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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. 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. 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.
  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. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  6. 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.
  7. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  8. 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.
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