{"id":"https://openalex.org/W2067768752","doi":"https://doi.org/10.1145/2465769.2465774","title":"The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions","display_name":"The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions","publication_year":2013,"publication_date":"2013-05-01","ids":{"openalex":"https://openalex.org/W2067768752","doi":"https://doi.org/10.1145/2465769.2465774","mag":"2067768752"},"language":"en","primary_location":{"id":"doi:10.1145/2465769.2465774","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2465769.2465774","pdf_url":null,"source":{"id":"https://openalex.org/S4210173995","display_name":"ACM Transactions on Economics and Computation","issn_l":"2167-8375","issn":["2167-8375","2167-8383"],"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 Transactions on Economics and Computation","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/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":true,"raw_author_name":"Paul W. Goldberg","raw_affiliation_strings":["University of Liverpool","#N##TAB##TAB##TAB##TAB# University of Liverpool#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"University of Liverpool","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Liverpool#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103200572","display_name":"Christos H. Papadimitriou","orcid":"https://orcid.org/0009-0000-7264-8015"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christos H. Papadimitriou","raw_affiliation_strings":["University of California at Berkeley"],"affiliations":[{"raw_affiliation_string":"University of California at Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084692264","display_name":"Rahul Savani","orcid":"https://orcid.org/0000-0003-1262-7831"},"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":"Rahul Savani","raw_affiliation_strings":["University of Liverpool","#N##TAB##TAB##TAB##TAB# University of Liverpool#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"University of Liverpool","institution_ids":["https://openalex.org/I146655781"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Liverpool#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5067662147"],"corresponding_institution_ids":["https://openalex.org/I146655781"],"apc_list":null,"apc_paid":null,"fwci":6.40370346,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.97123346,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"1","issue":"2","first_page":"1","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9997000098228455,"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":0.9997000098228455,"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/T10646","display_name":"Experimental Behavioral Economics Studies","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9925000071525574,"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/homotopy","display_name":"Homotopy","score":0.7271033525466919},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.6636946797370911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6075665354728699},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5826545357704163},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5393147468566895},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4792930483818054},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4151463806629181},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3917342722415924},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32386547327041626},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32368195056915283},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32195571064949036},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.19888237118721008},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1942189633846283},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10695061087608337}],"concepts":[{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.7271033525466919},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.6636946797370911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6075665354728699},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5826545357704163},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5393147468566895},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4792930483818054},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4151463806629181},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3917342722415924},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32386547327041626},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32368195056915283},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32195571064949036},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.19888237118721008},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1942189633846283},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10695061087608337},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2465769.2465774","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2465769.2465774","pdf_url":null,"source":{"id":"https://openalex.org/S4210173995","display_name":"ACM Transactions on Economics and Computation","issn_l":"2167-8375","issn":["2167-8375","2167-8383"],"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 Transactions on Economics and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4012125382","display_name":null,"funder_award_id":"EP/G069239/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8797618872","display_name":"Efficient Decentralised Approaches in Algorithmic Game Theory","funder_award_id":"EP/G069239/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309327","display_name":"Google","ror":"https://ror.org/00njsd438"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1486687115","https://openalex.org/W1605188341","https://openalex.org/W1826384874","https://openalex.org/W1981698216","https://openalex.org/W1991624978","https://openalex.org/W1999560964","https://openalex.org/W2002373723","https://openalex.org/W2017781790","https://openalex.org/W2018044965","https://openalex.org/W2033317849","https://openalex.org/W2057913812","https://openalex.org/W2070994188","https://openalex.org/W2080995113","https://openalex.org/W2089649903","https://openalex.org/W2097300295","https://openalex.org/W2108614294","https://openalex.org/W2109100253","https://openalex.org/W2149682812","https://openalex.org/W2154374772","https://openalex.org/W2160135758","https://openalex.org/W2169359757","https://openalex.org/W2591957553","https://openalex.org/W2934944248","https://openalex.org/W3023735859","https://openalex.org/W3124438177","https://openalex.org/W4299440932","https://openalex.org/W6761309814","https://openalex.org/W7082866967"],"related_works":["https://openalex.org/W4237277701","https://openalex.org/W2606674369","https://openalex.org/W2121424666","https://openalex.org/W1587028174","https://openalex.org/W4301250310","https://openalex.org/W2030928163","https://openalex.org/W2067700950","https://openalex.org/W1669998927","https://openalex.org/W1771259603","https://openalex.org/W1550126246"],"abstract_inverted_index":{"We":[0],"show":[1,34,92],"that":[2,35,59,69,93,102],"the":[3,15,30,57,67,74,82,103],"widely":[4,98],"used":[5],"homotopy":[6,107],"method":[7],"for":[8,20,29,40],"solving":[9],"fixpoint":[10],"problems,":[11],"as":[12,14],"well":[13],"Harsanyi-Selten":[16,31],"equilibrium":[17],"selection":[18],"process":[19],"games,":[21],"are":[22,45],"PSPACE-complete":[23,47,62],"to":[24,48,63],"implement.":[25,49],"Extending":[26],"our":[27,54,94],"result":[28,58,83],"process,":[32],"we":[33],"several":[36],"other":[37],"homotopy-based":[38],"algorithms":[39],"finding":[41],"equilibria":[42,68],"of":[43,53,66,81,105],"games":[44],"also":[46],"A":[50],"further":[51],"application":[52],"techniques":[55,95],"yields":[56],"it":[60],"is":[61,109],"compute":[64],"any":[65],"could":[70],"be":[71,97],"found":[72],"via":[73],"classical":[75],"Lemke-Howson":[76],"algorithm,":[77],"a":[78,110],"complexity-theoretic":[79],"strengthening":[80],"in":[84],"Savani":[85],"and":[86,100],"von":[87],"Stengel":[88],"[2006].":[89],"These":[90],"results":[91],"can":[96],"applied":[99],"suggest":[101],"PSPACE-completeness":[104],"implementing":[106],"methods":[108],"general":[111],"principle.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":8}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}