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UID:20250726T203510EDT-8670xF1A1O@132.216.98.100
DTSTAMP:20250727T003510Z
DESCRIPTION:Virtual Informal Systems Seminar (VISS)\, Centre for Intelligen
 t Machines (CIM) and Groupe d'Etudes et de Recherche en Analyse des Decisi
 ons (GERAD)\n	Daniel Lacker\n\n\n	Abstract:\n	We study a class of linear-quad
 ratic stochastic differential games in which each player interacts directl
 y only with its nearest neighbors in a given graph. We find a semi-explici
 t Markovian equilibrium for any transitive graph\, in terms of the empiric
 al eigenvalue distribution of the graph's normalized Laplacian matrix. Thi
 s facilitates large-population asymptotics for various graph sequences\, w
 ith several sparse and dense examples discussed in detail. In particular\,
  the mean field game is the correct limit only in the dense graph case\, i
 .e.\, when the degrees diverge in a suitable sense. Even though equilibriu
 m strategies are nonlocal\, depending on the behavior of all players\, we 
 use a correlation decay estimate to prove a propagation of chaos result in
  both the dense and sparse regimes\, with the sparse case owing to the lar
 ge distances between typical vertices. Without assuming the graphs are tra
 nsitive\, we show also that the mean field game solution can be used to co
 nstruct decentralized approximate equilibria on any sufficiently dense gra
 ph sequence. \n\nJoint work with Agathe Soret.\n	\n	Bio:\n	Daniel Lacker is a
 n assistant professor in Industrial Engineering & Operations Research at C
 olumbia University. He obtained his PhD from the Operations Research & Fin
 ancial Engineering department of Princeton University in 2015\, and he was
  an NSF postdoctoral fellow in the Division of Applied Mathematics at Brow
 n University from 2015-2017. Daniel's research is in applied probability a
 nd mathematical finance\, with a primary focus on mean field game theory a
 nd interacting particle systems.\n
DTSTART:20200925T150000Z
DTEND:20200925T160000Z
LOCATION:CA\, ZOOM
SUMMARY:A case study on stochastic games on large graphs in mean field and 
 sparse regimes
URL:/cim/channels/event/case-study-stochastic-games-la
 rge-graphs-mean-field-and-sparse-regimes-325039
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