201810 "Existence and Optimality of CournotNash Equilibria in a Bilateral Oligopoly with Atoms and an Atomless Part"
Francesca Busetto, Giulio Codognato, Sayantan Ghosal, Ludovic A. Julien, Simone Tonin
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 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 CournotNash 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 CournotNash allocation is Pareto optimal if and only if it is a Walras allocation.
 ClassificationJEL
 C72, D51
 Mot(s) clé(s)
 Shapley window model; Atoms; Atomless part; Cournot–Nash equilibrium; Optimality
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201249 "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem"
Francesca Busetto, Giulio Codognato, Sayantan Ghosal
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 Abstract
 In this paper, in an exchange economy with atoms and an atomless part, we analyze the relationship between the set of the CournotNash equilibrium allocations of a strategic market game and the set of the Walras equilibrium allocations of the exchange economy with which it is associated. In an example, we show that, even when atoms are countably infinite, CournotNash equilibria yield different allocations from the Walras equilibrium allocations of the underlying exchange economy. We partially replicate the exchange economy by increasing the number of atoms without affecting the atomless part while ensuring that the measure space of agents remains finite. We show that any sequence of CournotNash equilibrium allocations of the strategic market game associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.
 ClassificationJEL
 C72, D51
 Mot(s) clé(s)
 CournotNash equilibrium, strategic market games, limit theorem
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201236 "Integer Programming and Nondictatorial Arrovian Social Welfare Functions"
Francesca Busetto, Giulio Codognato, Simone Tonin
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 Abstract
 Following Sethuraman, Teo and Vohra ((2003), (2006)), we apply integer programming tools to the analysis of fundamental issues in social choice theory. We generalize Sethuraman et al.'s approach specifying integer programs in which variables are allowed to assume values in the set {0; 1/2 ; 1}. We show that there exists a onetoone correspondence between the solutions of an integer program defined on this set and the set of the Arrovian social welfare functions with ties (i.e. admitting indifference in the range). We use our generalized integer programs to analyze nondictatorial Arrovian social welfare functions, in the line opened by Kalai and Muller (1977). Our main theorem provides a complete characterization of the domains admitting non dictatorial Arrovian social welfare functions with ties by introducing a notion of strict decomposability.
 ClassificationJEL
 D71
 Mot(s) clé(s)
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