{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003624347,0.0002106322,0.0003414186,0.00007995636,0.0005890285,0.00006420882,0.0001020837,0.00008156212,0.0005479103],"category_scores_gemma":[0.0000055677,0.0002039086,0.0001737212,0.0001309766,0.00008554101,0.00009261551,0.000001504746,0.0001820464,0.00006863305],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004202393,"about_ca_system_score_gemma":0.00004632234,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002135407,"about_ca_topic_score_gemma":0.00002759517,"domain_scores_codex":[0.9985614,0.0001938682,0.0003452889,0.0001941073,0.0001724626,0.0005328427],"domain_scores_gemma":[0.998959,0.0004750344,0.0000975642,0.0001670773,0.00006501502,0.0002362745],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0007679597,0.004166798,0.005007112,0.0002306701,0.003903265,0.000004117507,0.03620667,0.01186011,0.01692591,0.2843328,0.002318075,0.6342765],"study_design_scores_gemma":[0.04840012,0.001513469,0.01971313,0.00050032,0.002946487,0.00003106497,0.007777453,0.8482627,0.003248596,0.05497476,0.007853813,0.004778075],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0935311,0.00003084558,0.9017375,0.002215305,0.0005774843,0.0008720048,0.0002054007,0.0001196339,0.0007107076],"genre_scores_gemma":[0.9983166,0.00000125158,0.0002555698,0.0008405197,0.000169026,0.0002039587,0.000002182523,0.00002157938,0.0001893403],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9047855,"threshold_uncertainty_score":0.831515,"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."}}