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Cycles Of Learning In The Centipede Game

  • Giovanni Ponti

Traditional game theoretic analysis often proposes the application of backward-induction and subgame-perfection as models of rational behavior in games with perfect information. However, there are many situations in which such application leads to counterintuitive results, casting doubts on the predictive power of the theory itself. The Centipede Game, firstly introduced by Rosenthal (1981), represents one of these critical cases, and experimental evidence has been provided to show how people in laboratory behave in a manner which is significatively different from what the theory expects. In our paper, we construct a dynamic model based on the Centipede Game. Our claim is that the source of these discrepancies between theory and experimental evidence may be explained by appealing to some form of bounded rationality in the players' reasoning. If this is the case, traditional game theoretical analysis could still accurately predict the players' behavior, provided that they are given time enough to correctly perceive the strategic environment in which they operate. To do so, we provide conditions for convergence to the subgame-perfect equilibrium outcome for a broad class of continuous time evolutionary dynamics, defined as Aggregate Monotonic Selection dynamics (Samuelson and Zhang (1992)). Moreover, by introducing a drift term in the dynamics, we show how the outcome of this learning process is intrinsically unstable, and how this instability is positively related with the length of the game.

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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 024.

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Handle: RePEc:els:esrcls:024
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  1. Ken Binmore, 1997. "Rationality and backward induction," Journal of Economic Methodology, Taylor & Francis Journals, vol. 4(1), pages 23-41.
  2. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  3. Hofbauer, Josef & Weibull, Jîrgen W., 1995. "Evolutionary selection against dominated strategies," CEPREMAP Working Papers (Couverture Orange) 9506, CEPREMAP.
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  5. Binmore, K. & Samuelson, L., 1995. "Evolutionary Drift and Equilibrium Selection," Working papers 9529, Wisconsin Madison - Social Systems.
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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.
  9. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
  10. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  11. David Kreps & Paul Milgrom & John Roberts & Bob Wilson, 2010. "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Levine's Working Paper Archive 239, David K. Levine.
  12. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
  13. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  14. Cressman, R., 1996. "Evolutionary Stability in the Finitely Repeated Prisoner 's Dilemma Game," Journal of Economic Theory, Elsevier, vol. 68(1), pages 234-248, January.
  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. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
  17. 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.
  18. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
  19. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  20. Ken Binmore & Avner Shared & John Sutton, 1989. "An Outside Option Experiment," The Quarterly Journal of Economics, Oxford University Press, vol. 104(4), pages 753-770.
  21. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  22. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
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