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Cycles of Learning in the Centipede Game

  • Ponti, Giovanni

Traditional game theoretic analysis often proposes the application of backward induction and subgame-perfection as models of rational behaviour in games with perfect information. However, there are many situations in which such application leads to counterinitiative results, casting doubts on the predictive power of theory itself. The Centipede Game, firstly, introduced by Rosenthal (1981), represents one of the critical cases and experimental evidence has been provided to show how people in laboratory behave in a manner which is a 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' behaviour, 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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 30 (2000)
Issue (Month): 1 (January)
Pages: 115-141

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Handle: RePEc:eee:gamebe:v:30:y:2000:i:1:p:115-141
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  2. 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.
  3. Binmore, K. & Samuelson, L., 1995. "Evolutionary Drift and Equilibrium Selection," Working papers 9529, Wisconsin Madison - Social Systems.
  4. 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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  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  20. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  21. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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