{"id":"https://openalex.org/W2911906860","doi":"https://doi.org/10.1134/s0005117919070117","title":"Pricing of Platforms in Two-Sided Markets with Heterogeneous Agents and Limited Market Size","display_name":"Pricing of Platforms in Two-Sided Markets with Heterogeneous Agents and Limited Market Size","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2911906860","doi":"https://doi.org/10.1134/s0005117919070117","mag":"2911906860"},"language":"en","primary_location":{"id":"doi:10.1134/s0005117919070117","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117919070117","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","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/A5063460883","display_name":"Zhe Feng","orcid":"https://orcid.org/0000-0001-6036-375X"},"institutions":[{"id":"https://openalex.org/I4210156834","display_name":"Institute of Economics","ror":"https://ror.org/04v31xa23","country_code":"CN","type":"facility","lineage":["https://openalex.org/I114218197","https://openalex.org/I4210156834"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Z. Feng","raw_affiliation_strings":["Institute of Economics, Tsinghua University, Beijing, P.R. China"],"affiliations":[{"raw_affiliation_string":"Institute of Economics, Tsinghua University, Beijing, P.R. China","institution_ids":["https://openalex.org/I99065089","https://openalex.org/I4210156834"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078551714","display_name":"T. Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210156834","display_name":"Institute of Economics","ror":"https://ror.org/04v31xa23","country_code":"CN","type":"facility","lineage":["https://openalex.org/I114218197","https://openalex.org/I4210156834"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"T. Liu","raw_affiliation_strings":["Institute of Economics, Tsinghua University, Beijing, P.R. China"],"affiliations":[{"raw_affiliation_string":"Institute of Economics, Tsinghua University, Beijing, P.R. China","institution_ids":["https://openalex.org/I99065089","https://openalex.org/I4210156834"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023223231","display_name":"Vladimir V. Mazalov","orcid":"https://orcid.org/0000-0003-2262-2620"},"institutions":[{"id":"https://openalex.org/I4210152247","display_name":"Karelian Research Centre","ror":"https://ror.org/05wgt8358","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210152247","https://openalex.org/I4210160366"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"V. V. Mazalov","raw_affiliation_strings":["Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, Petrozavodsk, Russia"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, Petrozavodsk, Russia","institution_ids":["https://openalex.org/I4210152247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064493794","display_name":"Jie Zheng","orcid":"https://orcid.org/0000-0001-9211-2875"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"J. Zheng","raw_affiliation_strings":["School of Economics and Management, Tsinghua University, Beijing, P.R. China"],"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Tsinghua University, Beijing, P.R. China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5023223231","https://openalex.org/A5064493794"],"corresponding_institution_ids":["https://openalex.org/I4210152247","https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":2.1704,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.89689874,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"80","issue":"7","first_page":"1347","last_page":"1357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11437","display_name":"Digital Platforms and Economics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11437","display_name":"Digital Platforms and Economics","score":0.9998999834060669,"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/T11499","display_name":"ICT Impact and Policies","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11043","display_name":"Merger and Competition Analysis","score":0.9955999851226807,"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/social-planner","display_name":"Social planner","score":0.8647924661636353},{"id":"https://openalex.org/keywords/duopoly","display_name":"Duopoly","score":0.8459240198135376},{"id":"https://openalex.org/keywords/monopoly","display_name":"Monopoly","score":0.829218327999115},{"id":"https://openalex.org/keywords/planner","display_name":"Planner","score":0.5706243515014648},{"id":"https://openalex.org/keywords/market-size","display_name":"Market size","score":0.5093320608139038},{"id":"https://openalex.org/keywords/microeconomics","display_name":"Microeconomics","score":0.4908181130886078},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.4779931902885437},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4545641541481018},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.41670602560043335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3533748388290405},{"id":"https://openalex.org/keywords/cournot-competition","display_name":"Cournot competition","score":0.2927340865135193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.17816150188446045}],"concepts":[{"id":"https://openalex.org/C2777706055","wikidata":"https://www.wikidata.org/wiki/Q7551303","display_name":"Social planner","level":2,"score":0.8647924661636353},{"id":"https://openalex.org/C180456769","wikidata":"https://www.wikidata.org/wiki/Q750207","display_name":"Duopoly","level":3,"score":0.8459240198135376},{"id":"https://openalex.org/C2781127519","wikidata":"https://www.wikidata.org/wiki/Q43637","display_name":"Monopoly","level":2,"score":0.829218327999115},{"id":"https://openalex.org/C2776999362","wikidata":"https://www.wikidata.org/wiki/Q2349274","display_name":"Planner","level":2,"score":0.5706243515014648},{"id":"https://openalex.org/C2983069542","wikidata":"https://www.wikidata.org/wiki/Q37654","display_name":"Market size","level":2,"score":0.5093320608139038},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.4908181130886078},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.4779931902885437},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4545641541481018},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.41670602560043335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3533748388290405},{"id":"https://openalex.org/C16520705","wikidata":"https://www.wikidata.org/wiki/Q601799","display_name":"Cournot competition","level":2,"score":0.2927340865135193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.17816150188446045},{"id":"https://openalex.org/C54750564","wikidata":"https://www.wikidata.org/wiki/Q26643","display_name":"Commerce","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0005117919070117","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0005117919070117","pdf_url":null,"source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322392","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1958341229","https://openalex.org/W2008975493","https://openalex.org/W2025987251","https://openalex.org/W2085225290","https://openalex.org/W2129998937","https://openalex.org/W2182882530","https://openalex.org/W2223279834","https://openalex.org/W2384774987","https://openalex.org/W2557530176","https://openalex.org/W2799468224","https://openalex.org/W3021909905","https://openalex.org/W3122409020","https://openalex.org/W3124299361","https://openalex.org/W3124640067"],"related_works":["https://openalex.org/W1983796782","https://openalex.org/W4226237690","https://openalex.org/W4243808738","https://openalex.org/W3121626461","https://openalex.org/W2068025765","https://openalex.org/W3122027809","https://openalex.org/W1780527415","https://openalex.org/W1998652201","https://openalex.org/W3021029342","https://openalex.org/W2154476367"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"equilibrium":[3,75,100],"in":[4,26,67,71,101,106],"a":[5,33,68,88,107],"two-sided":[6,108],"market":[7,45,76,109],"represented":[8],"by":[9],"network":[10],"platforms":[11],"and":[12,46],"heterogeneous":[13,49],"agents.":[14],"The":[15],"setup":[16],"below":[17],"is":[18],"based":[19],"on":[20,40],"the":[21,29,44,48,54,60,74,82,95,99,102],"Armstrong":[22],"monopoly":[23],"model":[24],"suggested":[25],"2006":[27],"under":[28],"following":[30],"assumptions:":[31],"(1)":[32],"continuum":[34],"of":[35,37,43,51,73,104],"agents":[36,52],"limited":[38],"size":[39],"each":[41],"side":[42],"(2)":[47],"utility":[50],"with":[53,110],"Hotelling":[55],"specification.":[56],"We":[57],"show":[58],"that":[59],"monopoly\u2019s":[61],"optimal":[62],"pricing":[63],"strategy":[64],"always":[65],"results":[66],"corner":[69,90],"solution":[70],"terms":[72],"share.":[77],"In":[78],"addition,":[79],"we":[80,93],"solve":[81],"social":[83],"planner\u2019s":[84],"optimization":[85],"problem,":[86],"obtaining":[87],"similar":[89],"solution.":[91],"Finally,":[92],"find":[94],"exact":[96],"values":[97],"for":[98],"case":[103],"duopoly":[105],"two":[111],"platforms.":[112]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}