{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:31:27Z","timestamp":1777447887605,"version":"3.51.4"},"reference-count":41,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2018,2,5]],"date-time":"2018-02-05T00:00:00Z","timestamp":1517788800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2018,2,5]]},"abstract":"<jats:p>In this paper, we consider a mean field game (MFG) model perturbed by small common noise. Our goal is to give an approximation of the Nash equilibrium strategy of this game using a solution from the original no common noise MFG whose solution can be obtained through a coupled system of partial differential equations. We characterize the first order approximation via linear mean-field forward-backward stochastic differential equations whose solution is a centered Gaussian process with respect to the common noise. The first order approximate strategy can be described as follows: at time [Formula: see text], applying the original MFG optimal strategy for a sub game over [Formula: see text] with the initial being the current state and distribution. We then show that this strategy gives an approximate Nash equilibrium of order [Formula: see text].<\/jats:p>","DOI":"10.3233\/asy-171446","type":"journal-article","created":{"date-parts":[[2018,2,6]],"date-time":"2018-02-06T12:58:24Z","timestamp":1517921904000},"page":"205-232","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Asymptotic analysis of mean field games with small common noise"],"prefix":"10.1177","volume":"106","author":[{"given":"Saran","family":"Ahuja","sequence":"first","affiliation":[{"name":"Department of Mathematics, Stanford University, Sloan Hall, Stanford, CA 94305, USA. E-mails:\u00a0,\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiluo","family":"Ren","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Stanford University, Sloan Hall, Stanford, CA 94305, USA. E-mails:\u00a0,\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tzu-Wei","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,2,5]]},"reference":[{"key":"ref001","unstructured":"Y.\u00a0Achdou, J.M.\u00a0Lasry, P.L.\u00a0Lions and B.\u00a0Moll, Heterogeneous agent models in continuous time, Technical report, mimeo, 2013."},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1137\/140974730"},{"key":"ref003","unstructured":"S.\u00a0Ahuja, W.\u00a0Ren and T.W.\u00a0Yang, Forward-backward stochastic differential equation with monotone functional and mean field games with common noise, arXiv preprint, 2016. 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