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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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File URL: http://swopec.hhs.se/hastef/papers/hastef0728.pdf
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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
Phone: +46-(0)8-736 90 00
Fax: +46-(0)8-31 01 57
Web page: http://www.hhs.se/
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  1. 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.
  2. Steiner, Jakub & Stewart, Colin, 2008. "Contagion through learning," Theoretical Economics, Econometric Society, vol. 3(4), December.
  3. 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.
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  7. Tore Ellingsen & Robert �stling, 2010. "When Does Communication Improve Coordination?," American Economic Review, American Economic Association, vol. 100(4), pages 1695-1724, September.
  8. Samuelson, Larry, 2001. "Analogies, Adaptation, and Anomalies," Journal of Economic Theory, Elsevier, vol. 97(2), pages 320-366, April.
  9. 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.
  10. Jacob K. Goeree & Charles A. Holt, 2000. "A Model of Noisy Introspection," Virginia Economics Online Papers 343, University of Virginia, Department of Economics.
  11. 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.
  12. Robson, Arthur J., 2003. "The evolution of rationality and the Red Queen," Journal of Economic Theory, Elsevier, vol. 111(1), pages 1-22, July.
  13. Samuelson, Larry, 2001. "Introduction to the Evolution of Preferences," Journal of Economic Theory, Elsevier, vol. 97(2), pages 225-230, April.
  14. Heller, Dana, 2004. "An evolutionary approach to learning in a changing environment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 31-55, January.
  15. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
  16. 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.
  17. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  18. Crawford, Vincent P., 2001. "Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions," University of California at San Diego, Economics Working Paper Series qt6k65014s, Department of Economics, UC San Diego.
  19. Ito, Takatoshi, 1979. "A Filippov solution of a system of differential equations with discontinuous right-hand sides," Economics Letters, Elsevier, vol. 4(4), pages 349-354.
  20. Mengel, Friederike, 2012. "Learning across games," Games and Economic Behavior, Elsevier, vol. 74(2), pages 601-619.
  21. Dekel, Eddie & Ely, Jeffrey & Yilankaya, Okan, 2004. "Evolution of Preferences," Microeconomics.ca working papers dekel-04-08-13-01-21-07, Vancouver School of Economics, revised 09 Jun 2006.
  22. Johan Stennek, 2000. "The survival value of assuming others to be rational," International Journal of Game Theory, Springer, vol. 29(2), pages 147-163.
  23. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
  24. Josephson, Jens, 2008. "A numerical analysis of the evolutionary stability of learning rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1569-1599, May.
  25. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
  26. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
  27. 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.
  28. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  29. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
  30. 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.
  31. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
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