Paper: arXiv 2502.10666

Authors: Hoang Vu, Tomoyuki Ichiba

Abstract

We investigate the full dynamics of capital allocation and wealth distribution of heterogeneous agents in a frictional economy during booms and busts using tools from mean-field games. Two groups in our models, namely the expert and the household, are interconnected within and between their classes through the law of capital processes and are bound by financial constraints. Such a mean-field interaction explains why experts accumulate a lot of capital in the good times and reverse their behavior quickly in the bad times even in the absence of aggregate macro-shocks. When common noises from the market are involved, financial friction amplifies the mean-field effect and leads to capital fire sales by experts. In addition, the implicit interlink between and within heterogeneous groups demonstrates the slow economic recovery and characterizes the deviating and fear-of-missing-out (FOMO) behaviors of households compared to their counterparts. Our model also gives a fairly explicit representation of the equilibrium solution without exploiting complicated numerical approaches.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a sophisticated theoretical framework using Mean-Field Games to solve a continuous-time macro-finance model with heterogeneous agents explicitly. However, it is entirely theoretical with no empirical backtesting or real-world data validation included in the text.

Research Flowchart

  flowchart TD
    A[Research Goal: Model capital allocation & wealth distribution in frictional economies] --> B[Framework: Mean-Field Games with 2 Groups: Experts & Households]
    B --> C[Inputs: Capital processes, financial constraints & market common noise]
    C --> D[Model Equilibrium Dynamics & Financial Frictions]
    D --> E[Outcome 1: Expert capital accumulation in booms & sudden reversals in busts]
    D --> F[Outcome 2: Amplified fire sales via common noise & slow recovery]
    D --> G[Outcome 3: Household fear-of-missing-out FOMO behaviors]

Cited References (26)

  1. The Linguistic Significance of Current B ritish Slang (1995)
  2. Blowup for Nonlinear Hyperbolic Equations (1995)
  3. Nonlinear Operators and Nonlinear Equations of Evolution in B anach Spaces (1976)
  4. Insensitive Functionals, Inconsistent Gradients, Spurious Minima, and Regularized Functionals in Flow Optimization Problems (2002)
  5. An Algorithm Using Quadratic Interpolation (1996)
  6. Positive Bases in Numerical Optimization (2003)
  7. Hilbert modular forms and the G alois representations associated to H ilbert- B lumenthal abelian varieties (1998)
  8. Practical Methods of Optimization (1980)
and 18 more
  1. AMPL : A Modeling Language for Mathematical Programming (2003)
  2. English title of a chapter in the translation of a book in a foreign language (1988)
  3. Practical Optimization (1981)
  4. Multi-start and strategic oscillation methods – principles to exploit adaptive memory (2000)
  5. APPSPACK ( A synchronous Parallel Pattern Search Package)
  6. Conjectured Statistics for the $q,t$ - C atalan Numbers (preprint (2003)) — link
  7. Hilbert Schemes, Polygraphs, and the M acdonald Positivity Conjecture (2001) — link
  8. A Stationary Point Convergence Theory of Evolutionary Algorithms (1997)
  9. Multiple Bumping of Components of Deformation Spaces of Hyperbolic 3-Manifolds (2003) — link
  10. Homogenization and Porous Media (1996)
  11. The resurgent J apanese economy and a J apan– U nited S tates free trade agreement (1997)
  12. On an Elliptic Curve over $Q(t)$ of Rank $\geq$14 (2001)
  13. Parallel GRASP with Path-Relinking for Job Shop Scheduling (1983)
  14. Title of a Book (1988)
  15. On the L agrange Functions of Quadratic Models that are Defined by Interpolation (2000)
  16. Matrix Algorithms. Volume 1: Basic Decompositions (1998)
  17. Finite Subgroups of Formal Groups (1997)
  18. Basic Number Theory (1995)

0 of 26 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.