IDEAS home Printed from https://ideas.repec.org/p/cla/levrem/321307000000000815.html
   My bibliography  Save this paper

Random matching in adaptive dynamics

Author

Listed:
  • Glenn Ellison
  • Drew Fudenberg
  • Lorens A. Imhof

Abstract

This paper studies the effect of randomness in per-period matching on the long-run outcome of non-equilibrium adaptive processes. If there are many matchings between each strategy revision, the randomness due to matching will be small; our question is when a very small noise due to matching has a negligible effect. We study two different senses of this idea, and provide sufficient conditions for each. The less demanding sense corresponds to sending the matching noise to zero while holding fixed all other aspects of the adaptive process. The second sense in which matching noise can be negligible is that it does not alter the limit distribution obtained as the limit of the invariant distributions as an exogenous "mutation rate" goes to zero.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Glenn Ellison & Drew Fudenberg & Lorens A. Imhof, 2007. "Random matching in adaptive dynamics," Levine's Bibliography 321307000000000815, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:321307000000000815
    as

    Download full text from publisher

    File URL: http://econweb.fas.harvard.edu/hier/2006papers/HIER2126.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. Fudenberg, Drew & Imhof, Lorens A., 2008. "Monotone imitation dynamics in large populations," Journal of Economic Theory, Elsevier, vol. 140(1), pages 229-245, May.
    5. Ellison, Glenn, 1997. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Games and Economic Behavior, Elsevier, vol. 19(2), pages 180-210, May.
    6. 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.
    7. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    8. Vega-Redondo, Fernando (ed.), 1996. "Evolution, Games, and Economic Behaviour," OUP Catalogue, Oxford University Press, number 9780198774723.
    9. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    10. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    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. Block, Juan I. & Fudenberg, Drew & Levine, David K., 2019. "Learning dynamics with social comparisons and limited memory," Theoretical Economics, Econometric Society, vol. 14(1), January.
    2. Robert Molzon, 2012. "Large Population Limits for Evolutionary Dynamics with Random Matching," Dynamic Games and Applications, Springer, vol. 2(1), pages 146-159, March.
    3. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
    4. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    5. Juan I Block & Drew Fudenberg & David K Levine, 2017. "Learning Dynamics Based on Social Comparisons," Levine's Working Paper Archive 786969000000001375, David K. Levine.

    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. Norman, Thomas W.L., 2009. "Rapid evolution under inertia," Games and Economic Behavior, Elsevier, vol. 66(2), pages 865-879, July.
    2. Ennio Bilancini & Leonardo Boncinelli, 2020. "The evolution of conventions under condition-dependent mistakes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 497-521, March.
    3. 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.
    4. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    5. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    6. Azomahou, T. & Opolot, D., 2014. "Stability and strategic diffusion in networks," MERIT Working Papers 2014-035, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    7. Ge Jiang & Simon Weidenholzer, 2017. "Local interactions under switching costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 571-588, October.
    8. Beggs, A.W., 2007. "Large deviations and equilibrium selection in large populations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 383-410, January.
    9. Sandholm, William H., 2012. "Stochastic imitative game dynamics with committed agents," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2056-2071.
    10. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
    11. Battalio,R. & Samuelson,L. & Huyck,J. van, 1998. "Risk dominance, payoff dominance and probabilistic choice learning," Working papers 2, Wisconsin Madison - Social Systems.
    12. Thomas Norman, 2010. "Cycles versus equilibrium in evolutionary games," Theory and Decision, Springer, vol. 69(2), pages 167-182, August.
    13. Veller, Carl & Hayward, Laura K., 2016. "Finite-population evolution with rare mutations in asymmetric games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 93-113.
    14. 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.
    15. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    16. 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.
    17. Jindani, Sam, 2022. "Learning efficient equilibria in repeated games," Journal of Economic Theory, Elsevier, vol. 205(C).
    18. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, vol. 1(4), pages 1-35, November.
    19. Sandholm, William H. & Staudigl, Mathias, 2016. "Large Deviations and Stochastic Stability in the Small Noise Double Limit, I: Theory," Center for Mathematical Economics Working Papers 505, Center for Mathematical Economics, Bielefeld University.
    20. Neary, Philip R., 2012. "Competing conventions," Games and Economic Behavior, Elsevier, vol. 76(1), pages 301-328.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cla:levrem:321307000000000815. 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: David K. Levine (email available below). General contact details of provider: http://www.dklevine.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.