This paper presents a theoretical extension of the DeTEcT framework proposed by Sadykhov et al., DeTEcT, where a formal analysis framework was introduced for modelling wealth distribution in token economies. DeTEcT is a framework for analysing economic activity, simulating macroeconomic scenarios, and algorithmically setting policies in token economies. This paper proposes four ways of parametrizing the framework, where dynamic vs static parametrization is considered along with the probabilistic vs non-probabilistic. Using these parametrization techniques, we demonstrate that by adding restrictions to the framework it is possible to derive the existing wealth distribution models from DeTEcT. In addition to exploring parametrization techniques, this paper studies how money supply in DeTEcT framework can be transformed to become dynamic, and how this change will affect the dynamics of wealth distribution. The motivation for studying dynamic money supply is that it enables DeTEcT to be applied to modelling token economies without maximum supply (i.e., Ethereum), and it adds constraints to the framework in the form of symmetries.

翻译：本文对Sadykhov等人提出的DeTEcT框架进行了理论扩展。DeTEcT原框架是为代币经济中的财富分配建模而引入的形式化分析框架，可用于分析经济活动、模拟宏观经济情景以及通过算法设定代币经济政策。本文提出了该框架的四种参数化方法，涵盖动态与静态参数化以及概率与非概率参数化。利用这些参数化技术，我们证明通过对框架添加约束，可以从DeTEcT推导出现有的财富分配模型。除探讨参数化技术外，本文还研究了如何将DeTEcT框架中的货币供应转变为动态形式，以及这种变化将如何影响财富分配的动态特性。研究动态货币供应的动机在于：这使得DeTEcT能够应用于无最大供应量的代币经济建模（如以太坊），并以对称性形式为框架增添约束条件。