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UID:20260915T193907EDT-5536WAKuxS@132.216.98.100
DTSTAMP:20260915T233907Z
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\n\n	Abstract:\n	Quantum games represen
 t the really 21st century branch of game theory\, tightly linked to the mo
 dern development of quantum computing and quantum technologies. The main a
 ccent in these developments so far was made on stationary or repeated game
 s. In the previous paper of the author the truly dynamic quantum game theo
 ry was initiated with strategies chosen by players in real time. Since dir
 ect continuous observations are known to destroy quantum evolutions (so-ca
 lled quantum Zeno paradox) the necessary new ingredient for quantum dynami
 c games represented the theory of non-direct observations and the correspo
 nding quantum filtering. Another remarkable 21st century branch of game th
 eory represent the so-called mean-field games (MFG)\, with impressive and 
 ever growing development. Here we are merging these two exciting new branc
 hes of game theory. Building a quantum analog of MFGs requires the full re
 construction of its foundations and methodology\, because in N-particle qu
 antum evolution particles are not separated in individual dynamics and the
  key concept of the classical MFG theory\, the empirical measure defined a
 s the sum of Dirac masses of the positions of the players\, is not applica
 ble in quantum setting. As a preliminary result we derive the new nonlinea
 r stochastic Schrödinger equation\, as the limit of continuously observed 
 and controlled system of large number of interacting quantum particles\, t
 he result that may have an independent value. This equation describes an i
 nfinite-dimensional complex-valued curvilinear (on a manifold) nonlinear d
 iffusion of McKean-Vlasov type. We then show that to a control quantum sys
 tem of interacting particles there corresponds a special system of classic
 al interacting particles with the identical limiting MFG system\, defined 
 on an appropriate Riemanian manifold. Solutions of this system are shown t
 o specify approximate Nash equilibria for N-agent quantum games. This talk
  will be based on three author's preprints: Dynamic Quantum Games [1]\,  Q
 uantum Mean Field Games [2]\, and The Law of Large Numbers for Quantum Sto
 chastic Filtering and Control of Many Particle Systems [3].\n\nThe talk co
 nsists of two parts:\n\nPart I (on Sept 11th)  will be devoted mostly to t
 he introduction to quantum filtering and control\, which form the theoreti
 cal basis for Part II. All required notions of quantum mechanics will be i
 ntroduced from scratch.\n\nPart II (on Sept 18th) will cover the developme
 nt of quantum dynamic games and MFGs.\n
DTSTART:20200911T150000Z
DTEND:20200911T160000Z
LOCATION:CA\, ZOOM
SUMMARY:Quantum Mean Field Games (Part I)
URL:https://www.mcgill.ca/cim/channels/event/quantum-mean-field-games-part-
 i-325041
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