{"id":"https://openalex.org/W4408734276","doi":"https://doi.org/10.1007/s10898-025-01475-8","title":"On a tractable single-level reformulation of a multilevel model of the European entry-exit gas market with market power","display_name":"On a tractable single-level reformulation of a multilevel model of the European entry-exit gas market with market power","publication_year":2025,"publication_date":"2025-03-22","ids":{"openalex":"https://openalex.org/W4408734276","doi":"https://doi.org/10.1007/s10898-025-01475-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-025-01475-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-025-01475-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-025-01475-8.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10898-025-01475-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034784735","display_name":"Veronika Grimm","orcid":"https://orcid.org/0000-0002-9025-9731"},"institutions":[{"id":"https://openalex.org/I3130238102","display_name":"Lutheran University of Applied Sciences Nuremberg","ror":"https://ror.org/01tbgce33","country_code":"DE","type":"education","lineage":["https://openalex.org/I3130238102"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Veronika Grimm","raw_affiliation_strings":["Energy Systems and Market Design Lab, University of Technology Nuremberg (UTN), Ulmenstrasse 52h, 90443, N\u00fcrnberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Energy Systems and Market Design Lab, University of Technology Nuremberg (UTN), Ulmenstrasse 52h, 90443, N\u00fcrnberg, Germany","institution_ids":["https://openalex.org/I3130238102"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012480793","display_name":"Julia Gr\u00fcbel","orcid":null},"institutions":[{"id":"https://openalex.org/I3130238102","display_name":"Lutheran University of Applied Sciences Nuremberg","ror":"https://ror.org/01tbgce33","country_code":"DE","type":"education","lineage":["https://openalex.org/I3130238102"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Julia Gr\u00fcbel","raw_affiliation_strings":["Energy Systems and Market Design Lab, University of Technology Nuremberg (UTN), Ulmenstrasse 52h, 90443, N\u00fcrnberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Energy Systems and Market Design Lab, University of Technology Nuremberg (UTN), Ulmenstrasse 52h, 90443, N\u00fcrnberg, Germany","institution_ids":["https://openalex.org/I3130238102"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002857019","display_name":"Martin Schmidt","orcid":"https://orcid.org/0000-0001-6208-5677"},"institutions":[{"id":"https://openalex.org/I89864525","display_name":"Universit\u00e4t Trier","ror":"https://ror.org/02778hg05","country_code":"DE","type":"education","lineage":["https://openalex.org/I89864525"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Schmidt","raw_affiliation_strings":["Department of Mathematics, Trier University, Universit\u00e4tsring 15, 54296, Trier, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6208-5677","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Trier University, Universit\u00e4tsring 15, 54296, Trier, Germany","institution_ids":["https://openalex.org/I89864525"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061950902","display_name":"Alexandra Schwartz","orcid":"https://orcid.org/0000-0001-7465-972X"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexandra Schwartz","raw_affiliation_strings":["Faculty of Mathematics, Technische Universit\u00e4t Dresden, Zellescher Weg 12-14, 01069, Dresden, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Technische Universit\u00e4t Dresden, Zellescher Weg 12-14, 01069, Dresden, Germany","institution_ids":["https://openalex.org/I78650965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087500787","display_name":"Ann-Kathrin Wiertz","orcid":"https://orcid.org/0000-0003-0297-9761"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ann-Kathrin Wiertz","raw_affiliation_strings":["Industrial Organization and Energy Markets, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Lange Gasse 20, 90403, N\u00fcrnberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial Organization and Energy Markets, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Lange Gasse 20, 90403, N\u00fcrnberg, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111974497","display_name":"Gregor Z\u00f6ttl","orcid":null},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gregor Z\u00f6ttl","raw_affiliation_strings":["Industrial Organization and Energy Markets, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Lange Gasse 20, 90403, N\u00fcrnberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Industrial Organization and Energy Markets, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Lange Gasse 20, 90403, N\u00fcrnberg, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5034784735"],"corresponding_institution_ids":["https://openalex.org/I3130238102"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2780},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06962482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"91","issue":"4","first_page":"953","last_page":"985"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12129","display_name":"Global Energy Security and Policy","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2100","display_name":"General Energy"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12129","display_name":"Global Energy Security and Policy","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2100","display_name":"General Energy"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11059","display_name":"Market Dynamics and Volatility","score":0.9941999912261963,"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/T12639","display_name":"Global Energy and Sustainability Research","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2105","display_name":"Renewable Energy, Sustainability and the Environment"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7082839012145996},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.5048354268074036},{"id":"https://openalex.org/keywords/market-power","display_name":"Market power","score":0.4312751889228821},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.4222135543823242},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4110746383666992},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.1685759425163269},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.14697051048278809}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7082839012145996},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.5048354268074036},{"id":"https://openalex.org/C2775881736","wikidata":"https://www.wikidata.org/wiki/Q1274157","display_name":"Market power","level":3,"score":0.4312751889228821},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4222135543823242},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4110746383666992},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.1685759425163269},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.14697051048278809},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2781127519","wikidata":"https://www.wikidata.org/wiki/Q43637","display_name":"Monopoly","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10898-025-01475-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-025-01475-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-025-01475-8.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:econstor.eu:10419/323688","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/323688","pdf_url":"https://www.econstor.eu/bitstream/10419/323688/1/10898_2025_Article_1475.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:91:y:2025:i:4:d:10.1007_s10898-025-01475-8","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-025-01475-8","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:open.fau.de:openfau/36740","is_oa":true,"landing_page_url":"https://open.fau.de/handle/openfau/36740","pdf_url":null,"source":{"id":"https://openalex.org/S7407055110","display_name":"OPUS FAU - Online publication system of Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10898-025-01475-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10898-025-01475-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10898-025-01475-8.pdf","source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Global Optimization","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6692072944","display_name":null,"funder_award_id":"Transregio 154","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7491996025","display_name":null,"funder_award_id":"TRR 154","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320318419","display_name":"Universit\u00e4t Trier","ror":"https://ror.org/02778hg05"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408734276.pdf"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W150908440","https://openalex.org/W1585597065","https://openalex.org/W1726816561","https://openalex.org/W1943385764","https://openalex.org/W1970923206","https://openalex.org/W1973338192","https://openalex.org/W1984147277","https://openalex.org/W1994312996","https://openalex.org/W1994433358","https://openalex.org/W2008125492","https://openalex.org/W2023858465","https://openalex.org/W2025269869","https://openalex.org/W2044065864","https://openalex.org/W2050339136","https://openalex.org/W2053366011","https://openalex.org/W2054607726","https://openalex.org/W2059354888","https://openalex.org/W2064091094","https://openalex.org/W2070816131","https://openalex.org/W2075073818","https://openalex.org/W2079104779","https://openalex.org/W2087764531","https://openalex.org/W2097408915","https://openalex.org/W2134636349","https://openalex.org/W2136431797","https://openalex.org/W2166455736","https://openalex.org/W2170709098","https://openalex.org/W2254879310","https://openalex.org/W2265653484","https://openalex.org/W2346664481","https://openalex.org/W2479349391","https://openalex.org/W2622645533","https://openalex.org/W2765099395","https://openalex.org/W3122684253","https://openalex.org/W3129003972","https://openalex.org/W3173274305","https://openalex.org/W3174839186","https://openalex.org/W3208100382","https://openalex.org/W4250852425","https://openalex.org/W4280556842","https://openalex.org/W4293177929","https://openalex.org/W4386387436","https://openalex.org/W4389880031","https://openalex.org/W4390234317"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"We":[1,136],"propose":[2],"a":[3,55,70,93,100,131],"framework":[4,62],"that":[5,122],"allows":[6,46],"to":[7,47,105,151],"quantitatively":[8],"analyze":[9],"the":[10,13,23,26,35,49,64,80,84,108,112,126,138,153],"interplay":[11],"of":[12,25,37,43,69,83,111,140,155],"different":[14],"agents":[15],"involved":[16],"in":[17,22],"gas":[18,75,85],"trade":[19],"and":[20,41,72,87,143],"transport":[21],"context":[24],"European":[27],"entry-exit":[28],"system.":[29],"Previous":[30],"contributions":[31],"have":[32],"focused":[33],"on":[34],"case":[36,68],"perfectly":[38],"competitive":[39],"buyers":[40,88],"sellers":[42,86],"gas,":[44],"which":[45,97],"replace":[48],"respective":[50],"market":[51],"equilibrium":[52],"problem":[53],"by":[54],"single":[56],"welfare":[57],"maximization":[58],"problem.":[59],"Our":[60],"novel":[61],"considers":[63],"mathematically":[65],"more":[66],"challenging":[67,127],"monopolistic":[71],"thus":[73],"strategic":[74],"seller.":[76],"In":[77],"this":[78,116,141],"framework,":[79],"objective":[81,95],"functions":[82],"cannot":[89],"be":[90],"aggregated":[91],"into":[92],"common":[94],"function,":[96],"is":[98,103],"why":[99],"multilevel":[101],"formulation":[102],"necessary":[104],"accurately":[106],"capture":[107],"sequential":[109],"nature":[110],"decisions":[113],"taken.":[114],"For":[115],"setup,":[117],"we":[118],"derive":[119],"sufficient":[120],"conditions":[121],"allow":[123],"for":[124,146],"reformulating":[125],"four-level":[128],"model":[129],"as":[130],"computationally":[132],"tractable":[133],"single-level":[134],"reformulation.":[135],"prove":[137],"correctness":[139],"reformulation":[142],"use":[144],"it":[145],"solving":[147],"several":[148],"test":[149],"instances":[150],"illustrate":[152],"applicability":[154],"our":[156],"approach.":[157]},"counts_by_year":[],"updated_date":"2025-12-28T23:10:05.387466","created_date":"2025-10-10T00:00:00"}