Abstract : We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called attainable by a player if there is a finite horizon T such that the player can guarantee that after time T the distance between the set and the cumulative payoff is arbitrarily small, regardless of the strategy Player 2 is using. We provide a necessary and sufficient condition for the attainability of a convex set, using the concept of B-sets. We then particularize the condition to the case in which the set is a singleton, and provide some equivalent conditions. We finally characterize when all vectors are attainable.
https://hal-paris1.archives-ouvertes.fr/hal-01302514
Contributor : Xavier Venel <>
Submitted on : Thursday, April 14, 2016 - 2:45:46 PM Last modification on : Tuesday, November 17, 2020 - 11:18:17 AM Long-term archiving on: : Friday, July 15, 2016 - 12:40:20 PM