IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/9704001.html
   My bibliography  Save this paper

An Evolutionary Analysis of Bagwell's Example

Author

Listed:
  • Jorg Oechssler

    (Humboldt University, Berlin)

  • Karl Schlag

    (University of Bonn)

Abstract

In a recent paper Bagwell (1995) pointed out that only the Cournot outcome, but not the Stackelberg outcome, can be supported by a pure Nash equilibrium when actions of the Stackelberg leader are observed with the slightest error. The Stackelberg outcome, however, remains close to the outcome of a mixed equilibrium. We compare the predictions in various classes of evolutionary and learning processes in this game. Only the continuous best response dynamic uniquely selects the Stackelberg outcome under noise. All other dynamics analyzed allow for the Cournot equilibrium to be selected. In typical cases Cournot is the unique long run outcome even for vanishing noise in the signal.

Suggested Citation

  • Jorg Oechssler & Karl Schlag, 1997. "An Evolutionary Analysis of Bagwell's Example," Game Theory and Information 9704001, University Library of Munich, Germany, revised 11 Apr 1997.
    • Handle: RePEc:wpa:wuwpga:9704001
    Note: Pages: 19
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9704/9704001.pdf
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9704/9704001.ps.gz
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    3. Bagwell, Kyle, 1995. "Commitment and observability in games," Games and Economic Behavior, Elsevier, vol. 8(2), pages 271-280.
    4. Adolph, B., 1996. "Commitment, Trembling Hand Imperfection and Observability in Games," SFB 373 Discussion Papers 1996,84, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. Guth, Werner & Kirchsteiger, Georg & Ritzberger, Klaus, 1998. "Imperfectly Observable Commitments inn-Player Games," Games and Economic Behavior, Elsevier, vol. 23(1), pages 54-74, April.
    8. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
    9. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
    10. van Damme, Eric & Hurkens, Sjaak, 1997. "Games with Imperfectly Observable Commitment," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 282-308, October.
    11. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    12. 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.
    13. Samuelson Larry, 1994. "Stochastic Stability in Games with Alternative Best Replies," Journal of Economic Theory, Elsevier, vol. 64(1), pages 35-65, October.
    14. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    15. 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.
    16. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    17. Binmore, K. & Samuelson, L. & Gale, J., 1993. "Learning to be Imperfect: The Ultimatum Game," Working papers 9325, Wisconsin Madison - Social Systems.
    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. Morgan, John & Vardy, Felix, 2007. "The value of commitment in contests and tournaments when observation is costly," Games and Economic Behavior, Elsevier, vol. 60(2), pages 326-338, August.
    2. repec:ebl:ecbull:v:3:y:2008:i:74:p:1-8 is not listed on IDEAS
    3. Bhaskar, V, 2005. "Commitment and Observability in an Economic Environment," Economics Discussion Papers 8887, University of Essex, Department of Economics.
    4. Guth, Werner & Muller, Wieland & Spiegel, Yossi, 2006. "Noisy leadership: An experimental approach," Games and Economic Behavior, Elsevier, vol. 57(1), pages 37-62, October.
    5. 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).
    6. Lagerlof, Johan, 2003. "Policy-Motivated Candidates, Noisy Platforms, and Non-robustness," Public Choice, Springer, vol. 114(3-4), pages 319-347, March.

    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. Jörg Oechssler & Karl H Schlag, 1997. "Loss of Commitment? An Evolutionary Analysis of Bagwell’s Example," Levine's Working Paper Archive 598, David K. Levine.
    2. 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.
    3. 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.
    4. repec:cdl:ucsbec:6-98 is not listed on IDEAS
    5. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    6. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    7. Gerard van der Laan & A.F. Tieman, 1996. "Evolutionary Game Theory and the Modelling of Economic Behavior," Tinbergen Institute Discussion Papers 96-172/8, Tinbergen Institute.
    8. 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.
    9. Huw Dixon & Ernesto Somma, "undated". "Coordination and Equilibrium selection in mean defined supermodular games under payoff monotonic selection dynamics," Discussion Papers 99/37, Department of Economics, University of York.
    10. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
    11. Huck, Steffen & Oechssler, Jorg, 1999. "The Indirect Evolutionary Approach to Explaining Fair Allocations," Games and Economic Behavior, Elsevier, vol. 28(1), pages 13-24, July.
    12. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.
    13. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    14. Ponti, Giovanni, 2000. "Continuous-time evolutionary dynamics: theory and practice," Research in Economics, Elsevier, vol. 54(2), pages 187-214, June.
    15. Christoph Kuzmics & Daniel Rodenburger, 2020. "A case of evolutionarily stable attainable equilibrium in the laboratory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 685-721, October.
    16. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    17. Huck, Steffen & Muller, Wieland, 2000. "Perfect versus Imperfect Observability--An Experimental Test of Bagwell's Result," Games and Economic Behavior, Elsevier, vol. 31(2), pages 174-190, May.
    18. Cressman, R., 1997. "Local stability of smooth selection dynamics for normal form games," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 1-19, August.
    19. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    20. 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.
    21. Ellingsen, Tore & Robles, Jack, 2002. "Does Evolution Solve the Hold-Up Problem?," Games and Economic Behavior, Elsevier, vol. 39(1), pages 28-53, April.

    More about this item

    Keywords

    imperfectly observable commitment; evolution; imitation; learning; equilibrium selection;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:wpa:wuwpga:9704001. 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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.