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

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  • 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
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    References listed on IDEAS

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    1. Cheung, Man-Wah, 2016. "Imitative dynamics for games with continuous strategy space," Games and Economic Behavior, Elsevier, vol. 99(C), pages 206-223.
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    3. 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.
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    10. 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.
    11. 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.
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    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.
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    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

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