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


  • 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)


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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    References listed on IDEAS

    1. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 817-868.
    2. Stefano DellaVigna & John A. List & Ulrike Malmendier, 2012. "Testing for Altruism and Social Pressure in Charitable Giving," The Quarterly Journal of Economics, Oxford University Press, vol. 127(1), pages 1-56.
    3. Dan Ariely & Anat Bracha & Stephan Meier, 2009. "Doing Good or Doing Well? Image Motivation and Monetary Incentives in Behaving Prosocially," American Economic Review, American Economic Association, vol. 99(1), pages 544-555, March.
    4. Jean Tirole & Roland Bénabou, 2006. "Incentives and Prosocial Behavior," American Economic Review, American Economic Association, vol. 96(5), pages 1652-1678, December.
    5. Roland Bénabou & Jean Tirole, 2011. "Identity, Morals, and Taboos: Beliefs as Assets," The Quarterly Journal of Economics, Oxford University Press, vol. 126(2), pages 805-855.
    6. Regner, Tobias & Barria, Javier A., 2009. "Do consumers pay voluntarily? The case of online music," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 395-406, August.
    7. Dufwenberg, Martin & Kirchsteiger, Georg, 2004. "A theory of sequential reciprocity," Games and Economic Behavior, Elsevier, vol. 47(2), pages 268-298, May.
    8. Gerald J. Pruckner & Rupert Sausgruber, 2013. "Honesty On The Streets: A Field Study On Newspaper Purchasing," Journal of the European Economic Association, European Economic Association, vol. 11(3), pages 661-679, June.
    9. Andreoni, James, 1990. "Impure Altruism and Donations to Public Goods: A Theory of Warm-Glow Giving?," Economic Journal, Royal Economic Society, vol. 100(401), pages 464-477, June.
    10. Axel Ockenfels & Gary E. Bolton, 2000. "ERC: A Theory of Equity, Reciprocity, and Competition," American Economic Review, American Economic Association, vol. 90(1), pages 166-193, March.
    11. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-877, October.
    12. Fehr, Ernst & Schmidt, Klaus M., 2006. "The Economics of Fairness, Reciprocity and Altruism - Experimental Evidence and New Theories," Handbook on the Economics of Giving, Reciprocity and Altruism, Elsevier.
    13. Johnson, Jennifer Wiggins & Cui, Annie Peng, 2013. "To influence or not to influence: External reference price strategies in pay-what-you-want pricing," Journal of Business Research, Elsevier, vol. 66(2), pages 275-281.
    14. Riener, Gerhard & Traxler, Christian, 2012. "Norms, moods, and free lunch: Longitudinal evidence on payments from a Pay-What-You-Want restaurant," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 41(4), pages 476-483.
    15. Kaltcheva, Velitchka D. & Parasuraman, A., 2009. "Personality-Relatedness and Reciprocity framework for analyzing retailer-consumer interactions," Journal of Business Research, Elsevier, vol. 62(6), pages 601-608, June.
    16. Sendhil Mullainathan & Marianne Bertrand, 2001. "Do People Mean What They Say? Implications for Subjective Survey Data," American Economic Review, American Economic Association, vol. 91(2), pages 67-72, May.
    17. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    18. Pieter A. Gautier & Bas van der Klaauw, 2012. "Selection in a field experiment with voluntary participation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(1), pages 63-84, January.
    19. repec:feb:framed:0087 is not listed on IDEAS
    20. Pierpaolo Battigalli & Martin Dufwenberg, 2007. "Guilt in Games," American Economic Review, American Economic Association, vol. 97(2), pages 170-176, May.
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    More about this item


    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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