{"paper":{"title":"Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR","q-bio.PE","q-bio.QM"],"primary_cat":"math.AP","authors_text":"Manh Hong Duong, The Anh Han","submitted_at":"2015-05-18T15:15:33Z","abstract_excerpt":"In this paper, we study the distribution and behaviour of internal equilibria in a $d$-player $n$-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main novelties of the paper are some qualitative and quantitative results on the expected density, $f_{n,d}$, and the expected number, $E(n,d)$, of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04676","kind":"arxiv","version":3},"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"}