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Three steps ahead

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  • 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
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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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  2. Frenkel, Sivan & Heller, Yuval & Teper, Roee, 2012. "Endowment as a blessing," MPRA Paper 39430, University Library of Munich, Germany, revised 30 Apr 2012.
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  8. 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.
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  17. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
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  23. Hyndman, Kyle & Terracol, Antoine & Vaksmann, Jonathan, 2013. "Beliefs and (In)Stability in Normal-Form Games," MPRA Paper 47221, University Library of Munich, Germany.
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Cited by:

  1. Heller, Yuval & Winter, Eyal, 2013. "Rule Rationality," MPRA Paper 48746, University Library of Munich, Germany.
  2. Heller, Yuval & Mohlin, Erik, 2014. "Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli," MPRA Paper 58255, University Library of Munich, Germany.
  3. Heller, Yuval, 2014. "Stability and trembles in extensive-form games," Games and Economic Behavior, Elsevier, vol. 84(C), pages 132-136.

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