Paper: arXiv 2503.16890

Abstract

We study the existence of equilibrium when agents’ preferences may not beconvex. For some specific utility functions, we provide a necessary and sufficientcondition under which there exists an equilibrium. The standard approach cannot be directly applied to our examples because the demand correspondence of some agents is neither single-valued nor convex-valued.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a theoretical general equilibrium model with non-convex preferences, featuring dense mathematical derivations, lemmas, and proofs, but includes no data, backtests, or implementation details for trading strategies.

Research Flowchart

  flowchart TD
  A["Research Goal<br/>Existence of equilibrium with<br/>non-convex preferences"] --> B["Key Methodology<br/>Modified General Equilibrium Approach"]
  B --> C["Computational Process<br/>Demand Correspondence Analysis"]
  C --> D["Analysis: Non-single-valued &<br/>Non-convex-valued demand"]
  D --> E["Key Finding<br/>Necessary & Sufficient Condition<br/>for Equilibrium Existence"]
  E --> F["Outcome<br/>Case-Specific Equilibrium Established"]