Existence and optimality of Cournot-Nash equilibria in a bilateral oligopoly with atoms and an atomless part

Francesca Busetto (1) , Giulio Codognato (1, 2) , Sayantan Ghosal (3) , Ludovic A. Julien (2) , Simone Tonin (1)

1 Università degli Studi di Udine - University of Udine [Italie]
2 EconomiX - EconomiX
3 Adam Smith Business School

We consider a bilateral oligopoly version of the Shapley window model with large traders, represented as atoms, and small traders, represented by an atomless part. For this model, we provide a general existence proof of a Cournot-Nash equilibrium that allows one of the two commodities to be held only by atoms. Then, we show, using a corollary proved by Shitovitz (Econometrica 41:467-501, 1973), that a Cournot-Nash allocation is Pareto optimal if and only if it is a Walras allocation.

Domaines: Economies et finances

Francesca Busetto, Giulio Codognato, Sayantan Ghosal, Ludovic A. Julien, Simone Tonin. Existence and optimality of Cournot-Nash equilibria in a bilateral oligopoly with atoms and an atomless part. International Journal of Game Theory, 2020, 49 (4), pp.933-951. ⟨10.1007/s00182-020-00719-z⟩. ⟨hal-02531404⟩