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Title:   Should i remember more than you? On the best response to factorbased strategies 
Authors:   Levínský, René Neyman, Abraham Zelený, Miroslav 
Issue Date:   2010 
Series/Report no.:   Jena economic research papers 2010,082 
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 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 multistage 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 [...]factorbased. Stationary 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 [...] on a finite string of action profiles [...] is a function of [...] 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.. 
Subjects:   bounded rationality factorbased strategies bounded recall strategies finite automata 
JEL:   C73 
Document Type:   Working Paper 
Appears in Collections:   Jena Economic Research Papers, MPI für Ökonomik

 

 
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