IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v84y2017icp32-42.html
   My bibliography  Save this article

On the dynamic stability of a price dispersion model using gradient dynamics

Author

Listed:
  • Rabanal, Jean Paul
  • Lee, Dongwook

Abstract

This paper studies the evolutionary stability of a unique Nash equilibrium in a price dispersion model (Burdett and Judd, 1983) using gradient dynamics. The numerical solution to the partial differential equation that governs the evolution of prices shows that the stationary equilibrium is not a Nash Equilibrium and that it differs from the cyclical behavior predicted by another family of dynamics, such as replicator and logit, in a continuous action space.

Suggested Citation

  • Rabanal, Jean Paul & Lee, Dongwook, 2017. "On the dynamic stability of a price dispersion model using gradient dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 32-42.
    • Handle: RePEc:eee:dyncon:v:84:y:2017:i:c:p:32-42
    DOI: 10.1016/j.jedc.2017.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016518891730180X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2017.08.007?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. Michael R. Baye & John Morgan & Patrick Scholten, 2004. "Price Dispersion In The Small And In The Large: Evidence From An Internet Price Comparison Site," Journal of Industrial Economics, Wiley Blackwell, vol. 52(4), pages 463-496, December.
    2. Michael D. Smith & Erik Brynjolfsson, 2001. "Consumer Decision-making at an Internet Shopbot: Brand Still Matters," NBER Chapters, in: E-commerce, pages 541-558, National Bureau of Economic Research, Inc.
    3. Ed Hopkins & Robert M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1157-1190, November.
    4. Cason, Timothy N. & Friedman, Daniel & Wagener, Florian, 2005. "The dynamics of price dispersion, or Edgeworth variations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 801-822, April.
    5. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2004. "Noisy Directional Learning and the Logit Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 581-602, October.
    6. Cheung, Man-Wah, 2016. "Imitative dynamics for games with continuous strategy space," Games and Economic Behavior, Elsevier, vol. 99(C), pages 206-223.
    7. repec:bla:jindec:v:49:y:2001:i:4:p:541-58 is not listed on IDEAS
    8. Jean Paul Rabanal, 2017. "On the Evolution of Continuous Types Under Replicator and Gradient Dynamics: Two Examples," Dynamic Games and Applications, Springer, vol. 7(1), pages 76-92, March.
    9. Friedman, Daniel & Ostrov, Daniel N., 2013. "Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 743-777.
    10. Chakrabarti, Anindya S. & Lahkar, Ratul, 2017. "Productivity dispersion and output fluctuations: An evolutionary model," Journal of Economic Behavior & Organization, Elsevier, vol. 137(C), pages 339-360.
    11. Glenn Ellison & Sara Fisher Ellison, 2009. "Search, Obfuscation, and Price Elasticities on the Internet," Econometrica, Econometric Society, vol. 77(2), pages 427-452, March.
    12. Fernando Louge & Frank Riedel, 2012. "Evolutionary Stability in First Price Auctions," Dynamic Games and Applications, Springer, vol. 2(1), pages 110-128, March.
    13. Liran Einav & Theresa Kuchler & Jonathan Levin & Neel Sundaresan, 2015. "Assessing Sale Strategies in Online Markets Using Matched Listings," American Economic Journal: Microeconomics, American Economic Association, vol. 7(2), pages 215-247, May.
    14. Friedman, Daniel & Ostrov, Daniel N., 2010. "Gradient dynamics in population games: Some basic results," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 691-707, September.
    15. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
    16. Lahkar, Ratul & Riedel, Frank, 2015. "The logit dynamic for games with continuous strategy sets," Games and Economic Behavior, Elsevier, vol. 91(C), pages 268-282.
    17. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    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. Ma, Junhai & Si, Fengshan & Zhang, Qin & Wang, Zongxian, 2024. "Impact of extended warranty service on product pricing in online direct retailers' competitive market," Energy Economics, Elsevier, vol. 129(C).

    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. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    3. Glenn Ellison & Sara Fisher Ellison, 2005. "Lessons About Markets from the Internet," Journal of Economic Perspectives, American Economic Association, vol. 19(2), pages 139-158, Spring.
    4. Chakrabarti, Anindya S. & Lahkar, Ratul, 2017. "Productivity dispersion and output fluctuations: An evolutionary model," Journal of Economic Behavior & Organization, Elsevier, vol. 137(C), pages 339-360.
    5. Lahkar, Ratul & Riedel, Frank, 2016. "The Continuous Logit Dynamic and Price Dispersion," Center for Mathematical Economics Working Papers 521, Center for Mathematical Economics, Bielefeld University.
    6. Robert Jump, 2016. "Evolutionary learning and the stability of wage posting equilibria," Journal of Evolutionary Economics, Springer, vol. 26(5), pages 1117-1135, December.
    7. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    8. Michael R. Baye & John Morgan & Patrick Scholten, 2004. "Price Dispersion In The Small And In The Large: Evidence From An Internet Price Comparison Site," Journal of Industrial Economics, Wiley Blackwell, vol. 52(4), pages 463-496, December.
    9. Hämäläinen, Saara, 2018. "Competitive search obfuscation," Journal of Economic Dynamics and Control, Elsevier, vol. 97(C), pages 38-63.
    10. Kováč, Eugen & Schmidt, Robert C., 2014. "Market share dynamics in a duopoly model with word-of-mouth communication," Games and Economic Behavior, Elsevier, vol. 83(C), pages 178-206.
    11. Böheim, René & Hackl, Franz & Hölzl-Leitner, Michael, 2021. "The impact of price adjustment costs on price dispersion in e-commerce," International Journal of Industrial Organization, Elsevier, vol. 77(C).
    12. Stühmeier Torben, 2015. "Price Disclosure Rules and Consumer Price Comparison," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 15(2), pages 815-835, April.
    13. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2021. "An Experimental Investigation of Price Dispersion and Cycles," Journal of Political Economy, University of Chicago Press, vol. 129(3), pages 789-841.
    14. Jean Paul Rabanal, 2017. "On the Evolution of Continuous Types Under Replicator and Gradient Dynamics: Two Examples," Dynamic Games and Applications, Springer, vol. 7(1), pages 76-92, March.
    15. Anirban Sengupta & Steven Wiggins, 2006. "Airline Pricing, Price Dispersion and Ticket Characteristics On and Off the Internet," Working Papers 06-07, NET Institute, revised Oct 2006.
    16. Haynes, Michelle & Thompson, Steve, 2008. "Price, price dispersion and number of sellers at a low entry cost shopbot," International Journal of Industrial Organization, Elsevier, vol. 26(2), pages 459-472, March.
    17. Kenneth Gillingham, Hao Deng, Ryan Wiser, Naim Darghouth, Gregory Nemet, Galen Barbose, Varun Rai, and Changgui Dong, 2016. "Deconstructing Solar Photovoltaic Pricing," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    18. Franz Hackl & Michael Hölzl‐Leitner & Rudolf Winter‐Ebmer & Christine Zulehner, 2021. "Successful retailer strategies in price comparison platforms," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(5), pages 1284-1305, July.
    19. Michael A. Arnold & Christine Saliba, 2003. "Price Dispersion in Online Markets: The Case of College Textbooks," Working Papers 03-02, University of Delaware, Department of Economics.
    20. Liran Einav & Theresa Kuchler & Jonathan Levin & Neel Sundaresan, 2015. "Assessing Sale Strategies in Online Markets Using Matched Listings," American Economic Journal: Microeconomics, American Economic Association, vol. 7(2), pages 215-247, May.

    More about this item

    Keywords

    Population games; Evolutionary dynamics; Gradient dynamics; Price dispersion;
    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
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

    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:eee:dyncon:v:84:y:2017:i:c:p:32-42. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.