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Bounded versus unbounded rationality: The tyranny of the weak

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  • Gilboa, Itzhak
  • Samet, Dov

Abstract

We examine the case of a two-person repeated game played by a boundedly rational player versus an unboundedly rational opponent. The former is restricted to strategies which are implementable by connected finite automata. It is shown that the "rational" player has a dominant strategy, and that in some cases the "weaker" (boundedly rational) player may exploit this fact to "blackmail" him. It is also shown that for a repeated zero-sum game, the rational player has a strategy which drives the automaton player's limit payoff down to his security (maxmin) level, even if he may choose any finite automaton.
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  • Gilboa, Itzhak & Samet, Dov, 1989. "Bounded versus unbounded rationality: The tyranny of the weak," Games and Economic Behavior, Elsevier, vol. 1(3), pages 213-221, September.
  • Handle: RePEc:eee:gamebe:v:1:y:1989:i:3:p:213-221
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    Cited by:

    1. Robson, Arthur J., 2003. "The evolution of rationality and the Red Queen," Journal of Economic Theory, Elsevier, vol. 111(1), pages 1-22, July.
    2. Sylvain Béal, 2010. "Perceptron versus automaton in the finitely repeated prisoner’s dilemma," Theory and Decision, Springer, vol. 69(2), pages 183-204, August.
    3. Ehud Kalai, 1987. "Bounded Rationality and Strategic Complexity in Repeated Games," Discussion Papers 783, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Gilboa Itzhak & Schmeidler David, 1994. "Infinite Histories and Steady Orbits in Repeated Games," Games and Economic Behavior, Elsevier, vol. 6(3), pages 370-399, May.
    5. Westhoff, Frank H. & Yarbrough, Beth V. & Yarbrough, Robert M., 1996. "Complexity, organization, and Stuart Kauffman's The Origins of Order," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 1-25, January.
    6. Lance Fortnow & Rahul Santhanam, 2009. "Bounding Rationality by Discounting Time," Discussion Papers 1481, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Neme, Alejandro & Quintas, Luis, 1992. "Equilibrium of repeated games with cost of implementation," Journal of Economic Theory, Elsevier, vol. 58(1), pages 105-109, October.
    8. Jeffrey E. Prisbrey, 1993. "A Bounded Rationality, Evolutionary Model for Behavior in Two Person Reciprocity Games," Game Theory and Information 9312003, EconWPA.
    9. Nachbar, John H & Zame, William R, 1996. "Non-computable Strategies and Discounted Repeated Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 103-122, June.
    10. Béal, Sylvain, 2007. "Perceptron Versus Automaton∗," Sonderforschungsbereich 504 Publications 07-58, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    11. Ehud Kalai, 1995. "Games," Discussion Papers 1141, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Daniel Monte, 2014. "Incentive constraints in games with bounded memory," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 137-143, February.
    13. Hvide, Hans K., 2002. "Pragmatic beliefs and overconfidence," Journal of Economic Behavior & Organization, Elsevier, vol. 48(1), pages 15-28, May.
    14. Aner Sela & Dorothea Herreiner, 1999. "Fictitious play in coordination games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 189-197.

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