IDEAS home Printed from https://ideas.repec.org/p/syd/wpaper/2123-8898.html
   My bibliography  Save this paper

Stochastic stability on general state spaces

Author

Listed:
  • Newton, Jonathan

Abstract

This paper studies stochastic stability methods applied to processes on general state spaces. This includes settings in which agents repeatedly interact and choose from an uncountable set of strategies. Dynamics exist for which the stochastically stable states differ from those of any reasonable finite discretization. When there are a finite number of rest points of the unperturbed dynamic, sufficient conditions for analogues of results from the finite state space literature are derived and studied. Illustrative examples are given.

Suggested Citation

  • Newton, Jonathan, 2012. "Stochastic stability on general state spaces," Working Papers 2012-16, University of Sydney, School of Economics, revised Jul 2014.
    • Handle: RePEc:syd:wpaper:2123/8898
    as

    Download full text from publisher

    File URL: http://www.econ-wpseries.com/2012/201216-2.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. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    4. van Damme, Eric & Weibull, Jorgen W., 2002. "Evolution in Games with Endogenous Mistake Probabilities," Journal of Economic Theory, Elsevier, vol. 106(2), pages 296-315, October.
    5. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    6. Schenk-Hoppe, Klaus Reiner, 2000. "The evolution of Walrasian behavior in oligopolies," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 35-55, February.
    7. Naidu, Suresh & Hwang, Sung-Ha & Bowles, Samuel, 2010. "Evolutionary bargaining with intentional idiosyncratic play," Economics Letters, Elsevier, vol. 109(1), pages 31-33, October.
    8. 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.
    9. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    10. Ilan Eshel & Larry Samuelson & Avner Shaked, "undated". "Altruists Egoists and Hooligans in a Local Interaction Model," ELSE working papers 005, ESRC Centre on Economics Learning and Social Evolution.
    11. 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.
    12. Eshel, Ilan & Samuelson, Larry & Shaked, Avner, 1998. "Altruists, Egoists, and Hooligans in a Local Interaction Model," American Economic Review, American Economic Association, vol. 88(1), pages 157-179, March.
    13. Ken Binmore & Larry Samuelson & Petyon Young, 2003. "Equilibrium Selection in Bargaining Models," Levine's Bibliography 506439000000000466, UCLA Department of Economics.
    14. Chong, Juin-Kuan & Camerer, Colin F. & Ho, Teck H., 2006. "A learning-based model of repeated games with incomplete information," Games and Economic Behavior, Elsevier, vol. 55(2), pages 340-371, May.
    15. Roberto Serrano & Oscar Volij, 2003. "MISTAKE IN COOPERATION:the Stochastic Stability of Edgeworth's Recontracting," Working Papers 2003-23, Brown University, Department of Economics.
    16. Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: The Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
    17. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    18. Selten, Reinhard & Apesteguia, Jose, 2005. "Experimentally observed imitation and cooperation in price competition on the circle," Games and Economic Behavior, Elsevier, vol. 51(1), pages 171-192, April.
    19. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    20. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    21. Feinberg Yossi, 2006. "Evolutionary Dynamics and Long-Run Selection," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-26, March.
    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. Sawa, Ryoji, 2021. "A prospect theory Nash bargaining solution and its stochastic stability," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 692-711.
    2. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    3. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.

    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:syd:wpaper:2123/9993 is not listed on IDEAS
    2. Hwang, Sung-Ha & Lim, Wooyoung & Neary, Philip & Newton, Jonathan, 2018. "Conventional contracts, intentional behavior and logit choice: Equality without symmetry," Games and Economic Behavior, Elsevier, vol. 110(C), pages 273-294.
    3. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    4. 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.
    5. 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.
    6. Sawa, Ryoji, 2021. "A prospect theory Nash bargaining solution and its stochastic stability," Journal of Economic Behavior & Organization, Elsevier, vol. 184(C), pages 692-711.
    7. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.
    8. Tatur, Tymon, 2023. "Evolutionarily rational mutations in structured populations," Journal of Economic Theory, Elsevier, vol. 212(C).
    9. Hwang, Sung-Ha & Rey-Bellet, Luc, 2021. "Positive feedback in coordination games: Stochastic evolutionary dynamics and the logit choice rule," Games and Economic Behavior, Elsevier, vol. 126(C), pages 355-373.
    10. 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.
    11. Lim, Wooyoung & Neary, Philip R., 2016. "An experimental investigation of stochastic adjustment dynamics," Games and Economic Behavior, Elsevier, vol. 100(C), pages 208-219.
    12. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, vol. 1(4), pages 1-35, November.
    13. Sawa, Ryoji, 2019. "Stochastic stability under logit choice in coalitional bargaining problems," Games and Economic Behavior, Elsevier, vol. 113(C), pages 633-650.
    14. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    15. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    16. 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.
    17. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2008. "Contagion and efficiency," Journal of Economic Theory, Elsevier, vol. 143(1), pages 251-274, November.
    18. Khan, Abhimanyu, 2022. "Expected utility versus cumulative prospect theory in an evolutionary model of bargaining," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    19. Jonas Hedlund, 2015. "Imitation in Cournot oligopolies with multiple markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(3), pages 567-587, November.
    20. 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.
    21. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.

    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:syd:wpaper:2123/8898. 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: Vanessa Holcombe (email available below). General contact details of provider: https://edirc.repec.org/data/deusyau.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.