@techreport{Levinsky2010Should,
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's perception of H is represented by a factor [...] where X reflects the cognitive complexity of the player. Formally, mapping [...] 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 [...] from H to X is a factor of a strategy [...] if there exists a function [...] from X to the set of actions of the player such that [...]. In this case we say that the strategy [...] is [...]-factor-based. 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 [...]-factor-base strategies need not be a [...]-factor-base strategy. However, if the factor [...] is recursive, namely its value [...] on a finite string of action profiles [...] is a function of [...] and [...], 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..},
address = {Jena},
author = {Ren\'{e} Lev\'{\i}nsk\'{y} and Abraham Neyman and Miroslav Zelen\'{y}},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
keywords = {C73; 330; bounded rationality; factor-based; strategies bounded; recall strategies; finite automata; Dynamisches Spiel; Beschr\"{a}nkte Rationalit\"{a}t; Wiederholte Spiele; Theorie},
language = {eng},
number = {2010,082},
publisher = {Univ. [u.a.]},
title = {Should i remember more than you? On the best response to factor-based strategies},
type = {Jena economic research papers},
url = {http://hdl.handle.net/10419/56815},
year = {2010}
}