Year: 2026
Type: article
Abstract: . We investigate a variant of the standard Bennati–Dragulescu–Yakovenko game [A. Dragulescu and V. M. Yakovenko, Eur. Phys. J. B, 17 (2000), pp. 723–729] inspired by the very recent work [K. Blom, D. E. Makarov, and A. Godec, Phys. Rev. Res., 7 (2024), 013279], where agents involved in a money exchange dynamics are classified into two distinct types called probabilistic cheaters and honest players, respectively. A probabilistic cheater has a positive probability of declaring to have no money to give to other agents in the system, resulting in potential financial benefits from being dishonest about his/her financial status. We provide a mean-field description of the agent-based model (in terms of a coupled infinite-dimensional system of nonlinear ODEs) in the large population limit where the number of players is sent to infinity, and we prove convergence of the coupled mean-field system to its stationary distribution (provided by a mixture of geometric distributions). In particular, the model gives rise to a novel formulation involving a mixture of probability distributions, thereby motivating the introduction of an unusual (generalized) entropy functional tailored to the associated mean-field system.
DOI: 10.1137/25m1786830
Author: Fei Cao
Institution: Amherst College
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4417514303