## Abstract

We investigate the uniform reshuffling model for money exchanges: two agents picked uniformly at random redistribute their dollars between them. This stochastic dynamics is of mean-field type and eventually leads to a exponential distribution of wealth. To better understand this dynamics, we investigate its limit as the number of agents goes to infinity. We prove rigorously the so-called propagation of chaos which links the stochastic dynamics to a (limiting) nonlinear partial differential equation (PDE). This deterministic description, which is well-known in the literature, has a flavor of the classical Boltzmann equation arising from statistical mechanics of dilute gases. We prove its convergence toward its exponential equilibrium distribution in the sense of relative entropy.

Original language | English (US) |
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Pages (from-to) | 829-875 |

Number of pages | 47 |

Journal | Mathematical Models and Methods in Applied Sciences |

Volume | 33 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2023 |

## Keywords

- Agent-based model
- propagation of chaos
- relative entropy
- uniform reshuffling

## ASJC Scopus subject areas

- Modeling and Simulation
- Applied Mathematics