BEGIN:VCALENDAR
PRODID:-//eluceo/ical//2.0/EN
VERSION:2.0
CALSCALE:GREGORIAN
BEGIN:VEVENT
UID:www.tcs.tifr.res.in/event/60
DTSTAMP:20230914T125908Z
SUMMARY:Refinement of the Generalized Nash Equilibrium
DESCRIPTION:Speaker: Ankur Kulkarni\nUniversity of Illinois at Urbana-Champ
 aign\n117\, Transportation Bldg\n104 S. Mathews Avenue\nUrba\n\nAbstract: 
 \nWe are concerned with generalized Nash games in which the players' strat
 egy sets are coupled by a shared constraint. A widely employed solution co
 ncept for these games is the generalized Nash equilibrium (GNE)\, which is
  the natural generalization of the Nash equilibrium.  The variational equi
 librium (VE) is a specific kind of GNE given by a solution of the variatio
 nal inequality formed from the common constraint and the mapping of the gr
 adients of player objectives. Our contribution is in providing conditions 
 under which the existence of a GNE is necessary and sufficient for the exi
 stence of a VE  in such an instance\, the VE is said to be a ``refinement 
  of the GNE. Establishment of this result is seen to be of relevance to pu
 re\, applied and computational game theorists. We present a theory that gi
 ves sufficient conditions for the VE to be a refinement of the GNE. For ce
 rtain games these conditions are shown to be necessary. This theory rests 
 on a result showing that the GNE and the VE are equivalent upto the Brouwe
 r degree of certains functions whose zeros are the GNE and VE respectively
 . In the primal space we show equality between the Brouwer degrees of the 
 natural maps of the quasi-variational inequality and the variational inequ
 ality\, whose solutions are the GNE and VE respectively. Using a novel equ
 ation reformulation of the VE\, this result is extended to the primal-dual
  space. These degree theoretic relationships pave the way for the aforesai
 d sufficient conditions. Our results unify  some known results about share
 d constraint games and provide mathematical justification for ideas that w
 ere known to be appealing to economic intuition.\n\nBio: Ankur is a doctor
 al student at the University of Illinois at Urbana-Champaign (UIUC)\, USA.
  He received his B.Tech. in Aerospace Engineering from Indian Institute of
  Technology\, Bombay in 2006 and M.S. in General Engineering from UIUC in 
 2008. He was a visiting scholar at the Tata Institute of Fundamental Resea
 rch\, Mumbai in 2008. His interests are in the theory of games\, economics
 \, mathematical programming and applied probability. His work has been bas
 ed on providing topological insights into equilibria of generalized Nash g
 ames and multi-leader-multi-follower games.\n
URL:https://www.tcs.tifr.res.in/web/events/60
DTSTART;VALUE=DATE:20100120
LOCATION:AG-80
END:VEVENT
END:VCALENDAR