 AZ
 Jena Economic Resea...
 Volume 4
 Should I remember m...
 author
 Published
 Wed Dec 1 2010
 Number of discussion paper

2010082
 keyword(s)

Bounded rationality
bounded recall strategies
factorbased strategies
finite automata
 abstract

In this paper we oﬀer a new approach to modeling strategies of bounded complexity, the socalled factorbased strategies. In our model, the strategy of a player in the multistage game does not directly map the set of histories to the set of her actions. Instead, the player’s perception of is represented by a factor : → �� where reﬂects the “cognitive complexity” of the player. Formally, mapping sends each history to an element of a factor space that represents its equivalence class. The play of the player can then be conditioned just on the elements of the set ��From the perspective of the original multistage game we say that a function from o is a factor of a strategy if there exists a function from to the set of actions of the player such that = ∘ �� In this case we say that the strategy is ��factorasedStationary strategies and strategies played by ﬁnite automata and strategies with bounded recall are the most prominent examples of factorbased strategies. In the discounted inﬁnitely repeated game with perfect monitoring, a best reply to a proﬁle of ��factorbase strategies need not be a ��factorbase strategy. However, if the factor is recursive, namely its value ��(1 , . . . , ) on a ﬁnite string of action proﬁles ( , . . . , ) is a function of ��(1 , . . . , − ) and , then for every proﬁle of factorbased strategies there is a best reply that is a pure factorbased strategy. We also study factorbased strategies in the more general case of stochastic games.
 article pub. typess JER
 Research article
 article languages JER
 Englisch
 JELClassification for JER
 C73  Stochastic and Dynamic Games; Evolutionary Games; Repeated Games