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SUMMARY:Constrained discounted stochastic games - Anna Jaskiewicz (Wroclaw
  University of Technology)
DTSTART:20220422T080000Z
DTEND:20220422T090000Z
UID:TALK171395@talks.cam.ac.uk
DESCRIPTION:I present a large class of constrained non-cooperative stochas
 ticMarkov games with countable state spaces and discounted cost criteria. 
 In one-player case\,i.e.\, constrained discounted Markov decision models\,
  it is possible to formulate a static opttimisationproblem whose solution 
 determines a stationary optimal strategy (alias controlor policy) in the d
 ynamical infinite horizon model. This solution lies in the compact convexs
 et of all occupation measures induced by strategies\, defined on the set o
 f state-action pairs.In case of $n$-person discounted games the occupation
  measures are induced by strategies ofall players. Therefore\, it is diffi
 cult to generalise the approach for constrained discountedMarkov decision 
 processes directly. It is not clear how to define the domain for the bestr
 esponse 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 spaces. One of our main re
 sults shows how to overcome this difficultyand define a constrained non-co
 operative static game.\\ This is done for games with bounded costfunctions
  and positive initial state distribution. An extension to a class of Marko
 v gameswith unbounded costs and arbitrary initial state distribution relie
 s on approximation of theunbounded game by bounded ones with positive init
 ial state distributions.In the case with a countably generated state space
 \, we prove existenceof approximate stationary equilibria and stationary w
 eak correlated equilibria.
LOCATION:Seminar Room 1\, Newton Institute
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