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SUMMARY:Continuous-time mean field games: a primal-dual characterization -
  Jiacheng Zhang (Chinese University of Hong Kong)
DTSTART:20251111T144000Z
DTEND:20251111T152000Z
UID:TALK238474@talks.cam.ac.uk
DESCRIPTION:This paper establishes a primal-dual formulation for continuou
 s-time mean field games (MFGs) and provides a complete analytical characte
 rization of the set of all Nash equilibria (NEs). We first show that for a
 ny given mean field flow\, the representative player&rsquo\;s control prob
 lem with measurable coefficients is equivalent to a linear program over th
 e space of occupation measures. We then establish the dual formulation of 
 this linear program as a maximization problem over smooth subsolutions of 
 the associated Hamilton-Jacobi-Bellman (HJB) equation\, which plays a fund
 amental role in characterizing NEs of MFGs. Finally\, a complete character
 ization of all NEs for MFGs is established by the strong duality between t
 he linear program and its dual problem. This strong duality is obtained by
  studying the solvability of the dual problem\, and in particular through 
 analyzing the regularity of the associated HJB equation. Compared with exi
 sting approaches for MFGs\, the primal-dual formulation and its NE charact
 erization do not require the convexity of the associated Hamiltonian or th
 e uniqueness of its optimizer\, and remain applicable when the HJB equatio
 n lacks classical or even continuous solutions.
LOCATION:Seminar Room 1\, Newton Institute
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