{"id":"https://openalex.org/W2121717744","doi":"https://doi.org/10.1145/1980522.1980525","title":"Computing Shapley's saddles","display_name":"Computing Shapley's saddles","publication_year":2009,"publication_date":"2009-12-01","ids":{"openalex":"https://openalex.org/W2121717744","doi":"https://doi.org/10.1145/1980522.1980525","mag":"2121717744"},"language":"en","primary_location":{"id":"doi:10.1145/1980522.1980525","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1980522.1980525","pdf_url":null,"source":{"id":"https://openalex.org/S4210233839","display_name":"ACM SIGecom Exchanges","issn_l":"1551-9031","issn":["1551-9031"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGecom Exchanges","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/A5001200543","display_name":"Felix Brandt","orcid":"https://orcid.org/0000-0002-4179-9897"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Felix Brandt","raw_affiliation_strings":["Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","institution_ids":["https://openalex.org/I8204097"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031193164","display_name":"Markus Brill","orcid":"https://orcid.org/0000-0001-9509-7017"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Brill","raw_affiliation_strings":["Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","institution_ids":["https://openalex.org/I8204097"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041652507","display_name":"Felix Fischer","orcid":"https://orcid.org/0000-0002-8403-9273"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Felix Fischer","raw_affiliation_strings":["Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","institution_ids":["https://openalex.org/I8204097"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017927930","display_name":"Paul Harrenstein","orcid":"https://orcid.org/0000-0001-9766-7618"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Paul Harrenstein","raw_affiliation_strings":["Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","institution_ids":["https://openalex.org/I8204097"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101496943","display_name":"Jan Hoffmann","orcid":"https://orcid.org/0000-0001-8326-0788"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jan Hoffmann","raw_affiliation_strings":["Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5001200543"],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":null,"apc_paid":null,"fwci":1.2498,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82790534,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"2","first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9995999932289124,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12137","display_name":"Economic theories and models","score":0.9905999898910522,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.8097496628761292},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.7652671337127686},{"id":"https://openalex.org/keywords/epsilon-equilibrium","display_name":"Epsilon-equilibrium","score":0.48898184299468994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4789160490036011},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4526776969432831},{"id":"https://openalex.org/keywords/criticism","display_name":"Criticism","score":0.4332856237888336},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.43198150396347046},{"id":"https://openalex.org/keywords/solution-concept","display_name":"Solution concept","score":0.4310183525085449},{"id":"https://openalex.org/keywords/shapley-value","display_name":"Shapley value","score":0.41480323672294617},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.358570396900177},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32105886936187744}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.8097496628761292},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.7652671337127686},{"id":"https://openalex.org/C141824439","wikidata":"https://www.wikidata.org/wiki/Q307521","display_name":"Epsilon-equilibrium","level":4,"score":0.48898184299468994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4789160490036011},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4526776969432831},{"id":"https://openalex.org/C7991579","wikidata":"https://www.wikidata.org/wiki/Q17955","display_name":"Criticism","level":2,"score":0.4332856237888336},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.43198150396347046},{"id":"https://openalex.org/C11343654","wikidata":"https://www.wikidata.org/wiki/Q780008","display_name":"Solution concept","level":3,"score":0.4310183525085449},{"id":"https://openalex.org/C199022921","wikidata":"https://www.wikidata.org/wiki/Q240046","display_name":"Shapley value","level":3,"score":0.41480323672294617},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.358570396900177},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32105886936187744},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/1980522.1980525","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1980522.1980525","pdf_url":null,"source":{"id":"https://openalex.org/S4210233839","display_name":"ACM SIGecom Exchanges","issn_l":"1551-9031","issn":["1551-9031"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM SIGecom Exchanges","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.9258","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.9258","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www7.in.tum.de/~brandtf/papers/saddle_short.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.157.473","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.473","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.tcs.ifi.lmu.de/~hoffmann/papers/shapleysaddles.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.157.681","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.681","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sigecom.org/exchanges/volume_8/2/brandt.pdf","raw_type":"text"},{"id":"pmh:oai:wrap.warwick.ac.uk:170780","is_oa":false,"landing_page_url":"http://wrap.warwick.ac.uk/170780/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1491494309","https://openalex.org/W1746666929","https://openalex.org/W1992958064","https://openalex.org/W2117657913","https://openalex.org/W2119586820","https://openalex.org/W2528816995","https://openalex.org/W2565699923","https://openalex.org/W6629380366"],"related_works":["https://openalex.org/W1853631319","https://openalex.org/W2013767790","https://openalex.org/W3125812435","https://openalex.org/W4301347782","https://openalex.org/W1667857601","https://openalex.org/W1978065715","https://openalex.org/W2282604764","https://openalex.org/W2408729172","https://openalex.org/W2025767136","https://openalex.org/W4299551322"],"abstract_inverted_index":{"Game-theoretic":[0],"solution":[1],"concepts,":[2],"such":[3],"as":[4],"Nash":[5,25],"equilibrium,":[6],"are":[7],"playing":[8],"an":[9],"ever":[10],"increasing":[11],"role":[12],"in":[13,40],"the":[14,33],"study":[15],"of":[16,18,24,35],"systems":[17],"autonomous":[19],"agents.":[20],"A":[21],"common":[22],"criticism":[23],"equilibrium":[26],"is":[27,43],"that":[28],"its":[29],"existence":[30],"relies":[31],"on":[32],"possibility":[34],"randomizing":[36],"over":[37],"actions,":[38],"which":[39],"many":[41],"cases":[42],"deemed":[44],"unsuitable,":[45],"impractical,":[46],"or":[47],"even":[48],"infeasible.":[49]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
