Paper 8The Constitution of Cost and the Stability of Structure: Evolutionary Dynamics on Endogenous Fitness Landscapes in Modular Systems

While our prior work (Paper 7) established the efficiency of competitive resource allocation, it assumed a fixed interaction topology. This paper addresses a more fundamental question: is such a structure evolutionarily stable? We model the interaction between functional modules as an evolutionary game played on an "endogenous fitness landscape," where a module’s fitness is defined by its ability to reduce predictive uncertainty. We first formalize "endogenous cost" as the conditional entropy of a module's output, proving that the system converges to a self-consistent equilibrium where resources are distributed according to marginal uncertainty reduction (Theorem A). We then apply evolutionary graph theory to analyze the stability of the Wuxing (Five-Elements) topology. Using a Moran process on the interaction graph, we derive fixation probabilities for "greedy" mutants that attempt to capture disproportionate resources. We prove that under the dual-cycle topology (cooperation and competition), the system exhibits strong resistance to structural drift, maintaining its balanced configuration against both noise and strategic deviation. 虽然此前研究(Paper 7)证明了竞争性资源分配的效率,但那是基于固定的交互拓扑。本文探讨了一个更基础的问题:这种结构在演化上是否稳定?我们将功能模块间的交互建模为在“内生适应度景观”上进行的演化博弈,其中模块的适应度定义为其降低预测不确定性的能力。 我们首先将“内生成本”形式化为模块输出的条件熵,证明系统会收敛于一个自洽平衡态,即资源按边际不确定性降低率进行分配(定理A)。随后,我们应用演化图论分析了五行拓扑的稳定性。通过在交互图上模拟 Moran 过程,我们推导了试图攫取超额资源的“贪婪”突变体的固定概率。证明结果显示,在双环拓扑(即生克双环)下,系统对结构漂移具有极强的抵抗力,能在噪声和策略性偏离面前保持平衡配置。