{"id":"W7142787166","doi":"10.23952/jano.8.2026.1.06","title":"Necessary condition of weak Nash equilibrium","year":2025,"lang":"","type":"article","venue":"Journal of Applied and Numerical Optimization","topic":"Economic theories and models","field":"Economics, Econometrics and Finance","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006093392,0.0002085681,0.0009611783,0.0004099917,0.00008102856,0.00008573633,0.0002029109,0.0002237129,0.0003640749],"category_scores_gemma":[0.00005433347,0.0002352509,0.0001915338,0.0003108128,0.0001587574,0.0003987071,0.00009649325,0.0002594111,0.000005455833],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009093111,"about_ca_system_score_gemma":0.00009309007,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008147858,"about_ca_topic_score_gemma":1.109851e-7,"domain_scores_codex":[0.9975486,0.00001860506,0.00188069,0.0002748367,0.00005051346,0.0002267101],"domain_scores_gemma":[0.9973701,0.0001343745,0.002068897,0.0001797797,0.00012688,0.000119985],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0006410307,0.0002448912,0.0006371061,0.0001966023,0.0002860117,0.000001116084,0.0002895999,0.435247,0.0001634812,0.5574687,0.0009528092,0.003871741],"study_design_scores_gemma":[0.006200438,0.0009310804,0.001831242,0.0003733669,0.0003111359,0.00002382699,0.001179263,0.6620767,0.001810785,0.3057368,0.01874874,0.000776722],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06268136,0.005882619,0.8379489,0.001557279,0.001678513,0.0003196208,0.0001142259,0.000009510901,0.08980796],"genre_scores_gemma":[0.9867168,0.003313978,0.009097685,0.0002472189,0.0001712553,0.000003018193,0.00001490014,0.00002037741,0.000414754],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9240354,"threshold_uncertainty_score":0.9593256,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009361214195226581,"score_gpt":0.2168356535861496,"score_spread":0.207474439390923,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}