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Should I remember more than you? - On the best response to factor-based strategies -

Author

Listed:
  • René Levínský

    () (Max Planck Institute of Economics, Jena)

  • Abraham Neyman

    (Institute of Mathematics and Center for the Study of Rationality, The Hebrew University of Jerusalem)

  • Miroslav Zelený

    (Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University)

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 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 multi-stage 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 -factor-asedStationary 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 (1 , . . . , ) on a finite string of action profiles ( , . . . , ) is a function of (1 , . . . , - ) 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.

Suggested Citation

  • René Levínský & Abraham Neyman & Miroslav Zelený, 2010. "Should I remember more than you? - On the best response to factor-based strategies -," Jena Economic Research Papers 2010-082, Friedrich-Schiller-University Jena.
  • Handle: RePEc:jrp:jrpwrp:2010-082
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    More about this item

    Keywords

    Bounded rationality; factor-based strategies; bounded recall strategies; finite automata;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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