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UID:20250725T065402EDT-6770LuODL5@132.216.98.100
DTSTAMP:20250725T105402Z
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	Vassili N. Kolokoltsov\n\nQuantum games represent the really 
 21st century branch of game theory\, tightly linked to the modern developm
 ent of quantum computing and quantum technologies. The main accent in thes
 e developments so far was made on stationary or repeated games. In the pre
 vious paper of the author the truly dynamic quantum game theory was initia
 ted with strategies chosen by players in real time. Since direct continuou
 s observations are known to destroy quantum evolutions (so-called quantum 
 Zeno paradox) the necessary new ingredient for quantum dynamic games repre
 sented the theory of non-direct observations and the corresponding quantum
  filtering. Another remarkable 21st century branch of game theory represen
 t the so-called mean-field games (MFG)\, with impressive and ever growing 
 development. Here we are merging these two exciting new branches of game t
 heory. Building a quantum analog of MFGs requires the full reconstruction 
 of its foundations and methodology\, because in N-particle quantum evoluti
 on particles are not separated in individual dynamics and the key concept 
 of the classical MFG theory\, the empirical measure defined as the sum of 
 Dirac masses of the positions of the players\, is not applicable in quantu
 m setting. As a preliminary result we derive the new nonlinear stochastic 
 Schrödinger equation\, as the limit of continuously observed and controlle
 d system of large number of interacting quantum particles\, the result tha
 t may have an independent value. This equation describes an infinite-dimen
 sional complex-valued curvilinear (on a manifold) nonlinear diffusion of M
 cKean-Vlasov type. We then show that to a control quantum system of intera
 cting particles there corresponds a special system of classical interactin
 g particles with the identical limiting MFG system\, defined on an appropr
 iate Riemanian manifold. Solutions of this system are shown to specify app
 roximate Nash equilibria for N-agent quantum games. This talk will be base
 d on three author's preprints: Dynamic Quantum Games [1]\,  Quantum Mean F
 ield Games [2]\, and The Law of Large Numbers for Quantum Stochastic Filte
 ring and Control of Many Particle Systems [3].\n\nThe talk consists of two
  parts:\n\nPart I (on Sept 11th)  has been devoted mostly to the introduct
 ion to quantum filtering and control\, which form the theoretical basis fo
 r Part II. All required notions of quantum mechanics are introduced from s
 cratch [4].\n\nPart II (on Sept 18th) will cover the development of quantu
 m dynamic games and MFGs.\n\n[1] https://arxiv.org/pdf/2002.00271.pdf\n	[2]
  https://arxiv.org/pdf/2005.02350.pdf\n	[3] https://arxiv.org/pdf/2008.0737
 5.pdf\n	[4] https://arxiv.org/pdf/2008.07355.pdf\n
DTSTART:20200918T150000Z
DTEND:20200918T160000Z
LOCATION:CA\, ZOOM
SUMMARY:Quantum Mean Field Games (Part II)
URL:/cim/channels/event/quantum-mean-field-games-part-
 ii-324653
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