IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v44y2015i2p499-514.html
   My bibliography  Save this article

Waiting times in evolutionary dynamics with time-decreasing noise

Author

Listed:
  • Katsuhiko Aiba

Abstract

Expected waiting times for equilibrium selection are exponentially increasing as the noise level goes to zero in evolutionary models with time-constant noise, raising questions about whether the history independent prediction of equilibrium selection is relevant in economic and social studies. However, by using the theoretical results on simulated annealing, we show that expected waiting times in models with time-decreasing noise need not tend toward infinity in the small noise limit. Our model thus describes conditions under which the waiting-time critique of the predictions of stochastic stability theory may have less force. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Katsuhiko Aiba, 2015. "Waiting times in evolutionary dynamics with time-decreasing noise," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 499-514, May.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:2:p:499-514
    DOI: 10.1007/s00182-014-0442-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00182-014-0442-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00182-014-0442-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    2. Pak, Maxwell, 2008. "Stochastic stability and time-dependent mutations," Games and Economic Behavior, Elsevier, vol. 64(2), pages 650-665, November.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    5. 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.
    6. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    7. Alan Beggs, 2005. "Waiting times and equilibrium selection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 599-628, April.
    8. Sandholm, William H., 1998. "Simple and clever decision rules for a model of evolution," Economics Letters, Elsevier, vol. 61(2), pages 165-170, November.
    9. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
    10. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    11. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    12. Robles, Jack, 1998. "Evolution with Changing Mutation Rates," Journal of Economic Theory, Elsevier, vol. 79(2), pages 207-223, April.
    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. Konstantin Avrachenkov & Vivek S. Borkar, 2019. "Metastability in Stochastic Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 9(2), pages 366-390, June.

    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. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    2. Lim, Wooyoung & Neary, Philip R., 2016. "An experimental investigation of stochastic adjustment dynamics," Games and Economic Behavior, Elsevier, vol. 100(C), pages 208-219.
    3. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.
    4. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
    5. Hsiao-Chi Chen & Yunshyong Chow & Li-Chau Wu, 2013. "Imitation, local interaction, and coordination," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 1041-1057, November.
    6. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, vol. 1(4), pages 1-35, November.
    7. Ianni, Antonella, 2001. "Learning correlated equilibria in population games," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 271-294, November.
    8. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    9. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Opolot, Daniel & Azomahou, Theophile, 2012. "Learning and convergence in networks," MERIT Working Papers 2012-074, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    11. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers 1001, University of Vienna, Department of Economics.
    12. Sandholm, William H., 2007. "Pigouvian pricing and stochastic evolutionary implementation," Journal of Economic Theory, Elsevier, vol. 132(1), pages 367-382, January.
    13. Okada, Daijiro & Tercieux, Olivier, 2012. "Log-linear dynamics and local potential," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1140-1164.
    14. Jackson, Matthew O. & Watts, Alison, 2002. "On the formation of interaction networks in social coordination games," Games and Economic Behavior, Elsevier, vol. 41(2), pages 265-291, November.
    15. Neary, Philip R., 2012. "Competing conventions," Games and Economic Behavior, Elsevier, vol. 76(1), pages 301-328.
    16. Staudigl, Mathias & Weidenholzer, Simon, 2014. "Constrained interactions and social coordination," Journal of Economic Theory, Elsevier, vol. 152(C), pages 41-63.
    17. Cui, Zhiwei & Zhai, Jian, 2010. "Escape dynamics and equilibria selection by iterative cycle decomposition," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1015-1029, November.
    18. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    19. Sawa, Ryoji & Wu, Jiabin, 2018. "Prospect dynamics and loss dominance," Games and Economic Behavior, Elsevier, vol. 112(C), pages 98-124.
    20. Mathias Staudigl, 2010. "On a General class of stochastic co-evolutionary dynamics," Vienna Economics Papers vie1001, University of Vienna, Department of Economics.

    More about this item

    Keywords

    Evolutionary game theory; Waiting times; Simulated annealing; C61; C72; C73;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • 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:spr:jogath:v:44:y:2015:i:2:p:499-514. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.