Three steps ahead
AbstractExperimental 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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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 40714.
Date of creation: 13 Jun 2012
Date of revision:
Indirect evolution; cognitive hierarchy; bounded forward-looking; Prisoner's Dilemma; Cooperation;
Other versions of this item:JEL classification:
- D03 - Microeconomics - - General - - - Behavioral Economics; Underlying Principles
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-03 (All new papers)
- NEP-EVO-2012-09-03 (Evolutionary Economics)
- NEP-EXP-2012-09-03 (Experimental Economics)
- NEP-HPE-2012-09-03 (History & Philosophy of Economics)
- NEP-NEU-2012-09-03 (Neuroeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Mohlin, Erik, 2010.
"Evolution of Theories of Mind,"
Working Paper Series in Economics and Finance
0728, Stockholm School of Economics, revised 12 May 2010.
- 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.
- Philippe Jehiel, 2005.
"Analogy-Based Expectation Equilibrium,"
784828000000000106, UCLA Department of Economics.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Frenkel, Sivan & Heller, Yuval & Teper, Roee, 2012. "Endowment as a blessing," MPRA Paper 39430, University Library of Munich, Germany, revised 30 Apr 2012.
- Rosemarie Nagel & Antoni Bosch-Domènech & Albert Satorra & José García Montalvo, 1999.
"One, two, (three), infinity: Newspaper and lab beauty-contest experiments,"
Economics Working Papers
438, Department of Economics and Business, Universitat Pompeu Fabra.
- Antoni Bosch-Dom�nech & Jos� G. Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, Two, (Three), Infinity, ...: Newspaper and Lab Beauty-Contest Experiments," American Economic Review, American Economic Association, vol. 92(5), pages 1687-1701, December.
- Antoni Bosch-Dom?nech & Jose Garcia-Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, two, (three), infinity: Newspaper and lab beauty-contest experiments," Artefactual Field Experiments 00011, The Field Experiments Website.
- 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.
- 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.
- Johan Stennek, 2000. "The survival value of assuming others to be rational," International Journal of Game Theory, Springer, vol. 29(2), pages 147-163.
- Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
- Robson, Arthur J., 2003. "The evolution of rationality and the Red Queen," Journal of Economic Theory, Elsevier, vol. 111(1), pages 1-22, July.
- Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2010. "Strategic Thinking," Levine's Working Paper Archive 661465000000001148, David K. Levine.
- R. McKelvey & T. Palfrey, 2010. "Quantal Response Equilibria for Normal Form Games," Levine's Working Paper Archive 510, David K. Levine.
- Hyndman, Kyle & Terracol, Antoine & Vaksmann, Jonathan, 2013. "Beliefs and (In)Stability in Normal-Form Games," MPRA Paper 47221, University Library of Munich, Germany.
- Heller, Yuval & Winter, Eyal, 2013. "Rule Rationality," MPRA Paper 48746, University Library of Munich, Germany.
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