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Approachability of Convex Sets in Generalized Quitting Games by Flesch, János; Laraki, Rida; Perchet, Vianney is a scholarly article available to read on EtoBox.

What is Approachability of Convex Sets in Generalized Quitting Games about?

We consider Blackwell approachability, a very powerful and geometric tool in game theory, used for example to design strategies of the uninformed player in repeated games with incomplete information. We extend this theory to "generalized quitting games" , a class of repeated stochastic games in which each player may have quitting actions, such as the Big-Match. 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. In the special case where only the approaching player can quit the game (Big-Match of type I), the three conditions are equivalent and coincide with Blackwell's condition. Consequently, we obtain a full characterization and prove that the game is weakly determined-every convex set is either weakly approachable or weakly excludable. In games where only the opponent can quit (Big-Match of type II), none of our condit

Author

Flesch, János; Laraki, Rida; Perchet, Vianney

Published

2016

Language

EN