{"id":"https://openalex.org/W1992083423","doi":"https://doi.org/10.1002/malq.200810021","title":"A Tractable and Expressive Class of Marginal Contribution Nets and Its Applications","display_name":"A Tractable and Expressive Class of Marginal Contribution Nets and Its Applications","publication_year":2009,"publication_date":"2009-07-17","ids":{"openalex":"https://openalex.org/W1992083423","doi":"https://doi.org/10.1002/malq.200810021","mag":"1992083423"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200810021","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200810021","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-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/A5050150656","display_name":"Edith Elkind","orcid":"https://orcid.org/0000-0001-6718-3436"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Edith Elkind","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, U.K.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, U.K.#TAB#","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029293569","display_name":"Leslie Ann Goldberg","orcid":"https://orcid.org/0000-0003-1879-6089"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Leslie Ann Goldberg","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, U.K","Department of Computer Science, University of Liverpool, U.K.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, U.K","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, U.K.#TAB#","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067662147","display_name":"Paul W. Goldberg","orcid":"https://orcid.org/0000-0002-5436-7890"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paul W. Goldberg","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, U.K","Department of Computer Science, University of Liverpool, U.K.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, U.K","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, U.K.#TAB#","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065393757","display_name":"Michael Wooldridge","orcid":"https://orcid.org/0000-0002-9329-8410"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Michael Wooldridge","raw_affiliation_strings":["Department of Computer Science, University of Liverpool, U.K","Department of Computer Science, University of Liverpool, U.K.#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, U.K","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"Department of Computer Science, University of Liverpool, U.K.#TAB#","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":14.9556,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.98479616,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"55","issue":"4","first_page":"362","last_page":"376"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9993000030517578,"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":0.9993000030517578,"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/T11031","display_name":"Game Theory and Applications","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9966999888420105,"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/computer-science","display_name":"Computer science","score":0.645404577255249},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5559602975845337},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5535863637924194},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.5458936095237732},{"id":"https://openalex.org/keywords/shapley-value","display_name":"Shapley value","score":0.47182637453079224},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4453483819961548},{"id":"https://openalex.org/keywords/net","display_name":"Net (polyhedron)","score":0.4136436879634857},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3715333938598633},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.365872323513031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34098905324935913},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2857940196990967},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23644426465034485},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.15852373838424683}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.645404577255249},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5559602975845337},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5535863637924194},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5458936095237732},{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.47182637453079224},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4453483819961548},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.4136436879634857},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3715333938598633},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.365872323513031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34098905324935913},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2857940196990967},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23644426465034485},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.15852373838424683},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1002/malq.200810021","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200810021","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:265285","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.141.1678","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.141.1678","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csc.liv.ac.uk/~leslie/papers/mcn.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.147.5989","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.147.5989","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csc.liv.ac.uk/~mjw/pubs/mlq2009.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.157.7643","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.7643","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csc.liv.ac.uk/~pwg/papers/MLQ-eggw09.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.304.2470","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.2470","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csc.liv.ac.uk/~leslie/papers/mcn.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.577.5377","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.577.5377","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.soton.ac.uk/265285/1/mcn.pdf","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:09c4baea-b5b1-44dc-99a2-cfaf3b0157fd","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:09c4baea-b5b1-44dc-99a2-cfaf3b0157fd","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Computer Science","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3818870529","display_name":null,"funder_award_id":"ES/F035845/1","funder_id":"https://openalex.org/F4320334630","funder_display_name":"Economic and Social Research Council"},{"id":"https://openalex.org/G5557473437","display_name":null,"funder_award_id":"GR/T10671/01","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6285924842","display_name":"EUROCORES LogiCCC (collaboration led by Dr. Edith Elkind): Computational Foundations of Social Choice.","funder_award_id":"ES/F035845/1","funder_id":"https://openalex.org/F4320334630","funder_display_name":"Economic and Social Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334630","display_name":"Economic and Social Research Council","ror":"https://ror.org/03n0ht308"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W40807208","https://openalex.org/W62192591","https://openalex.org/W175230508","https://openalex.org/W1549171560","https://openalex.org/W2046116913","https://openalex.org/W2064699170","https://openalex.org/W2071210909","https://openalex.org/W2072665610","https://openalex.org/W2101522887","https://openalex.org/W2107761114","https://openalex.org/W2109100253","https://openalex.org/W2167073044","https://openalex.org/W3124653719"],"related_works":["https://openalex.org/W2803105815","https://openalex.org/W1995780029","https://openalex.org/W1584952351","https://openalex.org/W2803150505","https://openalex.org/W2042580993","https://openalex.org/W2952811515","https://openalex.org/W2259808229","https://openalex.org/W2289231326","https://openalex.org/W2611507364","https://openalex.org/W2511887768"],"abstract_inverted_index":{"Abstract":[0],"Coalitional":[1],"games":[2,25,140,203],"raise":[3],"a":[4,61,79,89,98,113,157],"number":[5,145],"of":[6,12,14,48,100,115,124,138,146,160,176],"important":[7],"questions":[8],"from":[9],"the":[10,49,68,121,129,172,182],"point":[11],"view":[13],"computer":[15],"science,":[16],"key":[17],"among":[18],"them":[19],"being":[20],"how":[21,28,181],"to":[22,29,111,192],"represent":[23],"such":[24,35,127,147],"compactly,":[26],"and":[27,44,51,84,93],"efficiently":[30],"compute":[31],"solution":[32,125,198],"concepts":[33,126,199],"assuming":[34],"representations.":[36],"Marginal":[37],"contribution":[38,118],"nets":[39,119,155],"(MC\u2010nets),":[40],"introduced":[41],"by":[42],"Ieong":[43,92],"Shoham,":[45],"are":[46,60,109,134],"one":[47],"simplest":[50],"most":[52],"influential":[53],"representation":[54],"schemes":[55],"for":[56,97,186],"coalitional":[57,139],"games.":[58],"MC\u2010nets":[59,161,188],"rulebased":[62],"formalism,":[63],"in":[64,195,200],"which":[65],"rules":[66],"take":[67],"form":[69],"pattern":[70,76],"\u2192":[71],"value":[72,86],",":[73,156],"where":[74,107],"\u201c":[75,85],"\u201d":[77,87],"is":[78,88,163],"Boolean":[80],"condition":[81],"over":[82],"agents,":[83],"numeric":[90],"value.":[91,131],"Shoham":[94],"showed":[95],"that,":[96],"class":[99,159],"what":[101],"we":[102,184],"will":[103],"call":[104],"\u201cbasic\u201d":[105],"MC\u2010nets,":[106,169],"patterns":[108],"constrained":[110],"be":[112,190],"conjunction":[114],"literals,":[116],"marginal":[117],"permit":[120],"easy":[122],"computation":[123],"as":[128],"Shapley":[130],"However,":[132],"there":[133],"very":[135],"natural":[136],"classes":[137],"that":[141,162],"require":[142],"an":[143],"exponential":[144],"basic":[148,168,177],"MC\u2010net":[149],"rules.":[150],"We":[151,179],"present":[152],"read\u2010once":[153,187],"MC\u2010":[154],"new":[158],"provably":[164],"more":[165],"compact":[166],"than":[167],"while":[170],"retaining":[171],"attractive":[173],"computational":[174],"properties":[175],"MC\u2010nets.":[178],"show":[180],"techniques":[183],"develop":[185],"can":[189],"applied":[191],"other":[193],"domains,":[194],"particular,":[196],"computing":[197],"network":[201],"flow":[202],"on":[204],"series\u2010parallel":[205],"networks":[206],"(\u00a9":[207],"2009":[208],"WILEY\u2010VCH":[209],"Verlag":[210],"GmbH":[211],"&":[212],"Co.":[213],"KGaA,":[214],"Weinheim)":[215]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}