{"paper":{"title":"Dynamical systems associated to the $\\beta$-core in the repeated prisoner's dilemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Joanna Zwierzchowska, S{\\l}awomir Plaskacz","submitted_at":"2017-11-29T15:39:58Z","abstract_excerpt":"We consider the repeated prisoner's dilemma (PD). We assume that players make their choices knowing only average payoffs from the previous stages. A player's strategy is a function from the convex hull $\\mathfrak{S}$ of the set of payoffs into the set $\\{C,\\,D\\}$ ($C$ means cooperation, $D$ -- defection). S. Smale in \\cite{smale} presented an idea of good strategies in the repeated PD. If both players play good strategies then the average payoffs tends to the payoff corresponding to the profile $(C,C)$ in PD. We adopt the Smale idea to define semi-cooperative strategies - players do not take a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10923","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"}