{"id":"W4388444808","doi":"10.1109/tac.2025.3629145","title":"From Discrete to Continuous Binary Best-Response Dynamics: Discrete Fluctuations Almost Surely Vanish With Population Size","year":2025,"lang":"en","type":"preprint","venue":"IEEE Transactions on Automatic Control","topic":"Evolutionary Game Theory and Cooperation","field":"Social Sciences","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary; Brock University","funders":"","keywords":"Population; Mathematics; Statistical physics; Evolutionary dynamics; Population size; Scale (ratio); Dynamics (music); Stochastic differential equation; Action (physics); Discrete time and continuous time; Applied mathematics; Econometrics; Statistics; Physics","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":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.00111302,0.0005458478,0.0007870031,0.0003444513,0.001449496,0.0003630041,0.0005899771,0.0004933368,0.0008788069],"category_scores_gemma":[0.0003073928,0.0005345341,0.0003007301,0.0005929271,0.0002420103,0.0003742997,0.00001017709,0.0006264811,0.0001397109],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009819987,"about_ca_system_score_gemma":0.001060964,"about_ca_topic_candidate":true,"about_ca_topic_consensus":true,"about_ca_topic_score_codex":0.008784682,"about_ca_topic_score_gemma":0.0197843,"domain_scores_codex":[0.9949683,0.002001773,0.0008138596,0.0008520448,0.0008466524,0.0005173661],"domain_scores_gemma":[0.9954088,0.00276045,0.0003316656,0.0008530818,0.0003590489,0.0002869267],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.01043421,0.001582196,0.000439896,0.0002316856,0.002175953,0.00006937338,0.03613566,0.8677024,0.001605174,0.007010371,0.0005785379,0.0720346],"study_design_scores_gemma":[0.008109188,0.002235953,0.03500658,0.004998329,0.00408168,0.000009835157,0.0169896,0.9021509,0.0002019417,0.02072085,0.001770381,0.00372473],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.288945,0.00004779741,0.6914359,0.008582455,0.001444474,0.004165728,0.003608481,0.0006808295,0.001089243],"genre_scores_gemma":[0.986499,0.00002029237,0.002436495,0.0004644361,0.0002003084,0.001419839,0.0002016806,0.00004737629,0.008710619],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6975539,"threshold_uncertainty_score":0.9998505,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007970618612737651,"score_gpt":0.2762862629618794,"score_spread":0.2683156443491417,"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."}}