{"paper":{"title":"Monotone bargaining is Nash-solvable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"math.CO","authors_text":"Gleb Koshevoy, Vladimir Gurvich","submitted_at":"2017-11-02T21:20:48Z","abstract_excerpt":"Given two finite ordered sets $A = \\{a_1, \\ldots, a_m\\}$ and $B = \\{b_1, \\ldots, b_n\\}$, introduce the set of $m n$ outcomes of the game $O = \\{(a, b) \\mid a \\in A, b \\in B\\} = \\{(a_i, b_j) \\mid i \\in I = \\{1, \\ldots, m\\}, j \\in J = \\{1, \\ldots, n\\}$. Two players, Alice and Bob, have the sets of strategies $X$ and $Y$ that consist of all monotone non-decreasing mappings $x: A \\rightarrow B$ and $y: B \\rightarrow A$, respectively. It is easily seen that each pair $(x,y) \\in X \\times Y$ produces at least one {\\em deal}, that is, an outcome $(a,b) \\in O$ such that $x(a) = b$ and $y(b) = a$. Denot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00940","kind":"arxiv","version":2},"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"}