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Attainability in Repeated Games with Vector Payoffs
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.
Cited literature [19 references]
https://hal-paris1.archives-ouvertes.fr/hal-01302514
Contributor : Xavier Venel Connect in order to contact the contributor
Submitted on : Thursday, April 14, 2016 - 2:45:46 PM
Last modification on : Tuesday, January 19, 2021 - 11:08:30 AM
Long-term archiving on: : Friday, July 15, 2016 - 12:40:20 PM
Contributor : Xavier Venel Connect in order to contact the contributor
Submitted on : Thursday, April 14, 2016 - 2:45:46 PM
Last modification on : Tuesday, January 19, 2021 - 11:08:30 AM
Long-term archiving on: : Friday, July 15, 2016 - 12:40:20 PM
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Attainability-2014-June-3.pdf
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