{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T11:28:01Z","timestamp":1743852481753,"version":"3.38.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T00:00:00Z","timestamp":1714953600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T00:00:00Z","timestamp":1714953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1907684"],"award-info":[{"award-number":["1907684"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2025,3]]},"DOI":"10.1007\/s13235-024-00563-w","type":"journal-article","created":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T03:17:31Z","timestamp":1714965451000},"page":"48-73","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Equilibria in the Large-Scale Competition for Market Share in a Commodity with Resource-Buying"],"prefix":"10.1007","volume":"15","author":[{"given":"Luke C.","family":"Brown","sequence":"first","affiliation":[]},{"given":"David M.","family":"Ambrose","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,6]]},"reference":[{"issue":"2028","key":"563_CR1","first-page":"20130397, 19","volume":"372","author":"Y Achdou","year":"2014","unstructured":"Achdou Y, Buera FJ, Lasry J-M, Lions P-L, Moll B (2014) Partial differential equation models in macroeconomics. Philos Trans R Soc Lond Ser A Math Phys Eng Sci 372(2028):20130397, 19","journal-title":"Philos Trans R Soc Lond Ser A Math Phys Eng Sci"},{"key":"563_CR2","volume-title":"Sobolev spaces, volume 140 of pure and applied mathematics (Amsterdam)","author":"RA Adams","year":"2003","unstructured":"Adams RA, Fournier JJF (2003) Sobolev spaces, volume 140 of pure and applied mathematics (Amsterdam), 2nd edn. Elsevier\/Academic Press, Amsterdam","edition":"2"},{"issue":"1","key":"563_CR3","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s11854-021-0193-0","volume":"145","author":"PDS Andrade","year":"2021","unstructured":"Andrade PDS, Pimentel EA (2021) Stationary fully nonlinear mean-field games. J Anal Math 145(1):335\u2013356","journal-title":"J Anal Math"},{"issue":"3","key":"563_CR4","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/s11579-017-0206-z","volume":"12","author":"P Cardaliaguet","year":"2018","unstructured":"Cardaliaguet P, Lehalle C-A (2018) Mean field game of controls and an application to trade crowding. Math Financ Econ 12(3):335\u2013363","journal-title":"Math Financ Econ"},{"issue":"3","key":"563_CR5","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/s00245-014-9269-x","volume":"71","author":"P Chan","year":"2015","unstructured":"Chan P, Sircar R (2015) Bertrand and Cournot mean field games. Appl Math Optim 71(3):533\u2013569","journal-title":"Appl Math Optim"},{"issue":"3","key":"563_CR6","doi-asserted-by":"publisher","first-page":"588","DOI":"10.1137\/15M1031424","volume":"59","author":"P Chan","year":"2017","unstructured":"Chan P, Sircar R (2017) Fracking, renewables, and mean field games. SIAM Rev 59(3):588\u2013615","journal-title":"SIAM Rev"},{"issue":"8","key":"563_CR7","doi-asserted-by":"publisher","first-page":"1324","DOI":"10.1080\/03605302.2016.1192647","volume":"41","author":"M Cirant","year":"2016","unstructured":"Cirant M (2016) Stationary focusing mean-field games. Commun Partial Differ Equ 41(8):1324\u20131346","journal-title":"Commun Partial Differ Equ"},{"issue":"4","key":"563_CR8","doi-asserted-by":"publisher","first-page":"445","DOI":"10.3934\/jdg.2021006","volume":"8","author":"M Cirant","year":"2021","unstructured":"Cirant M, Gomes DA, Pimentel EA, S\u00e1nchez-Morgado H (2021) On some singular mean-field games. J Dyn Games 8(4):445\u2013465","journal-title":"J Dyn Games"},{"key":"563_CR9","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.na.2018.03.011","volume":"173","author":"D Evangelista","year":"2018","unstructured":"Evangelista D, Ferreira R, Gomes DA, Nurbekyan L, Voskanyan V (2018) First-order, stationary mean-field games with congestion. Nonlinear Anal 173:37\u201374","journal-title":"Nonlinear Anal"},{"issue":"4","key":"563_CR10","doi-asserted-by":"publisher","first-page":"1365","DOI":"10.1007\/s10884-017-9615-1","volume":"30","author":"D Evangelista","year":"2018","unstructured":"Evangelista D, Gomes DA (2018) On the existence of solutions for stationary mean-field games with congestion. J Dyn Differ Equ 30(4):1365\u20131388","journal-title":"J Dyn Differ Equ"},{"issue":"6","key":"563_CR11","doi-asserted-by":"publisher","first-page":"5969","DOI":"10.1137\/16M1106705","volume":"50","author":"R Ferreira","year":"2018","unstructured":"Ferreira R, Gomes D (2018) Existence of weak solutions to stationary mean-field games through variational inequalities. SIAM J Math Anal 50(6):5969\u20136006","journal-title":"SIAM J Math Anal"},{"issue":"11","key":"563_CR12","doi-asserted-by":"publisher","first-page":"4713","DOI":"10.1090\/proc\/14475","volume":"147","author":"R Ferreira","year":"2019","unstructured":"Ferreira R, Gomes D, Tada T (2019) Existence of weak solutions to first-order stationary mean-field games with Dirichlet conditions. Proc Amer Math Soc 147(11):4713\u20134731","journal-title":"Proc Amer Math Soc"},{"issue":"6","key":"563_CR13","doi-asserted-by":"publisher","first-page":"1897","DOI":"10.1007\/s00030-015-0349-7","volume":"22","author":"DA Gomes","year":"2015","unstructured":"Gomes DA, Mitake H (2015) Existence for stationary mean-field games with congestion and quadratic Hamiltonians. NoDEA Nonlinear Differ Equ Appl 22(6):1897\u20131910","journal-title":"NoDEA Nonlinear Differ Equ Appl"},{"issue":"2","key":"563_CR14","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s13235-017-0223-9","volume":"8","author":"DA Gomes","year":"2018","unstructured":"Gomes DA, Nurbekyan L, Prazeres M (2018) One-dimensional stationary mean-field games with local coupling. Dyn Games Appl 8(2):315\u2013351","journal-title":"Dyn Games Appl"},{"issue":"1","key":"563_CR15","doi-asserted-by":"publisher","first-page":"55","DOI":"10.4171\/ifb\/333","volume":"17","author":"DA Gomes","year":"2015","unstructured":"Gomes DA, Patrizi S (2015) Obstacle mean-field game problem. Interfaces Free Bound 17(1):55\u201368","journal-title":"Interfaces Free Bound"},{"key":"563_CR16","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.na.2013.12.016","volume":"99","author":"DA Gomes","year":"2014","unstructured":"Gomes DA, Patrizi S, Voskanyan V (2014) On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal Theory Methods Appl 99:49\u201379","journal-title":"Nonlinear Anal Theory Methods Appl"},{"issue":"2","key":"563_CR17","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1137\/130944503","volume":"54","author":"DA Gomes","year":"2016","unstructured":"Gomes DA, Voskanyan VK (2016) Extended deterministic mean-field games. SIAM J Control Optim 54(2):1030\u20131055","journal-title":"SIAM J Control Optim"},{"issue":"1","key":"563_CR18","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s00245-016-9366-0","volume":"77","author":"PJ Graber","year":"2018","unstructured":"Graber PJ, Bensoussan A (2018) Existence and uniqueness of solutions for Bertrand and Cournot mean field games. Appl Math Optim 77(1):47\u201371","journal-title":"Appl Math Optim"},{"issue":"148","key":"563_CR19","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.matpur.2021.02.002","volume":"9","author":"PJ Graber","year":"2021","unstructured":"Graber PJ, Ignazio V, Neufeld A (2021) Nonlocal Bertrand and Cournot mean field games with general nonlinear demand schedule. J Math Pures Appl 9(148):150\u2013198","journal-title":"J Math Pures Appl"},{"issue":"1","key":"563_CR20","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1007\/s00245-022-09875-y","volume":"86","author":"PJ Graber","year":"2022","unstructured":"Graber PJ, Laurel M (2022) Parameter sensitivity analysis for mean field games of production. Appl Math Optim 86(1):2\u201352","journal-title":"Appl Math Optim"},{"key":"563_CR21","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1051\/cocv\/2019008","volume":"26","author":"PJ Graber","year":"2020","unstructured":"Graber PJ, Mouzouni C (2020) On mean field games models for exhaustible commodities trade. ESAIM Control Optim Calc Var 26:11\u201338","journal-title":"ESAIM Control Optim Calc Var"},{"issue":"5","key":"563_CR22","doi-asserted-by":"publisher","first-page":"50, 34","DOI":"10.1007\/s00030-021-00712-9","volume":"28","author":"PJ Graber","year":"2021","unstructured":"Graber PJ, Mullenix A, Pfeiffer L (2021) Weak solutions for potential mean field games of controls. NoDEA Nonlinear Differ Equ Appl 28(5):50, 34","journal-title":"NoDEA Nonlinear Differ Equ Appl"},{"key":"563_CR23","unstructured":"Graber PJ, Sircar R (2021) Master equation for Cournot mean field games of control with absorption"},{"key":"563_CR24","doi-asserted-by":"crossref","unstructured":"Gu\u00e9ant O, Lasry J-M, Lions P-L (2011) Mean field games and applications. Springer, Berlin, pp 205\u2013266","DOI":"10.1007\/978-3-642-14660-2_3"},{"issue":"3","key":"563_CR25","doi-asserted-by":"publisher","first-page":"221","DOI":"10.4310\/CIS.2006.v6.n3.a5","volume":"6","author":"M Huang","year":"2006","unstructured":"Huang M, Caines PE, Malham\u00e9 RP (2006) Large population stochastic dynamic games: closed-loop McKean\u2013Vlasov systems and the Nash certainty equivalence principle. Commun Inf Syst 6(3):221\u2013252","journal-title":"Commun Inf Syst"},{"key":"563_CR26","doi-asserted-by":"publisher","first-page":"1560","DOI":"10.1109\/TAC.2007.904450","volume":"52","author":"M Huang","year":"2007","unstructured":"Huang M, Caines PE, Malham\u00e9 RP (2007) Large-population cost-coupled lQG problems with nonuniform agents: individual-mass behavior and decentralized $$\\epsilon $$-nash equilibria. IEEE Trans Autom Control 52:1560\u20131571","journal-title":"IEEE Trans Autom Control"},{"key":"563_CR27","doi-asserted-by":"publisher","DOI":"10.1142\/4319","volume-title":"Applied analysis","author":"JK Hunter","year":"2001","unstructured":"Hunter JK, Nachtergaele B (2001) Applied analysis. World Scientific, Singapore"},{"issue":"3","key":"563_CR28","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1080\/03605302.2021.1985518","volume":"47","author":"Z Kobeissi","year":"2022","unstructured":"Kobeissi Z (2022) On classical solutions to the mean field game system of controls. Commun Partial Differ Equ 47(3):453\u2013488","journal-title":"Commun Partial Differ Equ"},{"issue":"9","key":"563_CR29","first-page":"619","volume":"343","author":"J-M Lasry","year":"2006","unstructured":"Lasry J-M, Lions P-L (2006) Jeux \u00e0 Champ Moyen. I\u2014Le cas Stationnaire. CR Math 343(9):619\u2013625","journal-title":"CR Math"},{"issue":"10","key":"563_CR30","first-page":"679","volume":"343","author":"J-M Lasry","year":"2006","unstructured":"Lasry J-M, Lions P-L (2006) Jeux \u00e0 Champ Moyen. II\u2014Horizon Fini et Contr\u00f4le Optimal. CR Math 343(10):679\u2013684","journal-title":"CR Math"},{"key":"563_CR31","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s11537-007-0657-8","volume":"2","author":"J-M Lasry","year":"2007","unstructured":"Lasry J-M, Lions P-L (2007) Mean field games. Japan J Math 2:229\u2013260","journal-title":"Japan J Math"},{"issue":"6","key":"563_CR32","doi-asserted-by":"publisher","first-page":"1135","DOI":"10.1016\/j.matpur.2015.07.008","volume":"104","author":"AR M\u00e9sz\u00e1ros","year":"2015","unstructured":"M\u00e9sz\u00e1ros AR, Silva FJ (2015) A variational approach to second order mean field games with density constraints: the stationary case. J Math Pures Appl 104(6):1135\u20131159","journal-title":"J Math Pures Appl"},{"key":"563_CR33","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1007\/s00245-018-9484-y","volume":"81","author":"C Mouzouni","year":"2020","unstructured":"Mouzouni C (2020) On Quasi-Stationay mean field games models. Appl Math Optim 81:655\u2013684","journal-title":"Appl Math Optim"},{"key":"563_CR34","volume-title":"An introduction to game theory","author":"MJ Osborne","year":"2004","unstructured":"Osborne MJ (2004) An introduction to game theory. Oxford University Press, Oxford"},{"key":"563_CR35","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1214\/aoms\/1177729893","volume":"21","author":"J Sherman","year":"1950","unstructured":"Sherman J, Morrison WJ (1950) Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. Ann Math Stat 21:124\u2013127","journal-title":"Ann Math Stat"}],"container-title":["Dynamic Games and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-024-00563-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13235-024-00563-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-024-00563-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T13:49:56Z","timestamp":1741009796000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13235-024-00563-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,6]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["563"],"URL":"https:\/\/doi.org\/10.1007\/s13235-024-00563-w","relation":{},"ISSN":["2153-0785","2153-0793"],"issn-type":[{"type":"print","value":"2153-0785"},{"type":"electronic","value":"2153-0793"}],"subject":[],"published":{"date-parts":[[2024,5,6]]},"assertion":[{"value":"11 April 2024","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 May 2024","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not Applicable","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}]}}