GIULIO CODOGNATO

Noncooperative Oligopoly in Markets with a Continuum of Traders and a Strongly Connected Set of Commodities: A Limit Theorem

Francesca Busetto, Giulio Codognato, Sayantan Ghosal, Ludovic A. Julien, Damiano Turchet

Abstract

We consider a mixed version of the Shapley window model, where large traders are represented as atoms and small traders are represented by an atomless part. Our main theorem shows that any sequence of Cournot-Nash allocations of the strategic market games associated with the partial replications of the exchange economy has a limit point for each trader and that the assignment determined by these limit points is a Walrasian allocation of the original economy. Instead of relying on restrictive assumptions on the characteristics of atoms, as in Busetto et al. (2017), our limit theorem relies on the characteristics of agents in the atomless part and their endogenously price-taking behavior.

Mot(s) clé(s)

Cournot-Nash equilibrium, Walras equilibrium, Asymptotic equivalence

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

Francesca Busetto, Giulio Codognato, Sayantan Ghosal, Ludovic A. Julien, Simone Tonin

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.

Mot(s) clé(s)

Shapley window model; Atoms; Atomless part; Cournot–Nash equilibrium; Optimality

Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem

Francesca Busetto, Giulio Codognato, Sayantan Ghosal

Abstract

In this paper, in an exchange economy with atoms and an atomless part, we analyze the relationship between the set of the Cournot-Nash 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, Cournot-Nash 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 Cournot-Nash equilibrium allocations of the strategic market game associated with the partially replicated exchange economies approximates a Walras equilibrium allocation of the original exchange economy.

Mot(s) clé(s)

Cournot-Nash equilibrium, strategic market games, limit theorem

Integer Programming and Nondictatorial Arrovian Social Welfare Functions

Francesca Busetto, Giulio Codognato, Simone Tonin

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 one-to-one 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.

Mot(s) clé(s)