{"paper":{"title":"Parrondo games with two-dimensional spatial dependence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jiyeon Lee, S. N. Ethier","submitted_at":"2015-10-23T14:39:40Z","abstract_excerpt":"Parrondo games with one-dimensional spatial dependence were introduced by Toral and extended to the two-dimensional setting by Mihailovi\\'c and Rajkovi\\'c. $MN$ players are arranged in an $M\\times N$ array. There are three games, the fair, spatially independent game $A$, the spatially dependent game $B$, and game $C$, which is a random mixture or nonrandom pattern of games $A$ and $B$. Of interest is $\\mu_B$ (or $\\mu_C$), the mean profit per turn at equilibrium to the set of $MN$ players playing game $B$ (or game $C$). Game $A$ is fair, so if $\\mu_B\\le0$ and $\\mu_C>0$, then we say the Parrondo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06947","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}