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DeTEcT: Dynamic and Probabilistic Parameters Extension

Rem Sadykhov, Geoffrey Goodell, Philip Treleaven

TL;DR

DeTEcT addresses static parameter limitations and capped token supplies in token-economy wealth modelling. It proposes four parametrization schemes—static/deterministic, static/probabilistic, dynamic/deterministic, and dynamic/probabilistic—and adds a dynamic money supply extension to model time-varying and stochastic policy effects. The authors show how existing wealth distribution models (no saving, global saving, and individual saving) emerge from DeTEcT under these parametrizations and explore the implications of dynamic maximum supply, including time translation symmetry and a system-derived discount factor. This work broadens DeTEcT's applicability to unbounded token economies (e.g., Ethereum) and provides a framework for policy analysis and macroeconomic scenario testing in tokenised systems.

Abstract

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.

DeTEcT: Dynamic and Probabilistic Parameters Extension

TL;DR

DeTEcT addresses static parameter limitations and capped token supplies in token-economy wealth modelling. It proposes four parametrization schemes—static/deterministic, static/probabilistic, dynamic/deterministic, and dynamic/probabilistic—and adds a dynamic money supply extension to model time-varying and stochastic policy effects. The authors show how existing wealth distribution models (no saving, global saving, and individual saving) emerge from DeTEcT under these parametrizations and explore the implications of dynamic maximum supply, including time translation symmetry and a system-derived discount factor. This work broadens DeTEcT's applicability to unbounded token economies (e.g., Ethereum) and provides a framework for policy analysis and macroeconomic scenario testing in tokenised systems.

Abstract

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.
Paper Structure (27 sections, 1 theorem, 68 equations, 3 tables)

This paper contains 27 sections, 1 theorem, 68 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Scope
  3. Related Work
  4. DeTEcT Framework
  5. Wealth Distribution Models
  6. Basic Model Without Saving
  7. Model With Constant Global Saving Propensity
  8. Model With Individual Saving Propensities
  9. Summary
  10. Parametrization Extension and Derivation of Existing Wealth Distribution Models
  11. Parameter Modification Techniques
  12. Static Deterministic Parameters
  13. Static Probabilistic Parameters
  14. Dynamic Deterministic Parameters
  15. Dynamic Probabilistic Parameters
  16. ...and 12 more sections

Key Result

Theorem 4.1

If maximum supply is constant or has simple, compound, or stochastic incrementation (decrementation), there exists a time translation symmetry in the economy.

Theorems & Definitions (6)

  • Remark
  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 4.1: Time Translation Symmetry
  • proof