@article {3089,
	title = {Should I Remember more than you?? \&ndash; on the best response to factored based strategies},
	journal = {International Journal of Game Theory},
	volume = {49},
	number = {6},
	year = {2020},
	month = {2020},
	pages = {1105--1124},
	abstract = {In this paper we offer a new approach to modeling strategies of bounded complexity, the so-called factor-based strategies. In our model, the strategy of a player in the multi-stage game does not directly map the set of histories H to the set of her actions. Instead, the player{\textquoteright}s perception of H is represented by a factor ϕ : H {\textrightarrow} X, where X reflects the {\textquotedblleft}cognitive complexity{\textquotedblright} of the player. Formally, mapping ϕ sends each history to an element of a factor space X that represents its equivalence class. The play of the player can then be conditioned just on the elements of the set X. From the perspective of the original multi-stage game we say that a function ϕ from H to X is a factor of a strategy σ if there exists a function ω from X to the set of actions of the player such that σ = ω {\textopenbullet} ϕ. In this case we say that the strategy σ is ϕ-factorbased. Stationary strategies and strategies played by finite automata and strategies with bounded recall are the most prominent examples of factor-based strategies. In the discounted infinitely repeated game with perfect monitoring, a best reply to a profile of ϕ-factor-based strategies need not be a ϕ-factor-based strategy. However, if the factor ϕ is recursive, namely, its value ϕ(a(1), . . . , a(t)) on a finite string of action profiles (a(1), . . . , a(t)) is a function of ϕ(a(1), . . . , a(t-1)) and at, then for every profile of factor-based strategies there is a best reply that is a pure factor-based strategy. We also study factor-based strategies in the more general case of stochastic games.},
	url = {https://www.researchgate.net/publication/50252346_Should_I_remember_more_than_you_On_the_best_response_to_factor-based_strategies},
	author = {MIROSLAV ZELENY and Rene Levinsky and Abraham Neyman}
}
