{"id":"https://openalex.org/W2235120461","doi":"https://doi.org/10.37236/5417","title":"Guaranteed Scoring Games","display_name":"Guaranteed Scoring Games","publication_year":2016,"publication_date":"2016-08-19","ids":{"openalex":"https://openalex.org/W2235120461","doi":"https://doi.org/10.37236/5417","mag":"2235120461"},"language":"en","primary_location":{"id":"doi:10.37236/5417","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5417","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p27/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p27/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016874557","display_name":"Urban Larsson","orcid":"https://orcid.org/0000-0003-3663-1720"},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Urban Larsson","raw_affiliation_strings":["Dalhousie University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dalhousie University","institution_ids":["https://openalex.org/I129902397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080800191","display_name":"Richard J. Nowakowski","orcid":"https://orcid.org/0000-0002-4434-672X"},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Richard J. Nowakowski","raw_affiliation_strings":["Dalhousie University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dalhousie University","institution_ids":["https://openalex.org/I129902397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039476034","display_name":"Jo\u00e3o Pedro Neto","orcid":"https://orcid.org/0000-0002-3974-0685"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jo\u00e3o P. Neto","raw_affiliation_strings":["University of Lisboa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Lisboa","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087256557","display_name":"Carlos P. Santos","orcid":"https://orcid.org/0000-0001-6609-6541"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos P. Santos","raw_affiliation_strings":["Center for Functional Analysis, Linear Structures and Applications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Functional Analysis, Linear Structures and Applications","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5415,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.82403693,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9994999766349792,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9114000201225281,"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/T11197","display_name":"Digital Games and Media","score":0.9103999733924866,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.8431277275085449},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.7085574865341187},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.6961596608161926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.637336790561676},{"id":"https://openalex.org/keywords/combinatorial-game-theory","display_name":"Combinatorial game theory","score":0.6096682548522949},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5981432199478149},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5797640681266785},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5242260098457336},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.49496835470199585},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4441477656364441},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4162728488445282},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3888852298259735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35986337065696716},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.24377429485321045},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.22148090600967407},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.19551965594291687},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13220390677452087}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.8431277275085449},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.7085574865341187},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6961596608161926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.637336790561676},{"id":"https://openalex.org/C102234262","wikidata":"https://www.wikidata.org/wiki/Q1320931","display_name":"Combinatorial game theory","level":4,"score":0.6096682548522949},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5981432199478149},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5797640681266785},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5242260098457336},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.49496835470199585},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4441477656364441},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4162728488445282},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3888852298259735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35986337065696716},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.24377429485321045},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.22148090600967407},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.19551965594291687},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13220390677452087},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/5417","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5417","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p27/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1505.07905","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1505.07905","pdf_url":"https://arxiv.org/pdf/1505.07905","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2235120461","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1505.07905.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1505.07905","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1505.07905","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.37236/5417","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5417","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i3p27/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4399999976158142}],"awards":[{"id":"https://openalex.org/G1204600187","display_name":null,"funder_award_id":"UID/MULTI/04046/2013","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3526950217","display_name":null,"funder_award_id":"UID/MULTI/04046/2013","funder_id":"https://openalex.org/F4320323642","funder_display_name":"Minist\u00e9rio da Ci\u00eancia, Tecnologia e Ensino Superior"},{"id":"https://openalex.org/G671296436","display_name":null,"funder_award_id":"04046","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320322337","display_name":"Killam Trusts","ror":"https://ror.org/021cbtn85"},{"id":"https://openalex.org/F4320323642","display_name":"Minist\u00e9rio da Ci\u00eancia, Tecnologia e Ensino Superior","ror":"https://ror.org/045b9pr88"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2235120461.pdf","grobid_xml":"https://content.openalex.org/works/W2235120461.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W578709777","https://openalex.org/W1568383619","https://openalex.org/W1573036064","https://openalex.org/W1624181706","https://openalex.org/W1659210086","https://openalex.org/W1993050093","https://openalex.org/W2010138312","https://openalex.org/W2041147693","https://openalex.org/W2119309634","https://openalex.org/W2261622378","https://openalex.org/W2271211030","https://openalex.org/W2330301979","https://openalex.org/W2894564506","https://openalex.org/W6701849997","https://openalex.org/W6759864841"],"related_works":["https://openalex.org/W2963077207","https://openalex.org/W2949452823","https://openalex.org/W3124259244","https://openalex.org/W2129975393","https://openalex.org/W3122689862","https://openalex.org/W2897115502","https://openalex.org/W2329265633","https://openalex.org/W3037334692","https://openalex.org/W2951447937","https://openalex.org/W3133966590","https://openalex.org/W3139580956","https://openalex.org/W2221785310","https://openalex.org/W2243848361","https://openalex.org/W2547977190","https://openalex.org/W2185264952","https://openalex.org/W2249333371","https://openalex.org/W3154344524","https://openalex.org/W3122041208","https://openalex.org/W2953162154","https://openalex.org/W189732821"],"abstract_inverted_index":{"The":[0,114,140],"class":[1],"of":[2,45,55,171],"Guaranteed":[3],"Scoring":[4],"Games":[5],"(GS)":[6],"are":[7,20,97],"two-player":[8],"combinatorial":[9],"games":[10,16,31,145,163],"with":[11,74,88],"the":[12,29,43,48,71,78,82,138,162],"property":[13],"that":[14,95,100,126],"Normal-play":[15],"(Conway":[17],"et.":[18],"al.)":[19],"ordered":[21,63,90],"embedded":[22],"into":[23],"GS.":[24],"They":[25],"include,":[26],"as":[27,77],"subclasses,":[28],"scoring":[30],"considered":[32],"by":[33,136,148],"Milnor":[34],"(1953),":[35],"Ettinger":[36],"(1996)":[37],"and":[38,47,68,73,173],"Johnson":[39],"(2014).":[40],"We":[41,93],"present":[42],"structure":[44,83],"GS":[46,59],"techniques":[49],"needed":[50],"to":[51,160],"analyze":[52],"a":[53,61,85,107,118,128,165],"sum":[54,76],"guaranteed":[56],"games.":[57],"Firstly,":[58],"form":[60],"partially":[62,89],"monoid,":[64],"via":[65,164],"defined":[66,147],"Right-":[67],"Left-stops":[69],"over":[70],"reals,":[72],"disjunctive":[75,154],"operation.":[79],"In":[80],"fact,":[81],"is":[84,116,134,146],"quotient":[86],"monoid":[87,115],"congruence":[91,112],"classes.":[92],"show":[94],"there":[96],"four":[98],"reductions":[99],"when":[101],"applied,":[102],"in":[103,121,152],"any":[104,153],"order,":[105],"give":[106],"unique":[108],"representative":[109],"for":[110],"each":[111],"class.":[113],"not":[117],"group,":[119],"but":[120],"this":[122],"paper":[123],"we":[124,157],"prove":[125],"if":[127],"game":[129],"has":[130],"an":[131],"inverse":[132],"it":[133],"obtained":[135],"'switching":[137],"players'.":[139],"order":[141],"relation":[142],"between":[143],"two":[144],"comparing":[149],"their":[150],"stops":[151],"sum.":[155],"Here,":[156],"demonstrate":[158],"how":[159],"compare":[161],"finite":[166],"algorithm":[167],"instead,":[168],"extending":[169],"ideas":[170],"Ettinger,":[172],"also":[174],"Siegel":[175],"(2013).":[176]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}