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
Contributeur : Xavier Venel
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Soumis le : jeudi 14 avril 2016 - 14:45:46
Dernière modification le : mardi 30 octobre 2018 - 17:04:09
Document(s) archivé(s) le : vendredi 15 juillet 2016 - 12:40:20
