{"id":"https://openalex.org/W1977645093","doi":"https://doi.org/10.1142/s0219198904000150","title":"FORMALIZATION OF MULTI-LEVEL GAMES","display_name":"FORMALIZATION OF MULTI-LEVEL GAMES","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W1977645093","doi":"https://doi.org/10.1142/s0219198904000150","mag":"1977645093"},"language":"en","primary_location":{"id":"doi:10.1142/s0219198904000150","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219198904000150","pdf_url":null,"source":{"id":"https://openalex.org/S130757258","display_name":"International Game Theory Review","issn_l":"0219-1989","issn":["0219-1989","1793-6675"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Game Theory Review","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/A5059935218","display_name":"Kjell Hausken","orcid":"https://orcid.org/0000-0001-7319-3876"},"institutions":[{"id":"https://openalex.org/I92008406","display_name":"University of Stavanger","ror":"https://ror.org/02qte9q33","country_code":"NO","type":"education","lineage":["https://openalex.org/I92008406"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"KJELL HAUSKEN","raw_affiliation_strings":["School of Economics, Culture and Social Sciences, University of Stavanger, N-4068 Stavanger, Norway"],"affiliations":[{"raw_affiliation_string":"School of Economics, Culture and Social Sciences, University of Stavanger, N-4068 Stavanger, Norway","institution_ids":["https://openalex.org/I92008406"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037777111","display_name":"Ross Cressman","orcid":null},"institutions":[{"id":"https://openalex.org/I75381157","display_name":"Wilfrid Laurier University","ror":"https://ror.org/00fn7gb05","country_code":"CA","type":"education","lineage":["https://openalex.org/I75381157"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"ROSS CRESSMAN","raw_affiliation_strings":["Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada","Department of Mathematics, Wilfrid Laurier University Waterloo, Ontario, N2L 3C5, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada","institution_ids":["https://openalex.org/I75381157"]},{"raw_affiliation_string":"Department of Mathematics, Wilfrid Laurier University Waterloo, Ontario, N2L 3C5, Canada","institution_ids":["https://openalex.org/I75381157"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059935218"],"corresponding_institution_ids":["https://openalex.org/I92008406"],"apc_list":null,"apc_paid":null,"fwci":0.4506,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.67981394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"06","issue":"02","first_page":"195","last_page":"221"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.998199999332428,"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":0.998199999332428,"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/T13402","display_name":"Business Strategy and Innovation","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/1408","display_name":"Strategy and Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9703999757766724,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.7540261745452881},{"id":"https://openalex.org/keywords/outcome","display_name":"Outcome (game theory)","score":0.6513793468475342},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.5583310127258301},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.534206748008728},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.5285812020301819},{"id":"https://openalex.org/keywords/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.523891806602478},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5106425881385803},{"id":"https://openalex.org/keywords/best-response","display_name":"Best response","score":0.4550217092037201},{"id":"https://openalex.org/keywords/extensive-form-game","display_name":"Extensive-form game","score":0.4543357491493225},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4271649718284607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4074961841106415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37034815549850464},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.30462902784347534},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09510606527328491},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07163822650909424}],"concepts":[{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.7540261745452881},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.6513793468475342},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.5583310127258301},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.534206748008728},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.5285812020301819},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.523891806602478},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5106425881385803},{"id":"https://openalex.org/C32407928","wikidata":"https://www.wikidata.org/wiki/Q2733833","display_name":"Best response","level":3,"score":0.4550217092037201},{"id":"https://openalex.org/C146930158","wikidata":"https://www.wikidata.org/wiki/Q656416","display_name":"Extensive-form game","level":4,"score":0.4543357491493225},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4271649718284607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4074961841106415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37034815549850464},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.30462902784347534},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09510606527328491},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07163822650909424},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0219198904000150","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219198904000150","pdf_url":null,"source":{"id":"https://openalex.org/S130757258","display_name":"International Game Theory Review","issn_l":"0219-1989","issn":["0219-1989","1793-6675"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Game Theory Review","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:igtrxx:v:06:y:2004:i:02:n:s0219198904000150","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219198904000150","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:RePEc:wsi:igtrxx:v:06:y:2004:i:02:p:195-221","is_oa":false,"landing_page_url":"http://www.worldscinet.com/cgi-bin/details.cgi?type=html&amp;id=pii:S0219198904000150","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W87757974","https://openalex.org/W102012633","https://openalex.org/W1486212401","https://openalex.org/W1492324318","https://openalex.org/W1559682027","https://openalex.org/W1571072200","https://openalex.org/W1572455460","https://openalex.org/W1604756073","https://openalex.org/W1820512588","https://openalex.org/W1980947936","https://openalex.org/W1981917434","https://openalex.org/W1986698147","https://openalex.org/W1988097031","https://openalex.org/W1993125718","https://openalex.org/W2013714676","https://openalex.org/W2014939392","https://openalex.org/W2022773153","https://openalex.org/W2026926997","https://openalex.org/W2039987052","https://openalex.org/W2044601025","https://openalex.org/W2046307793","https://openalex.org/W2049155841","https://openalex.org/W2056803970","https://openalex.org/W2065359416","https://openalex.org/W2074935642","https://openalex.org/W2078393780","https://openalex.org/W2096545552","https://openalex.org/W2104848667","https://openalex.org/W2107678607","https://openalex.org/W2108378466","https://openalex.org/W2111647959","https://openalex.org/W2119670528","https://openalex.org/W2122274100","https://openalex.org/W2156762071","https://openalex.org/W2164355926","https://openalex.org/W2166373025","https://openalex.org/W2205524882","https://openalex.org/W2210200973","https://openalex.org/W2313896093","https://openalex.org/W2328959596","https://openalex.org/W2475481689","https://openalex.org/W2768978272","https://openalex.org/W3003490010","https://openalex.org/W3027820740","https://openalex.org/W3122711284","https://openalex.org/W3124984768","https://openalex.org/W3136305603","https://openalex.org/W3166004482","https://openalex.org/W4230450248","https://openalex.org/W4234761190","https://openalex.org/W4236026269","https://openalex.org/W4238895675","https://openalex.org/W4245695223","https://openalex.org/W4246439308","https://openalex.org/W4249291651","https://openalex.org/W4249557133","https://openalex.org/W4252853500","https://openalex.org/W4253810207","https://openalex.org/W4290016560","https://openalex.org/W4298314778","https://openalex.org/W4298770613","https://openalex.org/W4301407432","https://openalex.org/W4375820594"],"related_works":["https://openalex.org/W4244028092","https://openalex.org/W2185279757","https://openalex.org/W4312141693","https://openalex.org/W1514842472","https://openalex.org/W189396554","https://openalex.org/W3123289354","https://openalex.org/W175813753","https://openalex.org/W3194882106","https://openalex.org/W3121983853","https://openalex.org/W2494549992"],"abstract_inverted_index":{"The":[0],"article":[1],"presents":[2],"multilevel":[3,27,30,43,148],"game":[4,12,28],"theory,":[5],"as":[6,14,73,105],"a":[7,26,57,106,113,118,124],"generalization":[8],"of":[9,108],"conventional":[10,81],"single-level":[11],"theory":[13],"it":[15,136,138],"has":[16],"developed":[17],"since":[18],"von":[19],"Neumann":[20],"and":[21,33,39],"Morgenstern":[22],"(1944).":[23],"We":[24],"define":[25],"structure,":[29],"games,":[31],"payoffs":[32],"distribution":[34],"rules,":[35],"upward":[36],"feasible":[37],"strategies":[38,66,133],"the":[40,78,102,109,144,147],"solution":[41],"concept":[42],"Nash":[44],"equilibrium":[45],"(MNE)":[46],"in":[47,75,129],"such":[48],"games.":[49],"A":[50],"MNE":[51,99,125],"must":[52,100],"be,":[53],"for":[54,80],"each":[55],"player,":[56],"best":[58],"reply":[59],"against":[60],"itself":[61],"with":[62],"respect":[63],"to":[64,77],"alternative":[65],"that":[67,123],"may":[68,139],"have":[69],"other":[70],"players":[71],"deviate":[72],"well,":[74],"contrast":[76],"NE":[79,107,114],"games":[82],"where":[83],"simultaneous":[84],"deviations":[85],"by":[86],"more":[87],"than":[88],"one":[89],"player":[90],"are":[91],"not":[92,116,127,140],"considered.":[93],"Although":[94],"every":[95],"pure":[96,130],"or":[97,131],"mixed":[98,132],"give":[101],"same":[103],"outcome":[104],"extensive":[110],"form":[111],"representation,":[112],"is":[115,121,150],"necessarily":[117],"MNE.":[119],"It":[120],"shown":[122],"need":[126],"exist":[128],"and,":[134],"if":[135],"does,":[137],"be":[141],"unique.":[142],"In":[143],"former":[145],"case,":[146],"structure":[149],"considered":[151],"unmaintainable.":[152]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
