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The dynamic instability of dispersed price equilibria

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  • Ratul, Lahkar
Abstract
We adopt an evolutionary framework to explain price dispersion as a time varying phenomenon. By developing a finite strategy analogue of the Burdett and Judd (1983) price dispersion model, we show that all dispersed price equilibria are unstable under the class of perturbed best response dynamics. Instead, numerical simulations using the logit dynamic show that price dispersion manifests itself as a limit cycle. We verify that limit cycles persist even when the finite strategy model approaches the original continuous strategy model. For a particularly simple case of the model, we prove the existence of a limit cycle.

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  • Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    • Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:1796-1827
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    3. Benndorf, Volker & Martínez-Martínez, Ismael & Normann, Hans-Theo, 2021. "Games with coupled populations: An experiment in continuous time," Journal of Economic Theory, Elsevier, vol. 195(C).
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    6. 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.
    7. 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.
    8. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    9. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Álvarez, Francisco & Rey, José-Manuel, 2019. "(Quasi) uniqueness and restoring dynamics of price-dispersion market equilibria under search cost," Journal of Mathematical Economics, Elsevier, vol. 81(C), pages 1-13.
    11. 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.
    12. Robert Jump, 2016. "Evolutionary learning and the stability of wage posting equilibria," Journal of Evolutionary Economics, Springer, vol. 26(5), pages 1117-1135, December.

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