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Evolution of Theories of Mind

  • Mohlin, Erik


    (Dept. of Economics, Stockholm School of Economics)

This paper studies the evolution of peoples' models of how other people think -- their theories of mind. First, this is formalized within the level-k model, which postulates a hierarchy of types, such that type k plays a k times iterated best response to the uniform distribution. It is found that, under plausible conditions, lower types co-exist with higher types. The results are extended to a model of learning, in which type k plays a k times iterated best response the average of past play. The results are also extended to the cognitive hierarchy model, and to the introduction of a type that plays a Nash equilibrium.

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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 0728.

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Length: 53 pages
Date of creation: 04 May 2010
Date of revision: 12 May 2010
Handle: RePEc:hhs:hastef:0728
Contact details of provider: Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
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  1. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November.
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  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  9. Vincent P. Crawford, 2003. "Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions," American Economic Review, American Economic Association, vol. 93(1), pages 133-149, March.
  10. Dale O. Stahl, 1997. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," CARE Working Papers 9710, The University of Texas at Austin, Center for Applied Research in Economics.
  11. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
  12. Broseta, Bruno & Costa-Gomes, Miguel & Crawford, Vincent P., 2000. "Cognition and Behavior in Normal-Form Games: An Experimental Study," University of California at San Diego, Economics Working Paper Series qt0fp8278k, Department of Economics, UC San Diego.
  13. Miguel Costa-Gomes & Vincent P. Crawford, 2004. "Cognition And Behavior In Two-Person Guessing Games: An Experimental Study," Levine's Bibliography 122247000000000143, UCLA Department of Economics.
  14. Ellingsen, Tore & Östling, Robert, 2007. "When Does Communication Improve Coordination?," SSE/EFI Working Paper Series in Economics and Finance 680, Stockholm School of Economics, revised 19 Jun 2008.
  15. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
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  18. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, MIT Press, vol. 119(3), pages 861-898, August.
  19. Steiner, Jakub & Stewart, Colin, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
  20. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
  21. Johan Stennek, 2000. "The survival value of assuming others to be rational," International Journal of Game Theory, Springer, vol. 29(2), pages 147-163.
  22. Dale O. Stahl, 1999. "Evidence based rules and learning in symmetric normal-form games," International Journal of Game Theory, Springer, vol. 28(1), pages 111-130.
  23. Heller, Dana, 2004. "An evolutionary approach to learning in a changing environment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 31-55, January.
  24. Friederike Mengel, 2007. "Learning Across Games," Working Papers. Serie AD 2007-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  25. Samuelson, Larry, 2001. "Analogies, Adaptation, and Anomalies," Journal of Economic Theory, Elsevier, vol. 97(2), pages 320-366, April.
  26. Dale O. Stahl & Paul W. Wilson, 2010. "On Players' Models of Other Players: Theory and Experimental Evidence," Levine's Working Paper Archive 542, David K. Levine.
  27. Basu, Kaushik, 1994. "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory," American Economic Review, American Economic Association, vol. 84(2), pages 391-95, May.
  28. Samuelson, Larry, 2001. "Introduction to the Evolution of Preferences," Journal of Economic Theory, Elsevier, vol. 97(2), pages 225-230, April.
  29. Eddie Dekel & Jeffrey C. Ely & Okan Yilankaya, 2007. "Evolution of Preferences -super-1," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 685-704.
  30. Robson, Arthur J., 2003. "The evolution of rationality and the Red Queen," Journal of Economic Theory, Elsevier, vol. 111(1), pages 1-22, July.
  31. Sgroi, Daniel & Zizzo, Daniel John, 2009. "Learning to play 3×3 games: Neural networks as bounded-rational players," Journal of Economic Behavior & Organization, Elsevier, vol. 69(1), pages 27-38, January.
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