{"id":"https://openalex.org/W2004575589","doi":"https://doi.org/10.1109/icca.2013.6565205","title":"Application of STP to cooperative games","display_name":"Application of STP to cooperative games","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2004575589","doi":"https://doi.org/10.1109/icca.2013.6565205","mag":"2004575589"},"language":"en","primary_location":{"id":"doi:10.1109/icca.2013.6565205","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2013.6565205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 10th IEEE International Conference on Control and Automation (ICCA)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020035625","display_name":"Daizhan Cheng","orcid":"https://orcid.org/0000-0001-5088-3209"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Daizhan Cheng","raw_affiliation_strings":["Key Laboratory of Systems & Control, Institute of Systems Science, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, China","Key Lab. of Syst. & Control, Inst. of Syst. Sci., Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems & Control, Institute of Systems Science, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Key Lab. of Syst. & Control, Inst. of Syst. Sci., Beijing, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062549428","display_name":"Tingting Xu","orcid":"https://orcid.org/0000-0002-5043-737X"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tingting Xu","raw_affiliation_strings":["Key Laboratory of Systems & Control, Institute of Systems Science, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, China","Key Lab. of Syst. & Control, Inst. of Syst. Sci., Beijing, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Systems & Control, Institute of Systems Science, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Key Lab. of Syst. & Control, Inst. of Syst. Sci., Beijing, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020035625"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":null,"apc_paid":null,"fwci":4.5897,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.95087698,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1680","last_page":"1685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9855999946594238,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/shapley-value","display_name":"Shapley value","score":0.7798044681549072},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5985113382339478},{"id":"https://openalex.org/keywords/cooperative-game-theory","display_name":"Cooperative game theory","score":0.5704376697540283},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5515376329421997},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5442079305648804},{"id":"https://openalex.org/keywords/bondareva\u2013shapley-theorem","display_name":"Bondareva\u2013Shapley theorem","score":0.5430355668067932},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5429127216339111},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5269573330879211},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4728441834449768},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.45684635639190674},{"id":"https://openalex.org/keywords/unanimity","display_name":"Unanimity","score":0.4525368809700012},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38867196440696716},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35722148418426514},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31748807430267334},{"id":"https://openalex.org/keywords/combinatorial-game-theory","display_name":"Combinatorial game theory","score":0.21425938606262207},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.1874484121799469},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17641067504882812},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.17336323857307434}],"concepts":[{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.7798044681549072},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5985113382339478},{"id":"https://openalex.org/C2781416736","wikidata":"https://www.wikidata.org/wiki/Q105354050","display_name":"Cooperative game theory","level":3,"score":0.5704376697540283},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5515376329421997},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5442079305648804},{"id":"https://openalex.org/C51074407","wikidata":"https://www.wikidata.org/wiki/Q4941364","display_name":"Bondareva\u2013Shapley theorem","level":5,"score":0.5430355668067932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5429127216339111},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5269573330879211},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4728441834449768},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.45684635639190674},{"id":"https://openalex.org/C2781423480","wikidata":"https://www.wikidata.org/wiki/Q1309409","display_name":"Unanimity","level":2,"score":0.4525368809700012},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38867196440696716},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35722148418426514},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31748807430267334},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.21425938606262207},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.1874484121799469},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17641067504882812},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.17336323857307434},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icca.2013.6565205","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icca.2013.6565205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 10th IEEE International Conference on Control and Automation (ICCA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W140444299","https://openalex.org/W567151721","https://openalex.org/W1487386742","https://openalex.org/W1503525425","https://openalex.org/W1562353621","https://openalex.org/W2486512961","https://openalex.org/W2516137114","https://openalex.org/W2949651077","https://openalex.org/W3209952520","https://openalex.org/W4234761190"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2376932109","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W1972437902","https://openalex.org/W1596801655","https://openalex.org/W2387147530","https://openalex.org/W2373011076","https://openalex.org/W2688602461"],"abstract_inverted_index":{"Using":[0],"semi-tensor":[1],"product":[2],"(STP)":[3],"of":[4,18,45],"matrices,":[5],"a":[6,12,36,42,51],"characteristic":[7],"function":[8],"is":[9,48,54,82],"converted":[10],"into":[11],"pseudo-Boolean":[13],"function.":[14],"In":[15],"the":[16,32,70,85],"light":[17],"this":[19],"form,":[20],"two":[21,61],"fundamental":[22],"formulas":[23,62],"in":[24,77,84],"cooperative":[25],"game":[26,37],"theory":[27],"have":[28],"been":[29],"simplified.":[30],"First,":[31],"coefficient":[33],"formula":[34,53],"for":[35],"to":[38,56],"be":[39,75],"expressed":[40],"as":[41],"linear":[43],"combination":[44],"unanimity":[46],"games":[47],"obtained.":[49],"Second,":[50],"novel":[52],"proposed":[55],"calculate":[57],"Shapley":[58],"value.":[59],"These":[60],"are":[63],"simple.":[64],"They":[65],"can":[66],"not":[67],"only":[68],"reduce":[69],"computational":[71],"complexity":[72],"but":[73],"also":[74],"used":[76],"theoretical":[78],"analysis.":[79],"The":[80],"STP":[81],"introduced":[83],"appendix.":[86]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-06T13:50:29.536080","created_date":"2025-10-10T00:00:00"}