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Field Centipedes

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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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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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  1. Asheim, Geir B, 2000. "Deductive reasoning in Extensive Games," Research Papers in Economics 2000:7, Stockholm University, Department of Economics.
  2. Aumann, Robert J., 1998. "On the Centipede Game," Games and Economic Behavior, Elsevier, vol. 23(1), pages 97-105, April.
  3. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  4. Miguel A. Costa-Gomes & Vincent P. Crawford, 2004. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," ISER Discussion Paper 0613, Institute of Social and Economic Research, Osaka University.
  5. Binmore,K. & McCarthy,J. & Ponti,G. & ..., 1999. "A backward induction experiment," Working papers 34, Wisconsin Madison - Social Systems.
  6. P. Reny, 2010. "Common Belief and the Theory of Games with Perfect Information," Levine's Working Paper Archive 386, David K. Levine.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Ben-Porath, Elchanan, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Wiley Blackwell, vol. 64(1), pages 23-46, January.
  12. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July.
  13. 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.
  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. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-36, July.
  16. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  17. 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.
  18. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
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  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
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