{"id":"https://openalex.org/W4417503147","doi":"https://doi.org/10.3390/e28010004","title":"Single-Stage Causal Incentive Design via Optimal Interventions","display_name":"Single-Stage Causal Incentive Design via Optimal Interventions","publication_year":2025,"publication_date":"2025-12-19","ids":{"openalex":"https://openalex.org/W4417503147","doi":"https://doi.org/10.3390/e28010004","pmid":"https://pubmed.ncbi.nlm.nih.gov/41593911"},"language":"en","primary_location":{"id":"doi:10.3390/e28010004","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010004","pdf_url":"https://www.mdpi.com/1099-4300/28/1/4/pdf?version=1766150749","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://www.mdpi.com/1099-4300/28/1/4/pdf?version=1766150749","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070176556","display_name":"Sebasti\u00e1n Bejos","orcid":"https://orcid.org/0000-0001-8580-7361"},"institutions":[{"id":"https://openalex.org/I39824353","display_name":"National Institute of Astrophysics, Optics and Electronics","ror":"https://ror.org/00bpmmc63","country_code":"MX","type":"facility","lineage":["https://openalex.org/I39824353"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Sebasti\u00e1n Bejos","raw_affiliation_strings":["Computer Science Department, National Institute of Astrophysics, Optics and Electronics, Puebla 72840, Mexico"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, National Institute of Astrophysics, Optics and Electronics, Puebla 72840, Mexico","institution_ids":["https://openalex.org/I39824353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035687300","display_name":"Eduardo F. Morales","orcid":"https://orcid.org/0000-0002-7618-8762"},"institutions":[{"id":"https://openalex.org/I39824353","display_name":"National Institute of Astrophysics, Optics and Electronics","ror":"https://ror.org/00bpmmc63","country_code":"MX","type":"facility","lineage":["https://openalex.org/I39824353"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Eduardo F. Morales","raw_affiliation_strings":["Computer Science Department, National Institute of Astrophysics, Optics and Electronics, Puebla 72840, Mexico"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, National Institute of Astrophysics, Optics and Electronics, Puebla 72840, Mexico","institution_ids":["https://openalex.org/I39824353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044189592","display_name":"Luis Enrique Sucar","orcid":"https://orcid.org/0000-0002-3685-5567"},"institutions":[{"id":"https://openalex.org/I39824353","display_name":"National Institute of Astrophysics, Optics and Electronics","ror":"https://ror.org/00bpmmc63","country_code":"MX","type":"facility","lineage":["https://openalex.org/I39824353"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Luis Enrique Sucar","raw_affiliation_strings":["Computer Science Department, National Institute of Astrophysics, Optics and Electronics, Puebla 72840, Mexico"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, National Institute of Astrophysics, Optics and Electronics, Puebla 72840, Mexico","institution_ids":["https://openalex.org/I39824353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064277708","display_name":"Enrique Mu\u00f1oz de Cote","orcid":"https://orcid.org/0000-0002-3249-096X"},"institutions":[{"id":"https://openalex.org/I4210159477","display_name":"Total (United Kingdom)","ror":"https://ror.org/05q16h268","country_code":"GB","type":"company","lineage":["https://openalex.org/I103084370","https://openalex.org/I4210159477"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Enrique Munoz de Cote","raw_affiliation_strings":["Mutable Tactics, London CB2 9PJ, UK"],"affiliations":[{"raw_affiliation_string":"Mutable Tactics, London CB2 9PJ, UK","institution_ids":["https://openalex.org/I4210159477"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070176556"],"corresponding_institution_ids":["https://openalex.org/I39824353"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.3568,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.92135847,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"28","issue":"1","first_page":"4","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.24120000004768372,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.24120000004768372,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.20960000157356262,"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"}},{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.17030000686645508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/causal-inference","display_name":"Causal inference","score":0.508400022983551},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.45509999990463257},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4025000035762787},{"id":"https://openalex.org/keywords/frequentist-inference","display_name":"Frequentist inference","score":0.38100001215934753},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.3546000123023987},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.350600004196167},{"id":"https://openalex.org/keywords/budget-constraint","display_name":"Budget constraint","score":0.33880001306533813},{"id":"https://openalex.org/keywords/identifiability","display_name":"Identifiability","score":0.334199994802475}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5569000244140625},{"id":"https://openalex.org/C158600405","wikidata":"https://www.wikidata.org/wiki/Q5054566","display_name":"Causal inference","level":2,"score":0.508400022983551},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.48159998655319214},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.45509999990463257},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41499999165534973},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4025000035762787},{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.38100001215934753},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3546000123023987},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C8505890","wikidata":"https://www.wikidata.org/wiki/Q605095","display_name":"Budget constraint","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.3312999904155731},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3255000114440918},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.31299999356269836},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C11671645","wikidata":"https://www.wikidata.org/wiki/Q5054567","display_name":"Causal model","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.27410000562667847},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2612999975681305},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2567000091075897},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e28010004","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010004","pdf_url":"https://www.mdpi.com/1099-4300/28/1/4/pdf?version=1766150749","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:41593911","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41593911","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:6079b0c58a554df49eb5cdcce95301c4","is_oa":true,"landing_page_url":"https://doaj.org/article/6079b0c58a554df49eb5cdcce95301c4","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 28, Iss 1, p 4 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e28010004","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28010004","pdf_url":"https://www.mdpi.com/1099-4300/28/1/4/pdf?version=1766150749","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/G3794830189","display_name":null,"funder_award_id":"1562","funder_id":"https://openalex.org/F4320321739","funder_display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda"}],"funders":[{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417503147.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1533476743","https://openalex.org/W1986280275","https://openalex.org/W2047278710","https://openalex.org/W2099958618","https://openalex.org/W2143891888","https://openalex.org/W2166566250","https://openalex.org/W2326254517","https://openalex.org/W2770221405","https://openalex.org/W2904041175","https://openalex.org/W2998004401","https://openalex.org/W3156469768","https://openalex.org/W4211049957","https://openalex.org/W4245139159","https://openalex.org/W4384817778","https://openalex.org/W4390964981"],"related_works":[],"abstract_inverted_index":{"We":[0],"introduce":[1],"Causal":[2,161],"Incentive":[3],"Design":[4],"(CID),":[5],"a":[6,45,78,98,141,155,159,176,183,267,275,279,317],"framework":[7],"that":[8,208,271,287],"applies":[9],"causal":[10,35,58,61,249,268,321,325],"inference":[11,62,250],"to":[12,52,134,274,327,336],"canonical":[13],"single-stage":[14],"principal-agent":[15,259,331],"problems":[16,260],"(PAPs)":[17],"characterized":[18],"by":[19,283],"bilateral":[20],"private":[21,262],"information.":[22,263],"Within":[23],"CID,":[24],"the":[25,56,69,73,83,87,93,107,117,121,125,137,149,171,200,232,240,244,288,295,311],"operating":[26],"rules":[27],"of":[28,72,89,106,120,154,227,243,320],"PAPs":[29],"are":[30,40,223,334],"formalized":[31],"using":[32,175,212],"an":[33,102,113,192,205],"additive-noise":[34],"graphical":[36,322],"model":[37],"(CGM).":[38],"Incentives":[39],"modeled":[41],"as":[42,68],"interventions":[43,54],"on":[44,182],"function":[46],"space":[47],"variable,":[48],"\u0393,":[49],"which":[50,247,333],"correspond":[51],"policy":[53,80,201,256],"in":[55,82,225,258,278],"principal-follower":[57],"relation.":[59],"The":[60],"target":[63],"estimand":[64,94],"V(\u0393)":[65,95],"is":[66,132,146,166,293,299,306],"defined":[67,181],"expected":[70],"value":[71,202],"principal's":[74,108],"utility":[75,109],"variable":[76],"under":[77,216,261],"specified":[79],"intervention":[81],"post-intervention":[84],"distribution.":[85],"In":[86],"context":[88],"additive-Gaussian":[90],"independent":[91],"noise,":[92],"decomposes":[96],"into":[97],"two-layer":[99],"expectation:":[100],"(i)":[101],"inner":[103],"Gaussian":[104,178],"smoothing":[105],"regression;":[110],"and":[111,190,253,324,330,338],"(ii)":[112],"outer":[114],"averaging":[115],"over":[116],"conditional":[118],"probability":[119],"follower's":[122],"action":[123],"given":[124],"incentive":[126,157,277,328],"policy.":[127],"A":[128],"Gauss-Hermite":[129],"quadrature":[130],"method":[131],"employed":[133],"efficiently":[135],"estimate":[136],"first":[138],"layer,":[139],"while":[140],"policy-local":[142],"kernel":[143],"reweighting":[144],"approach":[145,265],"used":[147,290],"for":[148,231,291,301],"second.":[150],"For":[151],"offline":[152,213,297],"selection":[153],"single":[156],"policy,":[158],"Functional":[160],"Bayesian":[162],"Optimization":[163],"(FCBO)":[164],"algorithm":[165,169],"introduced.":[167],"This":[168,264],"models":[170,323],"objective":[172],"functional":[173,177],"\u03b3\u21a6V(\u03b3)":[174],"process":[179],"surrogate":[180],"Reproducing":[184],"Kernel":[185],"Hilbert":[186],"Space":[187],"(RKHS)":[188],"domain":[189],"utilizes":[191],"Upper":[193],"Confidence":[194],"Bound":[195],"(UCB)":[196],"acquisition":[197],"functional.":[198],"Consequently,":[199],"V(\u03b3)":[203],"becomes":[204],"interventional":[206],"query":[207],"can":[209],"be":[210],"answered":[211],"observational":[214],"data":[215,289],"standard":[217],"identifiability":[218],"assumptions.":[219],"High-probability":[220],"cumulative-regret":[221],"bounds":[222],"established":[224],"terms":[226],"differential":[228],"information":[229],"gain":[230],"proposed":[233],"FBO":[234],"algorithm.":[235],"Collectively,":[236],"these":[237],"elements":[238],"constitute":[239],"central":[241,335],"contributions":[242],"CID":[245],"framework,":[246],"integrates":[248],"through":[251],"identification":[252],"estimation":[254,292],"with":[255],"search":[257],"establishes":[266],"decision-making":[269],"pipeline":[270,298],"enables":[272],"commitment":[273],"high-performing":[276],"single-shot":[280],"game,":[281],"supported":[282],"regret":[284],"guarantees.":[285],"Provided":[286],"sufficient,":[294],"resulting":[296],"appropriate":[300],"scenarios":[302],"where":[303],"adaptive":[304],"deployment":[305],"impractical":[307],"or":[308],"costly.":[309],"Beyond":[310],"methodological":[312],"contribution,":[313],"this":[314],"work":[315],"introduces":[316],"novel":[318],"application":[319],"reasoning":[326],"design":[329],"problems,":[332],"economics":[337],"multi-agent":[339],"systems.":[340]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-12-19T00:00:00"}
