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Superstition and Rational Learning

  • Drew Fudenberg
  • David K. Levine

We argue that some but not all superstitions can persist when learning is rational and players are patient, and illustrate our argument with an example inspired by the code of Hammurabi. The code specified an “appeal by surviving in the river” as a way of deciding whether an accusation was true, so it seems to have relied on the superstition that the guilty are more likely to drown than the innocent. If people can be easily persuaded to hold this superstitious belief, why not the superstitious belief that the guilty will be struck dead by lightning? We argue that the former can persist but the latter cannot by giving a partial characterization of the outcomes that arise as the limit of steady states with rational learning as players become more patient. These “subgame-confirmed Nash equilibria” have self-confirming beliefs at information sets reachable by a single deviation. According to this theory a mechanism that uses superstitions two or more steps off the equilibrium path, such as “appeal by surviving in the river,” is more likely to persist than a superstition where the false beliefs are only one step off of the equilibrium path.

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Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 2114.

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Date of creation: 2006
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Handle: RePEc:fth:harver:2114
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  1. Levine, David & Dekel, Eddie & Fudenberg, Drew, 1999. "Payoff Information and Self-Confirming Equilibrium," Scholarly Articles 3200614, Harvard University Department of Economics.
  2. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
  3. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  4. A. Rubinstein & A. Wolinsky, 2010. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Levine's Working Paper Archive 369, David K. Levine.
  5. Philippe Jehiel & Dov Samet, 2010. "Learning To Play Games In Extensive Form By Valuation," Levine's Working Paper Archive 391749000000000034, David K. Levine.
  6. Ehud Kalai & Alejandro Neme, 1989. "The Strength of a Little Perfection," Discussion Papers 858, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  8. Fudenberg, Drew & Kreps, David M., 1995. "Learning in extensive-form games I. Self-confirming equilibria," Games and Economic Behavior, Elsevier, vol. 8(1), pages 20-55.
  9. Levine, David & Kreps, David & Fudenberg, Drew, 1988. "On the Robustness of Equilibrium Refinements," Scholarly Articles 3350444, Harvard University Department of Economics.
  10. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
  11. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
  13. Lambson, Val E. & Probst, Daniel A., 2004. "Learning by matching patterns," Games and Economic Behavior, Elsevier, vol. 46(2), pages 398-409, February.
  14. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  15. Fudenberg, Drew & Levine, David K, 1997. "Measuring Players' Losses in Experimental Games," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 507-36, May.
  16. Aoyagi, Masaki, 1996. "Evolution of Beliefs and the Nash Equilibrium of Normal Form Games," Journal of Economic Theory, Elsevier, vol. 70(2), pages 444-469, August.
  17. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
  18. Drew Fudenberg & David K. Levine, 1996. "Measuring Subject’s Losses in Experimental Games," Levine's Working Paper Archive 370, David K. Levine.
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