Approachability of convex sets in generalized quitting games

Janos Flesch, Rida Laraki, Vianney Perchet

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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. (C) 2017 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)411-431
Number of pages21
JournalGames and Economic Behavior
Volume108
DOIs
Publication statusPublished - Mar 2018

JEL classifications

  • c61 - "Optimization Techniques; Programming Models; Dynamic Analysis"
  • c65 - Miscellaneous Mathematical Tools
  • c73 - "Stochastic and Dynamic Games; Evolutionary Games; Repeated Games"

Keywords

  • Blackwell approachability
  • Stochastic games
  • Absorbing games
  • Determinacy
  • ASYMPTOTIC VALUE
  • EXISTENCE
  • CALIBRATION
  • INCOMPLETE INFORMATION
  • PAYOFFS
  • REGRET
  • CORRELATED EQUILIBRIUM
  • BELIEF-FREE EQUILIBRIA

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