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Cycles of Learning in the Centipede Game

  • Giovanni Ponti

    (University College London)

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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Paper provided by University College London, Department of Economics in its series Discussion Papers with number 96-22 ISSN 1350-6722.

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Length: 24 pages
Date of creation: Jun 1996
Date of revision:
Handle: RePEc:wuk:ucloec:9622
Contact details of provider: Postal: Gower Street, London WC1E 6BT
Web page: http://www.ucl.ac.uk/economics/

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  1. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, vol. 83(2), pages 260-285, December.
  2. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  3. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  4. Binmore, Ken & Shaked, Avner & Sutton, John, 1989. "An Outside Option Experiment," The Quarterly Journal of Economics, MIT Press, vol. 104(4), pages 753-70, November.
  5. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  6. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
  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. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
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