IDEAS home Printed from https://ideas.repec.org/p/wuk/ucloec/9622.html
   My bibliography  Save this paper

Cycles of Learning in the Centipede Game

Author

Listed:
  • 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.

Suggested Citation

  • Giovanni Ponti, 1996. "Cycles of Learning in the Centipede Game," Discussion Papers 96-22 ISSN 1350-6722, University College London, Department of Economics.
  • Handle: RePEc:wuk:ucloec:9622
    as

    Download full text from publisher

    File URL: ftp://ftp.repec.org/RePEc/wuk/ucloec/ucloec9622.ps
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    2. Ken Binmore, "undated". "Rationality and Backward Induction," ELSE working papers 047, ESRC Centre on Economics Learning and Social Evolution.
    3. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
    4. Ken Binmore, 1997. "Rationality and backward induction," Journal of Economic Methodology, Taylor & Francis Journals, vol. 4(1), pages 23-41.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    7. 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.
    8. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    9. McKelvey, Richard D & Palfrey, Thomas R, 1992. "An Experimental Study of the Centipede Game," Econometrica, Econometric Society, vol. 60(4), pages 803-836, July.
    10. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift And Equilibrium Selection," ELSE working papers 049, ESRC Centre on Economics Learning and Social Evolution.
    11. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    12. 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.
    13. 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.
    14. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution.
    15. 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.
    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. Ken Binmore & Avner Shared & John Sutton, 1989. "An Outside Option Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(4), pages 753-770.
    18. Binmore, K. & Samuelson, L., 1995. "Evolutionary Drift and Equilibrium Selection," Working papers 9529, Wisconsin Madison - Social Systems.
    19. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
    20. 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.
    21. Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-481, May.
    22. 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.
    23. 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.
    24. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:cdl:ucsbec:6-98 is not listed on IDEAS
    2. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    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. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2019. "Best experienced payoff dynamics and cooperation in the Centipede game," Theoretical Economics, Econometric Society, vol. 14(4), November.
    5. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
    6. Paolo Crosetto & Marco Mantovani, 2012. "Availability of Information and Representation Effects in the Centipede Game," Jena Economics Research Papers 2012-051, Friedrich-Schiller-University Jena.
    7. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, vol. 54(2), pages 187-214, June.
    8. Paolo Crosetto & Marco Mantovani, 2018. "Representation effects in the centipede game," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-13, October.
    9. 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).
    10. Farina, Francesco & Sbriglia, Patrizia, 2007. "Cooperation as self-interested reciprocity in the Centipede," MPRA Paper 3701, University Library of Munich, Germany.
    11. Kristian Lindgren & Vilhelm Verendel, 2013. "Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma—The Effect of Out-of-Equilibrium Play," Games, MDPI, vol. 4(1), pages 1-20, January.
    12. Olivier Compte, 2023. "Endogenous Barriers to Learning," Papers 2306.16904, arXiv.org.
    13. Hong, Jieying & Moinas, Sophie & Pouget, Sébastien, 2021. "Learning in speculative bubbles: Theory and experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 1-26.
    14. 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.
    15. Bernergård, Axel & Mohlin, Erik, 2019. "Evolutionary selection against iteratively weakly dominated strategies," Games and Economic Behavior, Elsevier, vol. 117(C), pages 82-97.
    16. 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.
    17. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    18. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:fth:calaec:16-97 is not listed on IDEAS
    2. repec:cdl:ucsbec:16-97 is not listed on IDEAS
    3. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, vol. 54(2), pages 187-214, June.
    4. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
    5. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    6. repec:cdl:ucsbec: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. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    9. Dai, Darong, 2012. "On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness," MPRA Paper 40560, University Library of Munich, Germany.
    10. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    11. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    12. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution.
    13. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. Uriarte, Jose Ramon, 2007. "A behavioural foundation for models of evolutionary drift," Journal of Economic Behavior & Organization, Elsevier, vol. 63(3), pages 497-513, July.
    15. Kristian Lindgren & Vilhelm Verendel, 2013. "Evolutionary Exploration of the Finitely Repeated Prisoners’ Dilemma—The Effect of Out-of-Equilibrium Play," Games, MDPI, vol. 4(1), pages 1-20, January.
    16. Graciela Kuechle, 2009. "What Happened To The Three‐Legged Centipede Game?," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 562-585, July.
    17. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    18. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    19. Weibull, Jörgen & Salomonsson, Marcus, 2005. "Natural selection and social preferences," SSE/EFI Working Paper Series in Economics and Finance 588, Stockholm School of Economics, revised 27 Sep 2005.
    20. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    21. Ramzi Mabsout, 2018. "The Backward Induction Controversy as a Metaphorical Problem," Economic Thought, World Economics Association, vol. 7(1), pages 24-49, March.
    22. Battalio,R. & Samuelson,L. & Huyck,J. van, 1998. "Risk dominance, payoff dominance and probabilistic choice learning," Working papers 2, Wisconsin Madison - Social Systems.
    23. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1999. "Stochastic Game Theory: Adjustment to Equilibrium Under Noisy Directional Learning," Virginia Economics Online Papers 327, University of Virginia, Department of Economics.

    More about this item

    Keywords

    Evolutionary Game Theory; Learning Theory; Backward-induction; Subgame-perfection; Replicator Dynamics.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wuk:ucloec:9622. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: WoPEc Project (email available below). General contact details of provider: https://edirc.repec.org/data/deucluk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.