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.
Existence and optimality of Cournot–Nash equilibria in a bilateral oligopoly with atoms and an atomless part
Busetto F.;Codognato G.;Tonin S.
2020-01-01
Abstract
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.File in questo prodotto:
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