Can boundedly rational sellers learn to play Nash?

Roger Waldeck (1, 2) , Eric Darmon

1 LEGO - Laboratoire d'Economie et de Gestion de l'Ouest
2 IMT Atlantique - LUSSI - Département Logique des Usages, Sciences sociales et Sciences de l'Information

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.

Mots clés: Imperfect information; Price competition; Price dispersion; Search market equilibrium; Reinforcement learning; Numerical computation

Domaines: Sciences de l'Homme et Société; Économie et finance quantitative [q-fin]

Roger Waldeck, Eric Darmon. Can boundedly rational sellers learn to play Nash?. Journal of Economic Interaction and Coordination, 2006, 1 (2), pp.147-169. ⟨hal-02312212⟩