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Three steps ahead

  • Heller, Yuval

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 39429.

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Date of creation: 13 Jun 2012
Date of revision:
Handle: RePEc:pra:mprapa:39429
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  1. 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.
  2. David Gill & Victoria Prowse, 2013. "Cognitive ability and learning to play equilibrium: A level-k analysis," Economics Series Working Papers 641, University of Oxford, Department of Economics.
  3. 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.
  4. 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.
  5. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
  6. Philippe Jehiel, 2005. "Analogy-Based Expectation Equilibrium," Levine's Bibliography 784828000000000106, UCLA Department of Economics.
  7. Russell Cooper & Douglas V. DeJong & Thomas W. Ross, 1992. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Papers 0036, Boston University - Industry Studies Programme.
  8. Ho, Teck Hua & Weigelt, Keith & Camerer, Colin, 1996. "Iterated Dominance and Iterated Best-Response in Experimental P-Beauty Contests," Working Papers 974, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
  10. Andreoni, J. & Miller, J.H., 1991. "Rational Cooperative in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Working papers 9102, Wisconsin Madison - Social Systems.
  11. Swinkels, J., 1991. "Evolutionary Stability with Equilibrium Entrants," Papers 9, Stanford - Institute for Thoretical Economics.
  12. 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.
  13. Lisa Bruttel & Werner Güth & Ulrich Kamecke, 2012. "Finitely repeated prisoners’ dilemma experiments without a commonly known end," International Journal of Game Theory, Springer, vol. 41(1), pages 23-47, February.
  14. Albert Satorra & Antoni Bosch-Domenech & Jose Garcia-Montalvo & Rosemarie Nagel, 2002. "One, two, (three), infinity: Newspaper and lab beauty-contest experiments," Artefactual Field Experiments 00011, The Field Experiments Website.
  15. 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.
  16. repec:oup:qjecon:v:119:y:2004:i:3:p:861-898 is not listed on IDEAS
  17. Hyndman, Kyle & Terracol, Antoine & Vaksmann, Jonathan, 2013. "Beliefs and (In)Stability in Normal-Form Games," MPRA Paper 47221, University Library of Munich, Germany.
  18. Frenkel, Sivan & Heller, Yuval & Teper, Roee, 2012. "Endowment as a blessing," MPRA Paper 39430, University Library of Munich, Germany, revised 30 Apr 2012.
  19. Heifetz, Aviad & Pauzner, Ady, 2005. "Backward induction with players who doubt others' faultlessness," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 252-267, November.
  20. Mohlin, Erik, 2010. "Evolution of Theories of Mind," SSE/EFI Working Paper Series in Economics and Finance 0728, Stockholm School of Economics, revised 12 May 2010.
  21. 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.
  22. 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.
  23. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
  24. Robson, Arthur J., 2003. "The evolution of rationality and the Red Queen," Journal of Economic Theory, Elsevier, vol. 111(1), pages 1-22, July.
  25. R. McKelvey & T. Palfrey, 2010. "Quantal Response Equilibria for Normal Form Games," Levine's Working Paper Archive 510, David K. Levine.
  26. Johan Stennek, 2000. "The survival value of assuming others to be rational," International Journal of Game Theory, Springer, vol. 29(2), pages 147-163.
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