{"id":"W3183790857","doi":"10.1007/s00182-025-00928-4","title":"Specifying a game-theoretic extensive form as an abstract 5-ary relation","year":2025,"lang":"en","type":"preprint","venue":"International Journal of Game Theory","topic":"Game Theory and Applications","field":"Decision Sciences","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Axiom; Mathematical economics; Relation (database); Mathematics; Set (abstract data type); Bijection; Node (physics); Action (physics); Successor cardinal; Extensive-form game; Tree (set theory); Combinatorial game theory; Discrete mathematics; Computer science; Theoretical computer science; Combinatorics; Game theory; Sequential game","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":[0.002737297,0.0005286734,0.0006056749,0.001206605,0.0007519801,0.003204344,0.0008170767,0.00077799,0.004662889],"category_scores_gemma":[0.003661516,0.0004465377,0.001213219,0.001097108,0.002182136,0.005715603,0.001854622,0.001354614,0.0006472008],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001225759,"about_ca_system_score_gemma":0.0007978536,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001992954,"about_ca_topic_score_gemma":0.002194869,"domain_scores_codex":[0.997121,0.001262079,0.0003940721,0.0005184512,0.0004526777,0.0002516899],"domain_scores_gemma":[0.9978641,0.001098812,0.0001684161,0.0004108657,0.0003481052,0.0001097156],"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":[0.00001940562,0.00001868716,0.000245578,0.00003234655,0.00001088128,0.0001176917,0.0003385804,0.01057091,0.0009498343,0.9800285,0.0004372006,0.007230364],"study_design_scores_gemma":[0.00001936763,0.00005862617,0.0002458245,0.00005264361,0.0000228326,0.0001799345,0.0002364718,0.0410038,0.001964573,0.9332965,0.022894,0.0000253811],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.03586284,0.0001509261,0.9459358,0.0004150277,0.00006319935,0.0001289561,0.0004484384,0.0002946413,0.01670012],"genre_scores_gemma":[0.5554014,0.0003486002,0.4343475,0.0003800959,0.00009128892,0.0003820406,0.0008373196,0.0001023439,0.008109371],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.004662889,"threshold_uncertainty_score":0.01559895,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0915849344649609,"score_gpt":0.4345450077200754,"score_spread":0.3429600732551145,"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."}}