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Can boundedly rational sellers learn to play Nash?

Author

Listed:
  • Roger Waldeck

    (LEGO - Laboratoire d'Economie et de Gestion de l'Ouest - UBS - Université de Bretagne Sud - UBO - Université de Brest - IMT - Institut Mines-Télécom [Paris] - IBSHS - Institut Brestois des Sciences de l'Homme et de la Société - UBO - Université de Brest - UBL - Université Bretagne Loire - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris], IMT Atlantique - LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris])

  • Eric Darmon

Abstract

How does Nash pricing compare to pricing with adaptive sellers using reinforcement learning (RL)? We consider a market game similar to Varian's model (Am Econ Rev 70:651–659, 1980) with two types of consumers differing by the size of their fixed sample search rule and derive the Nash search equilibrium (NSE) strategy (the density, the mean and the variance of the posted price distribution). Our findings are twofold. First, we find that the RL price distribution does not converge in a statistical sense to the NSE one except when competition is à la Bertrand. Second, we show that the qualitative properties of the NSE with respect to a change in buyers‘ search behavior are still valid for the RL distribution. The average price and the variance of both price distributions exhibit similar variations to a change in buyers' search.

Suggested Citation

  • Roger Waldeck & Eric Darmon, 2006. "Can boundedly rational sellers learn to play Nash?," Post-Print hal-02312212, HAL.
    • Handle: RePEc:hal:journl:hal-02312212
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    Cited by:

    1. Waldeck, Roger, 2008. "Search and price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 347-357, May.
    2. Roger Waldeck, 2008. "Search and price competition," Post-Print hal-02161480, HAL.
    3. 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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