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Three steps ahead

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Listed author(s):
  • Heller, Yuval

Abstract

Experimental evidence suggest that people only use 1-3 iterations of strategic reasoning, and that some people systematically use less iterations than others. In this paper, we present a novel evolutionary foundation for these stylized facts. In our model, agents interact in finitely repeated Prisoner's Dilemma, and each agent is characterized by the number of steps he thinks ahead. When two agents interact, each of them has an independent probability to observe the opponent's type. We show that if this probability is not too close to 0 or 1, then the evolutionary process admits a unique stable outcome, in which the population includes a mixture of “naive” agents who think 1 step ahead, and “sophisticated” agents who think 2-3 steps ahead.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40714.

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Date of creation: 13 Jun 2012
Handle: RePEc:pra:mprapa:40714
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Keywords: Indirect evolution; cognitive hierarchy; bounded forward-looking; Prisoner's Dilemma; Cooperation;

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Find related papers by JEL classification:
  • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
  • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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  1. Cooper, Russell & DeJong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1996. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Games and Economic Behavior, Elsevier, vol. 12(2), pages 187-218, February.
  2. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
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  4. Gill, David & Prowse, Victoria, 2012. "Cognitive ability and learning to play equilibrium: A level-k analysis," MPRA Paper 38317, University Library of Munich, Germany, revised 23 Apr 2012.
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  6. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 103(418), pages 570-585, May.
  7. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
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  9. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  10. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
  11. Frenkel, Sivan & Heller, Yuval & Teper, Roee, 2012. "Endowment as a blessing," MPRA Paper 39430, University Library of Munich, Germany, revised 30 Apr 2012.
  12. Ho, Teck-Hua & Camerer, Colin & Weigelt, Keith, 1998. "Iterated Dominance and Iterated Best Response in Experimental "p-Beauty Contests."," American Economic Review, American Economic Association, vol. 88(4), pages 947-969, September.
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  15. 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.
  16. Hyndman, Kyle & Terracol, Antoine & Vaksmann, Jonathan, 2013. "Beliefs and (In)Stability in Normal-Form Games," MPRA Paper 47221, University Library of Munich, Germany.
  17. Stahl, Dale II & Wilson, Paul W., 1994. "Experimental evidence on players' models of other players," Journal of Economic Behavior & Organization, Elsevier, vol. 25(3), pages 309-327, December.
  18. Heifetz, Aviad & Pauzner, Ady, 2005. "Backward induction with players who doubt others' faultlessness," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 252-267, November.
  19. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
  20. Matthijs van Veelen & Julian Garcia, 2010. "In and Out of Equilibrium: Evolution of Strategies in Repeated Games with Discounting," Tinbergen Institute Discussion Papers 10-037/1, Tinbergen Institute.
  21. Lisa Bruttel & Werner Güth & Ulrich Kamecke, 2012. "Finitely repeated prisoners’ dilemma experiments without a commonly known end," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 23-47, February.
  22. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
  23. T. Randolph Beard & Richard O. Beil, 1994. "Do People Rely on the Self-Interested Maximization of Others? An Experimental Test," Management Science, INFORMS, vol. 40(2), pages 252-262, February.
  24. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, Oxford University Press, vol. 119(3), pages 861-898.
  25. Johnson, Eric J. & Camerer, Colin & Sen, Sankar & Rymon, Talia, 2002. "Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining," Journal of Economic Theory, Elsevier, vol. 104(1), pages 16-47, May.
  26. Johan Stennek, 2000. "The survival value of assuming others to be rational," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 147-163.
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Cited by:

  1. Heller, Yuval, 2014. "Stability and trembles in extensive-form games," Games and Economic Behavior, Elsevier, vol. 84(C), pages 132-136.
  2. Sivan Frenkel & Yuval Heller & Roee Teper, 2017. "The Endowment Effect as a Blessing," Working Papers 2017-06, Bar-Ilan University, Department of Economics.
  3. Heller, Yuval & Mohlin, Erik, 2015. "Stable Observable Behavior," MPRA Paper 63013, University Library of Munich, Germany.
  4. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 997-1026, 08.
  5. Heller, Yuval & Mohlin, Erik, 2014. "Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli," MPRA Paper 58255, University Library of Munich, Germany.

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