Approachability of Convex Sets in Generalized Quitting Games

7^th February 2018, 13:00
Rida Laraki
University of Liverpool

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. Joint work with Janos Flesh (Maastricht University) and Vianney Perchet (ENS-Saclay, France).

Appeared in COLT 2016. To appear in Games and Economic Behavior (special Issue Shapley).