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Superstition and Rational Learning

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  • Drew Fudenberg
  • David K. Levine

Abstract

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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Bibliographic Info

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. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
  2. Drew Fudenberg & David M. Kreps & David K. Levine, 1986. "On the Robustness of Equilibrium Refinements," UCLA Economics Working Papers 398, UCLA Department of Economics.
  3. Jehiel, Philippe & Samet, Dov, 2005. "Learning to play games in extensive form by valuation," Journal of Economic Theory, Elsevier, vol. 124(2), pages 129-148, October.
  4. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
  5. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  6. 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.
  7. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  8. 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.
  9. G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
  10. 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.
  11. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
  12. Drew Fudenberg & David K. Levine, 1997. "Conditional Universal Consistency," Levine's Working Paper Archive 471, David K. Levine.
  13. Levine, David & Fudenberg, Drew, 1997. "Measuring Players' Losses in Experimental Games," Scholarly Articles 3160492, Harvard University Department of Economics.
  14. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  15. 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.
  16. Lambson, Val E. & Probst, Daniel A., 2004. "Learning by matching patterns," Games and Economic Behavior, Elsevier, vol. 46(2), pages 398-409, February.
  17. 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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Citations

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Cited by:
  1. Ng, Travis & Chong, Terence & Du, Xin, 2010. "The value of superstitions," Journal of Economic Psychology, Elsevier, vol. 31(3), pages 293-309, June.
  2. Woo, Chi-Keung & Horowitz, Ira & Luk, Stephen & Lai, Aaron, 2008. "Willingness to pay and nuanced cultural cues: Evidence from Hong Kong's license-plate auction market," Journal of Economic Psychology, Elsevier, vol. 29(1), pages 35-53, February.
  3. Fudenberg, Drew & Levine, David K., 2009. "Self-confirming equilibrium and the Lucas critique," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2354-2371, November.
  4. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2011. "Selfconfirming Equilibrium and Uncertainty," Working Papers 428, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  5. David Stifel & Marcel Fafchamps & Bart Minten, 2009. "Taboos, agriculture and poverty," CSAE Working Paper Series 2009-15, Centre for the Study of African Economies, University of Oxford.
  6. Zacharias Maniadis, 2008. "Essays in Aggregate Information, The Media and Special Interests," Levine's Working Paper Archive 122247000000002258, David K. Levine.
  7. Johnson, Noel D. & Nye, John V.C., 2011. "Does fortune favor dragons?," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 85-97.
  8. P Battigalli & S Cerreia-Vioglio & F Maccheroni & M Marinacci, 2012. "Selfconfirming Equilibrium and Model Uncertainty," Levine's Working Paper Archive 786969000000000376, David K. Levine.
  9. Paolo E. Giordani & Michele Ruta, 2012. "Self-Confirming Immigration Policy," CESifo Working Paper Series 3762, CESifo Group Munich.
  10. Robert Meyer & Joachim Vosgerau & Vishal Singh & Joel Urbany & Gal Zauberman & Michael Norton & Tony Cui & Brian Ratchford & Alessandro Acquisti & David Bell & Barbara Kahn, 2010. "Behavioral research and empirical modeling of marketing channels: Implications for both fields and a call for future research," Marketing Letters, Springer, vol. 21(3), pages 301-315, September.

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