2024PaperV3
The paper develops a feedback‑loop framework for a crowd of heterogeneous agents to explain how concentrated wealth and income distributions, including power‑law, lognormal and normal forms, arise from the interaction of agents’ response functions, reward mechanisms, and external forces. Agents adjust their decisions based on external signals (dE) and observed outcomes (dO) with coefficients Ci and Bi; their wealth (Ai) evolves according to a reward function that links wealth change to the alignment of actions with observations. When response coefficients Bi are zero, the system reduces to a random walk yielding normal or lognormal distributions. Non‑zero, heterogeneous Bi create endogenous feedback that amplifies trends, leading to general concentrated distributions and, under specific linear‑reward and boundary conditions, power‑law behavior. The paper contrasts mathematical representations (PDF, CDF, rank) of these distributions, demonstrates how lower‑tail behavior distinguishes them, and provides empirical case studies of US versus Japan income and wealth data, showing steeper power‑law tails in the US. Simulations illustrate wealth concentration over time, and the model is extended to a variety of domains (city sizes, market returns, firm sizes, citations, online content, collective intelligence, AI‑agent design). The conclusions emphasize that feedback loops and heterogeneous response functions are the primary drivers of concentration, that power‑law is a special case of a broader class of concentrated outcomes, and that monitoring Bi could aid in forecasting crises or designing desired system‑level distributions.
Topics
Feedback‑Loop Model of Heterogeneous Agents
Mathematical formulation linking agents' decisions (dS_i), external forces (dE), observations (dO), and wealth (A_i) through equations (1)–(10).
Empirical Contrast: US vs Japan Income and Wealth Distributions
Presentation of percentile‑rank tables, PDF calculations, and slope estimates showing steeper power‑law in the US and more lognormal‑like patterns in Japan.
Simulation of Wealth Concentration Over Discrete Time Steps
Numerical illustration (Figure 6) of wealth trajectories for agents with varying B_i, demonstrating emergence of super‑agents and collapse of lower‑rank wealth.
Broader Applications of the Feedback Model
Mapping the framework onto city‑size hierarchies, market‑return tails, firm‑size distributions, citation networks, online content popularity, collective intelligence dynamics, and AI‑agent design.