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.
翻译:我们研究了在严重信息约束下的层次化组件选择问题。组件质量不可直接观测,每个选择器仅能观察到所选路径的结果,且不存在跨越模块边界的显式评估通道。我们分析了一种比例再分配机制:每个选择器维护一个子节点的权重向量,并根据观测结果更新该向量。父节点权重变化的符号可被所选子节点局部解读为隐式二元评估信号,从而形成无需显式报告通道的分散化评估机制。我们给出了完整的理论分析:比例再分配在代数意义上保持了市场完整性;权重变化符号沿活跃路径无损传播;单选择器动力学存在唯一内点均衡——当$N{=}2$时均衡精确闭式,而一般$N$情况下等比例条件导出显式仿射均衡。层次化组合具有信息清洁性,每个节点的活跃轮次动力学等价于在稀疏时钟上观测的独立实例。所有结构结论、均衡公式及组合定理均得到完整证明。基于包含多达32,768个叶节点的合成层次结构以及三个自然层次数据集的示例研究,验证了该机制在构造条件与应用条件下的运行特性。