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Cycles of Learning in the Centipede Game

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  • Giovanni Ponti

    (University College London)

Abstract

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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File URL: ftp://ftp.repec.org/RePEc/wuk/ucloec/ucloec9622.ps
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Bibliographic Info

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

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Web page: http://www.ucl.ac.uk/economics/
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Keywords: Evolutionary Game Theory; Learning Theory; Backward-induction; Subgame-perfection; Replicator Dynamics.;

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References

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  1. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  2. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers, Princeton, Woodrow Wilson School - John M. Olin Program 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  3. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, Elsevier, vol. 83(2), pages 260-285, December.
  4. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
  5. Binmore, Ken & Shaked, Avner & Sutton, John, 1989. "An Outside Option Experiment," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 104(4), pages 753-70, November.
  6. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, Elsevier, vol. 74(1), pages 40-61, May.
  7. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, Springer, vol. 19(1), pages 59-89.
  8. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(1), pages 92-100, August.
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Citations

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Cited by:
  1. Farina, Francesco & Sbriglia, Patrizia, 2007. "Cooperation as self-interested reciprocity in the Centipede," MPRA Paper 3701, University Library of Munich, Germany.
  2. Alessandro Innocenti & Mauro Caminati & Roberto Ricciuti, 2003. "Drift effect and timing without observability: experimental evidence," Department of Economics University of Siena, Department of Economics, University of Siena 405, Department of Economics, University of Siena.
  3. Antonio Cabrales & Giovanni Ponti, 1997. "Implementation, elimination of weakly dominated strategies and evolutionary dynamics," Economics Working Papers 221, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Kristian Lindgren & Vilhelm Verendel, 2013. "Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma—The Effect of Out-of-Equilibrium Play," Games, MDPI, Open Access Journal, MDPI, Open Access Journal, vol. 4(1), pages 1-20, January.
  5. 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, Elsevier, vol. 43(2), pages 239-265, May.
  6. repec:fth:calaec:6-98 is not listed on IDEAS
  7. Lindgren, Kristian & Verendel, Vilhelm, 2013. "Evolutionary Exploration of the Finitely Repeated Prisoners' Dilemma--The Effect of Out-of-Equilibrium Play," MPRA Paper 43662, University Library of Munich, Germany.
  8. Caminati, Mauro & Innocenti, Alessandro & Ricciuti, Roberto, 2006. "Drift effect under timing without observability: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 61(3), pages 393-414, November.
  9. Giovanni Ponti, 2000. "Splitting The Baby In Two: How To Solve Solomon'S Dilemma When Agents Are Boundedly Rational," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2000-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  10. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, Elsevier, vol. 54(2), pages 187-214, June.
  11. Paolo Crosetto & Marco Mantovani, 2012. "Availability of Information and Representation Effects in the Centipede Game," Jena Economic Research Papers 2012-051, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.

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