{"id":"https://openalex.org/W7204277409","doi":"https://doi.org/10.48550/arxiv.2608.23915","title":"Equilibrium in closed constant-function market maker economies","display_name":"Equilibrium in closed constant-function market maker economies","publication_year":2026,"publication_date":"2026-08-24","ids":{"openalex":"https://openalex.org/W7204277409","doi":"https://doi.org/10.48550/arxiv.2608.23915"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.23915","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23915","pdf_url":"https://arxiv.org/pdf/2608.23915","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.23915","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101308359","display_name":"Muqiao Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Huang, Muqiao","raw_affiliation_strings":["Department of Statistics and Actuarial Science , University of Waterloo , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Actuarial Science , University of Waterloo , Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148304145","display_name":"Ruodu Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wang, Ruodu","raw_affiliation_strings":["Department of Statistics and Actuarial Science , University of Waterloo , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Actuarial Science , University of Waterloo , Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5148335680","display_name":"Yiyun Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wang, Yiyun","raw_affiliation_strings":["Department of Statistics and Actuarial Science , University of Waterloo , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Actuarial Science , University of Waterloo , Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9643999934196472,"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"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9643999934196472,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.029100000858306885,"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/T10047","display_name":"Financial Markets and Investment Strategies","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"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/constant-function-market-makers","display_name":"constant function market makers","score":0.9459999799728394},{"id":"https://openalex.org/keywords/decentralized-exchanges","display_name":"decentralized exchanges","score":0.5260000228881836},{"id":"https://openalex.org/keywords/pareto-optimality","display_name":"Pareto optimality","score":0.7960000038146973},{"id":"https://openalex.org/keywords/representative-agent","display_name":"representative agent","score":0.9309999942779541},{"id":"https://openalex.org/keywords/homothetic-preferences","display_name":"homothetic preferences","score":0.9800000190734863},{"id":"https://openalex.org/keywords/two-agent-economy","display_name":"two-agent economy","score":0.5910000205039978}],"concepts":[{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.6406999826431274},{"id":"https://openalex.org/C91709909","wikidata":"https://www.wikidata.org/wiki/Q583960","display_name":"Homothetic transformation","level":2,"score":0.6204000115394592},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.5594000220298767},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5533999800682068},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.527899980545044},{"id":"https://openalex.org/C2986314615","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto optimal","level":3,"score":0.47369998693466187},{"id":"https://openalex.org/C2780964549","wikidata":"https://www.wikidata.org/wiki/Q5156353","display_name":"Competitive equilibrium","level":2,"score":0.46459999680519104},{"id":"https://openalex.org/C2778599509","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto efficiency","level":3,"score":0.45089998841285706},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4205999970436096},{"id":"https://openalex.org/C109354906","wikidata":"https://www.wikidata.org/wiki/Q6015174","display_name":"Incomplete markets","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3635999858379364},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.35530000925064087},{"id":"https://openalex.org/C103382277","wikidata":"https://www.wikidata.org/wiki/Q282640","display_name":"General equilibrium theory","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C64112148","wikidata":"https://www.wikidata.org/wiki/Q160151","display_name":"Market price","level":2,"score":0.3231000006198883},{"id":"https://openalex.org/C2778348673","wikidata":"https://www.wikidata.org/wiki/Q739302","display_name":"Production (economics)","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C66887028","wikidata":"https://www.wikidata.org/wiki/Q382444","display_name":"Marginal cost","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C18991353","wikidata":"https://www.wikidata.org/wiki/Q1137319","display_name":"Market maker","level":4,"score":0.2797999978065491},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.27230000495910645},{"id":"https://openalex.org/C2777673361","wikidata":"https://www.wikidata.org/wiki/Q5281228","display_name":"Disadvantage","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C2775962089","wikidata":"https://www.wikidata.org/wiki/Q16721782","display_name":"Exchange economy","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C44527139","wikidata":"https://www.wikidata.org/wiki/Q841032","display_name":"Marginal revenue","level":3,"score":0.25870001316070557},{"id":"https://openalex.org/C2776303733","wikidata":"https://www.wikidata.org/wiki/Q836133","display_name":"Economic equilibrium","level":2,"score":0.2540999948978424},{"id":"https://openalex.org/C138551086","wikidata":"https://www.wikidata.org/wiki/Q842271","display_name":"Marginal utility","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.23915","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23915","pdf_url":"https://arxiv.org/pdf/2608.23915","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,"listed_in":[],"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":"doi:10.48550/arxiv.2608.23915","doi":"https://doi.org/10.48550/arxiv.2608.23915","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.23915","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,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.23915","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23915","pdf_url":"https://arxiv.org/pdf/2608.23915","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,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204277409.pdf","grobid_xml":"https://content.openalex.org/works/W7204277409.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W3176749601","https://openalex.org/W4291961646","https://openalex.org/W4388747991"],"related_works":["https://openalex.org/W3122963343","https://openalex.org/W4250130880","https://openalex.org/W4233675768","https://openalex.org/W7030285039","https://openalex.org/W2538160733","https://openalex.org/W3123549921","https://openalex.org/W2027330494","https://openalex.org/W269388567","https://openalex.org/W1975844057","https://openalex.org/W1995925678"],"abstract_inverted_index":{"We":[0],"study":[1],"equilibria":[2,47],"in":[3],"a":[4,22,75,116],"closed,":[5],"fee-free":[6],"constant-function":[7],"market":[8],"maker":[9],"(CFMM)":[10],"economy":[11],"with":[12],"two":[13,16],"assets":[14],"and":[15],"agents.":[17],"An":[18],"interior":[19,41,90,104],"state":[20,92],"is":[21,61,93],"unilateral":[23,46,119],"no-trade":[24],"equilibrium":[25,66],"exactly":[26,81],"when":[27,82],"the":[28,53,85],"CFMM":[29,55],"marginal":[30,35],"price":[31],"equals":[32],"both":[33],"agents'":[34],"rates":[36],"of":[37],"substitution.":[38],"For":[39],"an":[40,101],"initial":[42],"state,":[43],"individually":[44,102],"rational":[45,103],"are":[48],"Pareto":[49,117],"optimal":[50,118],"relative":[51],"to":[52,115],"fixed":[54,65],"invariant.":[56],"A":[57],"weak":[58],"representative":[59,78],"agent":[60,79],"obtained":[62],"at":[63],"each":[64],"by":[67],"weighted":[68],"sup-convolution,":[69],"whereas,":[70],"under":[71],"some":[72],"regularity":[73],"assumptions,":[74],"state-independent":[76],"strong":[77],"exists":[80],"agents":[83],"share":[84],"same":[86],"homothetic":[87],"preference.":[88],"Every":[89],"feasible":[91],"reachable":[94],"through":[95],"finitely":[96],"many":[97],"valid":[98],"trades,":[99],"but":[100],"target":[105],"need":[106],"not":[107],"be":[108],"improvement":[109],"reachable.":[110],"Alternating":[111],"utility-maximizing":[112],"trades":[113],"converge":[114],"equilibrium.":[120]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-27T00:00:00"}
