector observes only the outcome of the chosen pathway, and no explicit evaluation channel crosses module boundaries. We analyse a proportional-redistribution mechanism in which each selector maintains a weight vector over its children and updates that vector from observed outcomes. The sign of a parent's weight change can be read locally as an implicit binary evaluation signal by the selected child, yielding a decentralised evaluation mechanism with no explicit reporting channel. We give a full formal treatment. Proportional redistribution preserves market integrity algebraically. The sign of the weight change propagates without loss through the active path. The single-selector dynamics admit a unique interior equilibrium; for $N{=}2$ the equilibrium is exact and closed-form, while for general $N$ an equi-ratio condition yields an explicit affine equilibrium. Hierarchical composition is informationally clean, with each node's active-round dynamics identical to a standalone instance observed on a thinned clock. All structural results, the equilibrium formula, and the composition theorem are fully proved. Illustrative cases on synthetic hierarchies with up to 32,768 leaves and on three natural-hierarchy datasets confirm the mechanism's operation under constructed and applied conditions.