Linear-Quadratic Mean Field Social Optimization with a Major Player Article Swipe
Minyi Huang
,
Son Luu Nguyen
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1904.03346
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1904.03346
This paper considers a linear-quadratic (LQ) mean field control problem involving a major player and a large number of minor players, where the dynamics and costs depend on random parameters. The objective is to optimize a social cost as a weighted sum of the individual costs under decentralized information. We apply the person-by-person optimality principle in team decision theory to the finite population model to construct two limiting variational problems whose solutions, subject to the requirement of consistent mean field approximations, yield a system of forward-backward stochastic differential equations (FBSDEs). We show the existence and uniqueness of a solution to the FBSDEs and obtain decentralized strategies nearly achieving social optimality in the original large but finite population model.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/1904.03346
- https://arxiv.org/pdf/1904.03346
- OA Status
- green
- Cited By
- 4
- References
- 43
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2928295949
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2928295949Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.1904.03346Digital Object Identifier
- Title
-
Linear-Quadratic Mean Field Social Optimization with a Major PlayerWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2019Year of publication
- Publication date
-
2019-04-06Full publication date if available
- Authors
-
Minyi Huang, Son Luu NguyenList of authors in order
- Landing page
-
https://arxiv.org/abs/1904.03346Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/1904.03346Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1904.03346Direct OA link when available
- Concepts
-
Field (mathematics), Quadratic equation, Mathematical optimization, Mathematics, Computer science, Pure mathematics, GeometryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
4Total citation count in OpenAlex
- Citations by year (recent)
-
2023: 1, 2022: 1, 2021: 1, 2020: 1Per-year citation counts (last 5 years)
- References (count)
-
43Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W2928295949 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.1904.03346 |
| ids.doi | https://doi.org/10.48550/arxiv.1904.03346 |
| ids.mag | 2928295949 |
| ids.openalex | https://openalex.org/W2928295949 |
| fwci | |
| type | preprint |
| title | Linear-Quadratic Mean Field Social Optimization with a Major Player |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11829 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.9957000017166138 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2611 |
| topics[0].subfield.display_name | Modeling and Simulation |
| topics[0].display_name | Mathematical Biology Tumor Growth |
| topics[1].id | https://openalex.org/T10067 |
| topics[1].field.id | https://openalex.org/fields/20 |
| topics[1].field.display_name | Economics, Econometrics and Finance |
| topics[1].score | 0.9950000047683716 |
| topics[1].domain.id | https://openalex.org/domains/2 |
| topics[1].domain.display_name | Social Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2003 |
| topics[1].subfield.display_name | Finance |
| topics[1].display_name | Stochastic processes and financial applications |
| topics[2].id | https://openalex.org/T12592 |
| topics[2].field.id | https://openalex.org/fields/31 |
| topics[2].field.display_name | Physics and Astronomy |
| topics[2].score | 0.9745000004768372 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/3109 |
| topics[2].subfield.display_name | Statistical and Nonlinear Physics |
| topics[2].display_name | Opinion Dynamics and Social Influence |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C9652623 |
| concepts[0].level | 2 |
| concepts[0].score | 0.513267993927002 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q190109 |
| concepts[0].display_name | Field (mathematics) |
| concepts[1].id | https://openalex.org/C129844170 |
| concepts[1].level | 2 |
| concepts[1].score | 0.4497798979282379 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q41299 |
| concepts[1].display_name | Quadratic equation |
| concepts[2].id | https://openalex.org/C126255220 |
| concepts[2].level | 1 |
| concepts[2].score | 0.38559719920158386 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[2].display_name | Mathematical optimization |
| concepts[3].id | https://openalex.org/C33923547 |
| concepts[3].level | 0 |
| concepts[3].score | 0.36565884947776794 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[3].display_name | Mathematics |
| concepts[4].id | https://openalex.org/C41008148 |
| concepts[4].level | 0 |
| concepts[4].score | 0.3547421395778656 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[4].display_name | Computer science |
| concepts[5].id | https://openalex.org/C202444582 |
| concepts[5].level | 1 |
| concepts[5].score | 0.09023162722587585 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[5].display_name | Pure mathematics |
| concepts[6].id | https://openalex.org/C2524010 |
| concepts[6].level | 1 |
| concepts[6].score | 0.06856325268745422 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[6].display_name | Geometry |
| keywords[0].id | https://openalex.org/keywords/field |
| keywords[0].score | 0.513267993927002 |
| keywords[0].display_name | Field (mathematics) |
| keywords[1].id | https://openalex.org/keywords/quadratic-equation |
| keywords[1].score | 0.4497798979282379 |
| keywords[1].display_name | Quadratic equation |
| keywords[2].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[2].score | 0.38559719920158386 |
| keywords[2].display_name | Mathematical optimization |
| keywords[3].id | https://openalex.org/keywords/mathematics |
| keywords[3].score | 0.36565884947776794 |
| keywords[3].display_name | Mathematics |
| keywords[4].id | https://openalex.org/keywords/computer-science |
| keywords[4].score | 0.3547421395778656 |
| keywords[4].display_name | Computer science |
| keywords[5].id | https://openalex.org/keywords/pure-mathematics |
| keywords[5].score | 0.09023162722587585 |
| keywords[5].display_name | Pure mathematics |
| keywords[6].id | https://openalex.org/keywords/geometry |
| keywords[6].score | 0.06856325268745422 |
| keywords[6].display_name | Geometry |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:1904.03346 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/1904.03346 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/1904.03346 |
| locations[1].id | doi:10.48550/arxiv.1904.03346 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://doi.org/10.48550/arxiv.1904.03346 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5082825311 |
| authorships[0].author.orcid | https://orcid.org/0000-0003-1145-5281 |
| authorships[0].author.display_name | Minyi Huang |
| authorships[0].countries | CA |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I67031392 |
| authorships[0].affiliations[0].raw_affiliation_string | Carleton University |
| authorships[0].institutions[0].id | https://openalex.org/I67031392 |
| authorships[0].institutions[0].ror | https://ror.org/02qtvee93 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I67031392 |
| authorships[0].institutions[0].country_code | CA |
| authorships[0].institutions[0].display_name | Carleton University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Minyi Huang |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Carleton University |
| authorships[1].author.id | https://openalex.org/A5040313884 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-6082-6686 |
| authorships[1].author.display_name | Son Luu Nguyen |
| authorships[1].countries | PR |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I200399037 |
| authorships[1].affiliations[0].raw_affiliation_string | University of Puerto Rico |
| authorships[1].institutions[0].id | https://openalex.org/I200399037 |
| authorships[1].institutions[0].ror | https://ror.org/02yg0nm07 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I200399037 |
| authorships[1].institutions[0].country_code | PR |
| authorships[1].institutions[0].display_name | University of Puerto Rico System |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Son Luu Nguyen |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | University of Puerto Rico |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/1904.03346 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Linear-Quadratic Mean Field Social Optimization with a Major Player |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T11829 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.9957000017166138 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2611 |
| primary_topic.subfield.display_name | Modeling and Simulation |
| primary_topic.display_name | Mathematical Biology Tumor Growth |
| related_works | https://openalex.org/W2748952813, 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/W2600246793 |
| cited_by_count | 4 |
| counts_by_year[0].year | 2023 |
| counts_by_year[0].cited_by_count | 1 |
| counts_by_year[1].year | 2022 |
| counts_by_year[1].cited_by_count | 1 |
| counts_by_year[2].year | 2021 |
| counts_by_year[2].cited_by_count | 1 |
| counts_by_year[3].year | 2020 |
| counts_by_year[3].cited_by_count | 1 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:1904.03346 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/1904.03346 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/1904.03346 |
| primary_location.id | pmh:oai:arXiv.org:1904.03346 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/1904.03346 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/1904.03346 |
| publication_date | 2019-04-06 |
| publication_year | 2019 |
| referenced_works | https://openalex.org/W2289473542, https://openalex.org/W2149953340, https://openalex.org/W2292219073, https://openalex.org/W2963198158, https://openalex.org/W659339155, https://openalex.org/W2082094090, https://openalex.org/W2123807026, https://openalex.org/W2102063802, https://openalex.org/W1980821524, https://openalex.org/W2129951390, https://openalex.org/W2026814250, https://openalex.org/W586490843, https://openalex.org/W1998973734, https://openalex.org/W2791784110, https://openalex.org/W1983997656, https://openalex.org/W2038686546, https://openalex.org/W2092025421, https://openalex.org/W1927857046, https://openalex.org/W2069495202, https://openalex.org/W2092834085, https://openalex.org/W1983321045, https://openalex.org/W2086302242, https://openalex.org/W1826160640, https://openalex.org/W1576577548, https://openalex.org/W2067437055, https://openalex.org/W1076438846, https://openalex.org/W1988310975, https://openalex.org/W2964078161, https://openalex.org/W2900643393, https://openalex.org/W2050593112, https://openalex.org/W2097730910, https://openalex.org/W2078532197, https://openalex.org/W2571136727, https://openalex.org/W1719735919, https://openalex.org/W2588150466, https://openalex.org/W2963678139, https://openalex.org/W2750843808, https://openalex.org/W2963980460, https://openalex.org/W1965098697, https://openalex.org/W2074598069, https://openalex.org/W1977377218, https://openalex.org/W1611358990, https://openalex.org/W2086139156 |
| referenced_works_count | 43 |
| abstract_inverted_index.a | 3, 11, 15, 35, 39, 82, 97 |
| abstract_inverted_index.We | 49, 90 |
| abstract_inverted_index.as | 38 |
| abstract_inverted_index.in | 55, 110 |
| abstract_inverted_index.is | 32 |
| abstract_inverted_index.of | 18, 42, 76, 84, 96 |
| abstract_inverted_index.on | 27 |
| abstract_inverted_index.to | 33, 59, 64, 73, 99 |
| abstract_inverted_index.The | 30 |
| abstract_inverted_index.and | 14, 24, 94, 102 |
| abstract_inverted_index.but | 114 |
| abstract_inverted_index.sum | 41 |
| abstract_inverted_index.the | 22, 43, 51, 60, 74, 92, 100, 111 |
| abstract_inverted_index.two | 66 |
| abstract_inverted_index.(LQ) | 5 |
| abstract_inverted_index.This | 0 |
| abstract_inverted_index.cost | 37 |
| abstract_inverted_index.mean | 6, 78 |
| abstract_inverted_index.show | 91 |
| abstract_inverted_index.team | 56 |
| abstract_inverted_index.apply | 50 |
| abstract_inverted_index.costs | 25, 45 |
| abstract_inverted_index.field | 7, 79 |
| abstract_inverted_index.large | 16, 113 |
| abstract_inverted_index.major | 12 |
| abstract_inverted_index.minor | 19 |
| abstract_inverted_index.model | 63 |
| abstract_inverted_index.paper | 1 |
| abstract_inverted_index.under | 46 |
| abstract_inverted_index.where | 21 |
| abstract_inverted_index.whose | 70 |
| abstract_inverted_index.yield | 81 |
| abstract_inverted_index.FBSDEs | 101 |
| abstract_inverted_index.depend | 26 |
| abstract_inverted_index.finite | 61, 115 |
| abstract_inverted_index.model. | 117 |
| abstract_inverted_index.nearly | 106 |
| abstract_inverted_index.number | 17 |
| abstract_inverted_index.obtain | 103 |
| abstract_inverted_index.player | 13 |
| abstract_inverted_index.random | 28 |
| abstract_inverted_index.social | 36, 108 |
| abstract_inverted_index.system | 83 |
| abstract_inverted_index.theory | 58 |
| abstract_inverted_index.control | 8 |
| abstract_inverted_index.problem | 9 |
| abstract_inverted_index.subject | 72 |
| abstract_inverted_index.decision | 57 |
| abstract_inverted_index.dynamics | 23 |
| abstract_inverted_index.limiting | 67 |
| abstract_inverted_index.optimize | 34 |
| abstract_inverted_index.original | 112 |
| abstract_inverted_index.players, | 20 |
| abstract_inverted_index.problems | 69 |
| abstract_inverted_index.solution | 98 |
| abstract_inverted_index.weighted | 40 |
| abstract_inverted_index.(FBSDEs). | 89 |
| abstract_inverted_index.achieving | 107 |
| abstract_inverted_index.considers | 2 |
| abstract_inverted_index.construct | 65 |
| abstract_inverted_index.equations | 88 |
| abstract_inverted_index.existence | 93 |
| abstract_inverted_index.involving | 10 |
| abstract_inverted_index.objective | 31 |
| abstract_inverted_index.principle | 54 |
| abstract_inverted_index.consistent | 77 |
| abstract_inverted_index.individual | 44 |
| abstract_inverted_index.optimality | 53, 109 |
| abstract_inverted_index.population | 62, 116 |
| abstract_inverted_index.solutions, | 71 |
| abstract_inverted_index.stochastic | 86 |
| abstract_inverted_index.strategies | 105 |
| abstract_inverted_index.uniqueness | 95 |
| abstract_inverted_index.parameters. | 29 |
| abstract_inverted_index.requirement | 75 |
| abstract_inverted_index.variational | 68 |
| abstract_inverted_index.differential | 87 |
| abstract_inverted_index.information. | 48 |
| abstract_inverted_index.decentralized | 47, 104 |
| abstract_inverted_index.approximations, | 80 |
| abstract_inverted_index.forward-backward | 85 |
| abstract_inverted_index.linear-quadratic | 4 |
| abstract_inverted_index.person-by-person | 52 |
| cited_by_percentile_year | |
| countries_distinct_count | 2 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/16 |
| sustainable_development_goals[0].score | 0.6600000262260437 |
| sustainable_development_goals[0].display_name | Peace, Justice and strong institutions |
| citation_normalized_percentile |