{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:29:12Z","timestamp":1787225352736,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100005376","name":"American Mathematical Society","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005376","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We investigate a variant of the standard Bennati\u2013Dragulescu\u2013Yakovenko game [A. Dragulescu and V. M. Yakovenko, Eur.\u00a0Phys.\u00a0J.\u00a0B, 17 (2000), pp.\u00a0723\u2013729] inspired by the very recent work [K. Blom, D. E. Makarov, and A. Godec, Phys.\u00a0Rev.\u00a0Res., 7 (2024), 013279], where agents involved in a money exchange dynamics are classified into two distinct types called probabilistic cheaters and honest players, respectively.\u00a0A 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,\u00a0and 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.<\/jats:p>","DOI":"10.1137\/25m1786830","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T08:00:31Z","timestamp":1779436831000},"page":"945-960","source":"Crossref","is-referenced-by-count":0,"title":["Mean-Field Analysis of a Random Asset Exchange Model with Probabilistic Cheaters"],"prefix":"10.1137","volume":"86","author":[{"given":"Fei","family":"Cao","sequence":"first","affiliation":[{"name":"Department of Mathematics, Amherst College, Amherst, MA 01002 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,5,22]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.7.013279"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-021-02807-0"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1002\/mma.8711"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"F. Cao, From Gini Index as a Lyapunov Functional to Convergence in Wasserstein Distance, https:\/\/arxiv.org\/abs\/2409.15225, 2024.","DOI":"10.22541\/au.176286442.24486097\/v1"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/24M1682269"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792524000184"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/ad8c8c"},{"key":"ref8","unstructured":"F. Cao and N. Loy, The Bennati-Dragulescu-Yakovenko Model in the Continuous Setting:\u00a0PDE Derivation and Long-Time Behavior, https:\/\/arxiv.org\/abs\/2512.06101, 2025."},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2023007"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/22M1518621"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/24M1654622"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1051\/mmnp\/2025007"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/24M1700661"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2022017"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2022018"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s100510070173"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2003.11.014"},{"key":"ref18","volume-title":"Elements of Information Theory","author":"Cover T. 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Tosin, Essentials of the Kinetic Theory of Multi-agent Systems, https:\/\/arxiv.org\/abs\/2503.11554, 2025."},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-007-9462-2"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOP1336"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ad369b"},{"key":"ref31","volume-title":"Interacting Multiagent Systems:\u00a0Kinetic Equations and Monte Carlo Methods","author":"Pareschi L.","year":"2013"},{"key":"ref32","volume-title":"Econophysics:\u00a0Background and Applications in Economics, Finance, and Sociophysics","author":"Savoiu G.","year":"2013"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0085169"},{"key":"ref34","first-page":"3","volume":"1","author":"Villani C.","year":"2002","journal-title":"Handb. Math. 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