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Field Centipedes

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Abstract

We conduct a field experiment in which highly-ranked chess players play the centipede game in a natural setting. This game represents one of the main paradoxes of backward induction. In the experiment two players alternately are faced with the decision of either taking an exponentially growing pile of money and ending the game, or letting the other player make the decision. The player who decides to stop the game takes the larger portion of the pile, and the other player gets the remaining amount. All standard equilibrium concepts dictate that the player who decides first must stop the game immediately. There is vast experimental evidence, however, that this rarely occurs. Contrary to this evidence our results show that 69% of chess players stop the game immediately. When we restrict attention to chess Grandmasters this percentage escalates to 100%. We also conduct standard laboratory experiments where college students and chess players play ten repetitions of the game. We find that chess players playing versus other chess players rapidly converge to the equilibrium outcome, whereas students playing versus other students systematically depart from it. However, when students play against chess players the occurrence of the backward induction outcome increases tenfold.

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Bibliographic Info

Paper provided by Oscar Volij in its series Economic theory and game theory with number 020.

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Publication status: Forthcoming in the American Economic Review.
Handle: RePEc:nid:ovolij:020

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Postal: Oscar Volij, Department of Economics, Ben-Gurion University, Beer-Sheva 84105, Israel
Web page: http://volij.co.il/

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Keywords: Rationality; centipede game; experiments; chess players.;

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References

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  1. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  2. Binmore, Ken & McCarthy, John & Ponti, Giovanni & Samuelson, Larry & Shaked, Avner, 2002. "A Backward Induction Experiment," Journal of Economic Theory, Elsevier, vol. 104(1), pages 48-88, May.
  3. Asheim,G.B. & Dufwenberg,M., 2000. "Deductive reasoning in extensive games," Memorandum 08/2000, Oslo University, Department of Economics.
  4. Miguel A. Costa-Gomes & Vincent P. Crawford, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," Levine's Bibliography 321307000000000336, UCLA Department of Economics.
  5. Fey, Mark & McKelvey, Richard D & Palfrey, Thomas R, 1996. "An Experimental Study of Constant-Sum Centipede Games," International Journal of Game Theory, Springer, vol. 25(3), pages 269-87.
  6. Zauner, Klaus G., 1999. "A Payoff Uncertainty Explanation of Results in Experimental Centipede Games," Games and Economic Behavior, Elsevier, vol. 26(1), pages 157-185, January.
  7. 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.
  8. Gary Bornstein & Tamar Kugler & Anthony Ziegelmeyer, 2002. "Individual and Group Decisions in the Centipede Game: Are Groups More “Rational” Players?," Discussion Paper Series dp298, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  9. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  10. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
  11. Reny Philip J., 1993. "Common Belief and the Theory of Games with Perfect Information," Journal of Economic Theory, Elsevier, vol. 59(2), pages 257-274, April.
  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. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
  14. Rapoport, Amnon & Stein, William E. & Parco, James E. & Nicholas, Thomas E., 2003. "Equilibrium play and adaptive learning in a three-person centipede game," Games and Economic Behavior, Elsevier, vol. 43(2), pages 239-265, May.
  15. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
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Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. Never date a game theorist? Lessons from the centipede game
    by Presh Talwalkar in Mind Your Decisions on 2012-07-10 05:01:03
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:
  1. Andrea Morone & Piergiuseppe Morone, 2012. "Individual and Group Behaviours in the Traveller's Dilemma: An Experimental Study," Working Papers 2012/09, Economics Department, Universitat Jaume I, Castellón (Spain).
  2. Gerdes, Christer & Gränsmark, Patrik, 2010. "Strategic Behavior across Gender: A Comparison of Female and Male Expert Chess Players," IZA Discussion Papers 4793, Institute for the Study of Labor (IZA).
  3. S. Dellavigna., 2011. "Psychology and Economics: Evidence from the Field," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.
  4. Englmaier, Florian & Gebhardt, Georg, 2010. "Free Riding in the Lab and in the Field," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 344, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  5. Steven Levitt & John List & Sally Sadoff, 2010. "Checkmate: Exploring backward induction among chess players," Artefactual Field Experiments 00081, The Field Experiments Website.
  6. Christoph Bühren & Björn Frank, 2010. "Chess players' performance beyond 64 squares: A case study on the limitations of cognitive abilities transfer," MAGKS Papers on Economics 201019, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
  7. Andreas Ortmann, 2010. "'The Way in Which an Experiment is Conducted is Unbelievably Important': On the Experimentation Practices of Economists and Psychologists," Discussion Papers 2010-06, School of Economics, The University of New South Wales.
  8. Gerdes, Christer & Gränsmark, Patrik & Rosholm, Michael, 2011. "Chicken or Checkin'? Rational Learning in Repeated Chess Games," IZA Discussion Papers 5862, Institute for the Study of Labor (IZA).
  9. Paolo Crosetto & Marco Mantovani, 2012. "Availability of Information and Representation Effects in the Centipede Game," Jena Economic Research Papers 2012-051, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
  10. 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.
  11. Michèle Belot & Raymond Duch & Luis Miller, 2010. "Who should be called to the lab? A comprehensive comparison of students and non-students in classic experimental games," Discussion Papers 2010001, University of Oxford, Nuffield College.

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