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Existence and Optimality of Cournot-Nash Equilibria in a Bilateral Oligopoly with Atoms and an Atomless Part

Francesca Busetto, Giulio Codognato, Sayantan Ghosal, Ludovic Julien and Simone Tonin

No 2018-10, EconomiX Working Papers from University of Paris Nanterre, EconomiX

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 (1973), that a Cournot-Nash allocation is Pareto optimal if and only if it is a Walras allocation.

Keywords: Shapley window model; Atoms; Atomless part; Cournot–Nash equilibrium; Optimality (search for similar items in EconPapers)
JEL-codes: C72 D51 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-com, nep-gth and nep-mic
Date: 2018
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