Mean-field analysis of a random asset exchange model with probabilistic cheaters
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912369893965824 |
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| author | Cao, Fei |
| author_facet | Cao, Fei |
| contents | We investigate a variant of the standard Bennati-Dragulescu-Yakovenko (BDY) game \cite{dragulescu_statistical_2000} inspired by the very recent work \cite{blom_hallmarks_2024}, where agents involving in a money exchange dynamics are classified into two distinct types which are termed as 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 a 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 proves 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 a unusual (generalized) entropy functional tailored to the associated mean-field system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06767 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean-field analysis of a random asset exchange model with probabilistic cheaters Cao, Fei Probability 91B80, 91B70, 82C31, 35Q91 We investigate a variant of the standard Bennati-Dragulescu-Yakovenko (BDY) game \cite{dragulescu_statistical_2000} inspired by the very recent work \cite{blom_hallmarks_2024}, where agents involving in a money exchange dynamics are classified into two distinct types which are termed as 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 a 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 proves 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 a unusual (generalized) entropy functional tailored to the associated mean-field system. |
| title | Mean-field analysis of a random asset exchange model with probabilistic cheaters |
| topic | Probability 91B80, 91B70, 82C31, 35Q91 |
| url | https://arxiv.org/abs/2505.06767 |