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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. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information 9905002, EconWPA, revised 23 Mar 2000.
  2. Philippe Jehiel & Dov Samet, 2001. "Learning to play games in extensive form by valuation," Game Theory and Information 0012001, EconWPA.
  3. Eddie Dekel & Drew Fudenberg & David K. Levine, . "Payoff Information and Self-Confirming Equilibrium," ELSE working papers 040, ESRC Centre on Economics Learning and Social Evolution.
  4. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  5. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  6. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  7. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. Drew Fudenberg & David Kreps & David K. Levine, 1988. "On the Robustness of Equilibrium Refinements," Levine's Working Paper Archive 227, David K. Levine.
  9. Ariel Rubinstein & Asher Wolinsky, 1991. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Discussion Papers 933, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
  11. Kalai, E & Neme, A, 1992. "The Strength of a Little Perfection," International Journal of Game Theory, Springer, vol. 20(4), pages 335-55.
  12. 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.
  13. Levine, David & Fudenberg, Drew, 1997. "Measuring Players' Losses in Experimental Games," Scholarly Articles 3160492, Harvard University Department of Economics.
  14. Lambson, Val E. & Probst, Daniel A., 2004. "Learning by matching patterns," Games and Economic Behavior, Elsevier, vol. 46(2), pages 398-409, February.
  15. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  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. 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.
  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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