Paper: arXiv 2312.16173

Authors: Pierre Gosselin, Aïleen Lotz

Abstract

This paper provides a general method to translate a standard economic model with a large number of agents into a field-formalism model. This formalism preserves the system’s interactions and microeconomic features at the individual level but reveals the emergence of collective states.We apply this method to a simple microeconomic framework of investors and firms. Both macro and micro aspects of the formalism are studied.At the macro-scale, the field formalism shows that, in each sector, three patterns of capital accumulation may emerge. A distribution of patterns across sectors constitute a collective state. Any change in external parameters or expectations in one sector will affect neighbouring sectors, inducing transitions between collective states and generating permanent fluctuations in patterns and flows of capital. Although changes in expectations can cause abrupt changes in collective states, transitions may be slow to occur. Due to its relative inertia, the real economy is bound to be more affected by these constant variations than the financial markets.At the micro-scale we compute the transition functions of individual agents and study their probabilistic dynamics in a given collective state, as a function of their initial state. We show that capital accumulation of an individual agent depends on various factors. The probability associated with each firm’s trajectories is the result of several contradictory effects: the firm tends to shift towards sectors with the greatest long-term return, but must take into account the impact of its shift on its attractiveness for investors throughout its trajectory. Since this trajectory depends largely on the average capital of transition sectors, a firm’s attractiveness during its relocation depends on the relative level of capital in those sectors. Moreover, the firm must also consider the effects of competition in the intermediate sectors that tends to oust under-capitalized firm towards sectors with lower average capital. For investors, capital allocation depends on their short and long-term returns and investors will tend to reallocate their capital to maximize both. The higher their level of capital, the stronger the re-allocation will be.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly novel and mathematically sophisticated application of quantum/statistical field theory to agent-based capital allocation and macroeconomics. However, it is purely theoretical with virtually no empirical backtesting, empirical data validation, or quantitative empirical rigor.

Research Flowchart

  flowchart TD
    A["Research Goal: Translate multi-agent microeconomic models into a field-formalism to study capital dynamics"] --> B["Methodology: Micro-to-field translation of individual agent interactions (Investors & Firms)"]
    B --> C["Inputs: Micro parameters (returns, expectations, capital levels, competition)"]
    C --> D["Computational Analysis: Macro-scale field dynamics & Micro-scale agent transition functions"]
    D --> E["Macro Outcomes: Emergence of 3 sector accumulation patterns & slow, persistent macro state transitions"]
    D --> F["Micro Outcomes: Trajectory probabilities driven by return-maximizing reallocation vs. sector competition"]