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Cycles of Learning in the Centipede Game

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  • Ponti, Giovanni

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. R. Cressman & K.H. Schlag, . "The Dynamic (In)Stability of Backwards Induction," ELSE working papers 027, ESRC Centre on Economics Learning and Social Evolution.
  2. 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.
  3. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  4. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  5. 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.
  6. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
  7. 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.
  8. Binmore, K.G. & Shaked, A. & Sutton, J., 1989. "An outside option experiment," Open Access publications from University College London http://discovery.ucl.ac.u, University College London.
  9. 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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Citations

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Cited by:
  1. Cabrales, Antonio & Ponti, Giovanni, . "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4310, Universidad Carlos III de Madrid.
  2. 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, vol. 4(1), pages 1-20, January.
  3. 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.
  4. Caminati, Mauro & Innocenti, Alessandro & Ricciuti, Roberto, 2006. "Drift effect under timing without observability: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 61(3), pages 393-414, November.
  5. repec:fth:calaec:6-98 is not listed on IDEAS
  6. Giovanni Ponti, 1999. "- Continuous-Time Evolutionary Dynamics: Theory And Practice," Working Papers. Serie AD 1999-31, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. Giovanni Ponti, 2000. "Splitting The Baby In Two: How To Solve Solomon'S Dilemma When Agents Are Boundedly Rational," Working Papers. Serie AD 2000-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. 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.
  9. Farina, Francesco & Sbriglia, Patrizia, 2007. "Cooperation as self-interested reciprocity in the Centipede," MPRA Paper 3701, University Library of Munich, Germany.
  10. 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, vol. 43(2), pages 239-265, May.
  11. Alessandro Innocenti & Mauro Caminati & Roberto Ricciuti, 2003. "Drift effect and timing without observability: experimental evidence," Department of Economics University of Siena 405, Department of Economics, University of Siena.

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