@article{01d42af021c64d4b8a8df2e29ee6d04d,
title = "Approachability with bounded memory",
abstract = "We study Blackwell's approachability in repeated games with vector payoffs when the approaching player is restricted to use strategies with bounded memory: either strategies with bounded recall, or strategies that can be implemented by finite automata. Our main finding is that the following three statements are equivalent for closed sets. (i) The set is approachable with bounded recall strategies. (ii) The set is approachable with strategies that can be implemented with finite automata. (iii) The set contains a convex approachable set. Using our results we show that (i) there are almost-regret-free strategies with bounded memory, (ii) there is a strategy with bounded memory to choose the best among several experts, and (iii) Hart and Mas-Colell's adaptive learning procedure can be achieved using strategies with bounded memory.",
keywords = "Adaptive learning, Approachability, Automata, Bounded memory, Bounded recall, No-regret, Repeated games, Vector payoffs",
author = "Ehud Lehrer and Eilon Solan",
note = "Funding Information: ✩ The work of the first author was supported by the Israel Science Foundation (Grant #762/045). The work of the second author was supported by the Israel Science Foundation (Grant #69/01). We thank two anonymous referees for insightful comments that improved the presentation. * Corresponding author. E-mail addresses:
[email protected] (E. Lehrer),
[email protected] (E. Solan).",
year = "2009",
month = jul,
doi = "10.1016/j.geb.2007.07.011",
language = "אנגלית",
volume = "66",
pages = "995--1004",
journal = "Games and Economic Behavior",
issn = "0899-8256",
publisher = "Academic Press Inc.",
number = "2",
}