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Approachability of convex sets in generalized quitting games

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Date
2018
Dewey
Probabilités et mathématiques appliquées
Sujet
Blackwell approachability; Stochastic games; Absorbing games; Determinacy
JEL code
C.C6.C61; C.C6.C65; C.C7.C73
Journal issue
Games and Economic Behavior
Volume
108
Publication date
03-2018
Article pages
411-431
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.geb.2017.12.007
URI
https://basepub.dauphine.fr/handle/123456789/19914
Collections
  • LAMSADE : Publications
Metadata
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Author
Flesh, Janos
253509 Department of Quantitative Economics [Maastricht]
Laraki, Rida
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Perchet, Vianney
62 Centre de Mathématiques et de Leurs Applications [CMLA]
Type
Article accepté pour publication ou publié
Abstract (EN)
We examine Blackwell approachability in so-called generalized quitting games. These are repeated games in which each player may have quitting actions that terminate the game. We provide three simple geometric and strongly related conditions for the weak approachability of a convex target set. The first is sufficient: it guarantees that, for any fixed horizon, a player has a strategy ensuring that the expected time-average payoff vector converges to the target set as horizon goes to infinity. The third is necessary: if it is not satisfied, the opponent can weakly exclude the target set. We analyze in detail the special cases where only one of the players has quitting actions. Finally, we study uniform approachability where the strategy should not depend on the horizon and demonstrate that, in contrast with classical Blackwell approachability for convex sets, weak approachability does not imply uniform approachability.

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