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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Constrained discounted stochastic games - Anna Jas
kiewicz (Wroclaw University of Technology)
DTSTART;TZID=Europe/London:20220422T090000
DTEND;TZID=Europe/London:20220422T100000
UID:TALK171395AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/171395
DESCRIPTION:I present a large class of constrained non-coopera
tive stochasticMarkov games with countable state s
paces and discounted cost criteria. In one-player
case\,i.e.\, constrained discounted Markov decisio
n models\, it is possible to formulate a static op
ttimisationproblem whose solution determines a sta
tionary optimal strategy (alias controlor policy)
in the dynamical infinite horizon model. This solu
tion lies in the compact convexset of all occupati
on measures induced by strategies\, defined on the
set of state-action pairs.In case of $n$-person d
iscounted games the occupation measures are induce
d by strategies ofall players. Therefore\, it is d
ifficult to generalise the approach for constraine
d discountedMarkov decision processes directly. It
is not clear how to define the domain for the bes
tresponse correspondence whose fixed point induces
a stationary equilibrium in the Markovgame. This
domain should be the Cartesian product of compact
convex setsin locally convex topological vector sp
aces. One of our main results shows how to overcom
e this difficultyand define a constrained non-coop
erative static game.\\ This is done for games with
bounded costfunctions and positive initial state
distribution. An extension to a class of Markov ga
meswith unbounded costs and arbitrary initial stat
e distribution relies on approximation of theunbou
nded game by bounded ones with positive initial st
ate distributions.In the case with a countably gen
erated state space\, we prove existenceof approxim
ate stationary equilibria and stationary weak corr
elated equilibria.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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