{"id":"https://openalex.org/W7161781268","doi":"https://doi.org/10.3390/e28050571","title":"Does More Flexible Pricing Always Pay? Profit-Driven Pricing and Market Stability Under Platform Regulation","display_name":"Does More Flexible Pricing Always Pay? Profit-Driven Pricing and Market Stability Under Platform Regulation","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161781268","doi":"https://doi.org/10.3390/e28050571","pmid":"https://pubmed.ncbi.nlm.nih.gov/42187986"},"language":"en","primary_location":{"id":"doi:10.3390/e28050571","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28050571","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/e28050571","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088317335","display_name":"L Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Le-Bin Wang","raw_affiliation_strings":["School of Economics and Management, Xidian University, Xi\u2019an 710126, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Xidian University, Xi\u2019an 710126, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136546729","display_name":"Jian Chai","orcid":"https://orcid.org/0000-0002-9167-9121"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Chai","raw_affiliation_strings":["School of Economics and Management, Xidian University, Xi\u2019an 710126, China"],"raw_orcid":"https://orcid.org/0000-0002-9167-9121","affiliations":[{"raw_affiliation_string":"School of Economics and Management, Xidian University, Xi\u2019an 710126, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107695138","display_name":"Ying Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Yang","raw_affiliation_strings":["School of Economics and Management, Xidian University, Xi\u2019an 710126, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Xidian University, Xi\u2019an 710126, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.69585089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"5","first_page":"571","last_page":"571"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11437","display_name":"Digital Platforms and Economics","score":0.8184000253677368,"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":0.8184000253677368,"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/T11043","display_name":"Merger and Competition Analysis","score":0.044199999421834946,"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/T11031","display_name":"Game Theory and Applications","score":0.021199999377131462,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.6177999973297119},{"id":"https://openalex.org/keywords/volatility","display_name":"Volatility (finance)","score":0.5397999882698059},{"id":"https://openalex.org/keywords/profit","display_name":"Profit (economics)","score":0.5364000201225281},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5268999934196472},{"id":"https://openalex.org/keywords/stackelberg-competition","display_name":"Stackelberg competition","score":0.516700029373169},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5156999826431274},{"id":"https://openalex.org/keywords/state-variable","display_name":"State variable","score":0.4153999984264374},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.4090999960899353}],"concepts":[{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.6177999973297119},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.5593000054359436},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.5397999882698059},{"id":"https://openalex.org/C181622380","wikidata":"https://www.wikidata.org/wiki/Q26911","display_name":"Profit (economics)","level":2,"score":0.5364000201225281},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5268999934196472},{"id":"https://openalex.org/C199510392","wikidata":"https://www.wikidata.org/wiki/Q1184602","display_name":"Stackelberg competition","level":2,"score":0.516700029373169},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5156999826431274},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4871000051498413},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.424699991941452},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.4153999984264374},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3659000098705292},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3393999934196472},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32710000872612},{"id":"https://openalex.org/C82149807","wikidata":"https://www.wikidata.org/wiki/Q7242623","display_name":"Price of anarchy","level":4,"score":0.32670000195503235},{"id":"https://openalex.org/C188466206","wikidata":"https://www.wikidata.org/wiki/Q7242626","display_name":"Price of stability","level":3,"score":0.3208000063896179},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.3070000112056732},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.29010000824928284},{"id":"https://openalex.org/C3019439881","wikidata":"https://www.wikidata.org/wiki/Q1200230","display_name":"Price setting","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28050571","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28050571","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:42187986","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42187986","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:226c08472ef04fd5b456f884904c81dc","is_oa":true,"landing_page_url":"https://doaj.org/article/226c08472ef04fd5b456f884904c81dc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 28, Iss 5, p 571 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13205686","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13205686/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e28050571","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28050571","pdf_url":null,"source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G664069066","display_name":null,"funder_award_id":"72373116","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2,47],"a":[3,25,108],"dynamic":[4],"price":[5,39,69,182],"adjustment":[6,40,50,84,113,175],"system":[7,94,151],"in":[8],"platform":[9],"markets,":[10],"where":[11],"sellers":[12],"continuously":[13],"revise":[14],"prices,":[15],"and":[16,38,68,77,102,115,127,153],"examines":[17],"its":[18],"implications":[19],"for":[20],"market":[21,125],"stability.":[22],"We":[23,71,105],"develop":[24],"platform-led":[26],"discrete-time":[27],"Stackelberg":[28],"game":[29],"model":[30,55],"to":[31,142,149,160],"describe":[32],"the":[33,73,90,93,97,168,171],"evolution":[34],"of":[35,173],"sellers'":[36,83],"prices":[37],"speeds":[41,114],"under":[42],"bounded":[43],"rationality.":[44],"Unlike":[45],"previous":[46],"that":[48,79,117,132],"treat":[49],"speed":[51,88],"as":[52,57],"exogenous,":[53],"we":[54],"it":[56],"an":[58,154],"endogenous":[59],"state":[60],"variable":[61],"shaped":[62],"by":[63],"profit":[64],"incentives,":[65],"behavioral":[66],"inertia,":[67],"fluctuations.":[70],"derive":[72],"interior":[74],"symmetric":[75],"equilibrium":[76],"show":[78],"profit-driven":[80],"acceleration":[81,134,139],"increases":[82],"speed.":[85],"When":[86],"this":[87],"exceeds":[89],"stability":[91,122],"threshold,":[92],"may":[95],"leave":[96],"stable":[98],"region,":[99],"causing":[100],"bifurcations":[101],"complex":[103],"dynamics.":[104],"then":[106],"introduce":[107],"platform-imposed":[109],"upper":[110],"bound":[111],"on":[112,181],"demonstrate":[116],"appropriate":[118],"regulation":[119],"can":[120,140],"restore":[121],"while":[123,164],"balancing":[124],"responsiveness":[126],"efficiency.":[128],"Numerical":[129],"simulations":[130],"illustrate":[131],"moderate":[133],"improves":[135],"profitability,":[136],"whereas":[137],"excessive":[138,162],"lead":[141],"low-profit":[143],"regimes.":[144],"Entropy-based":[145],"metrics":[146],"are":[147],"used":[148],"quantify":[150],"complexity,":[152],"entropy-triggered":[155],"feedback-control":[156],"mechanism":[157],"is":[158],"proposed":[159],"mitigate":[161],"volatility":[163],"maintaining":[165],"flexibility.":[166],"Overall,":[167],"study":[169],"highlights":[170],"importance":[172],"governing":[174],"dynamics":[176],"rather":[177],"than":[178],"solely":[179],"focusing":[180],"levels.":[183]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2026-05-21T00:00:00"}