{"id":"W2136776938","doi":"10.1109/tac.2012.2215399","title":"Nash, Social and Centralized Solutions to Consensus Problems via Mean Field Control Theory","year":2012,"lang":"en","type":"article","venue":"IEEE Transactions on Automatic Control","topic":"Opinion Dynamics and Social Influence","field":"Physics and Astronomy","cited_by":97,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University; Polytechnique Montréal; McGill University; Group for Research in Decision Analysis","funders":"","keywords":"Nash equilibrium; Population; Mathematical optimization; Mean field theory; Mathematics; Mathematical economics; Field (mathematics); Social choice theory; Applied mathematics; Computer science; Pure mathematics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001190034,0.0005970041,0.0005571003,0.0006584956,0.0007045315,0.001367282,0.0009091374,0.001130078,0.002144363],"category_scores_gemma":[0.002743887,0.0002876845,0.0006662269,0.0004182998,0.001705651,0.00161869,0.001186069,0.001092264,0.0002463587],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001641679,"about_ca_system_score_gemma":0.001485985,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003853434,"about_ca_topic_score_gemma":0.002677646,"domain_scores_codex":[0.9994026,0.000226858,0.00001954227,0.00009049659,0.0001972131,0.00006327629],"domain_scores_gemma":[0.9994251,0.000293024,0.00009462725,0.00003628698,0.0001008482,0.00005024432],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001519877,0.00002164276,0.000180033,0.00004471574,0.00002316709,0.00004897664,0.00009078081,0.3594435,0.0007179021,0.6300017,0.00105633,0.008355993],"study_design_scores_gemma":[0.00001297454,0.000017148,0.00008740364,0.000009207411,0.000005697444,0.00001388801,0.00002603699,0.631324,0.0001617766,0.3669589,0.001374032,0.000008996394],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.02742298,0.0008081111,0.9453979,0.001398054,0.00008895532,0.00004373395,0.0000549673,0.0001265186,0.02465882],"genre_scores_gemma":[0.9029324,0.0009683954,0.07996165,0.0003170553,0.0001973309,0.0002695092,0.00007596878,0.00006977013,0.01520791],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.003853434,"threshold_uncertainty_score":0.01191127,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01394526567013215,"score_gpt":0.2605162270609899,"score_spread":0.2465709613908578,"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."}}