Simone Tonin

Atomic Cournotian traders may be Walrasian

In a bilateral oligopoly, with large traders, represented as atoms, and small traders, represented by an atomless part, when is there a nonempty intersection between the sets of Walras and Cournot–Nash allocations? Using a two-commodity version of the Shapley window model, we show that a necessary and sufficient condition for a Cournot–Nash allocation to be a Walras allocation is that all atoms demand a null amount of one of the two commodities. We provide four examples which show that this characterization holds non-vacuously. When our condition fails to hold, we also confirm, through some examples, the result obtained by Okuno et al. (1980): small traders always have a negligible influence on prices, while the large traders keep their strategic power even when their behavior turns out to be Walrasian in the cooperative framework considered by Gabszewicz and Mertens (1971) and Shitovitz (1973).

Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities.

We show the existence of a Cournot–Nash equilibrium for a mixed version of the Shapley window model, where large traders are represented as atoms and small traders are represented by an atomless part. Previous existence theorems for the Shapley window model, provided by Sahi and Yao (1989) in the case of economies with a finite number of traders and by Busetto et al. (2011) in the case of mixed exchange economies, are essentially based on the assumption that there are at least two atoms with strictly positive endowments and indifference curves contained in the strict interior of the commodity space. Our result does not require this restriction. It relies on the characteristics of the atomless part of the economy and exploits the fact that traders belonging to the atomless part have an endogenous “Walrasian” behavior.

Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

In the line opened by Kalai and Muller (1977), we explore new con- ditions on preference domains which make it possible to avoid Arrows impossibility result. In our main theorem, we provide a complete char- acterization of the domains admitting nondictatorial Arrovian social welfare functions with ties (i.e. including indi erence in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach rst applied to so- cial choice theory by Sethuraman, Teo and Vohra ((2003), (2006)). In order to obtain a representation of Arrovian social welfare functions whose range can include indi erence, we generalize Sethuraman et al.s work and specify integer programs in which variables are allowed to assume values in the set indeed, we show that there exists a one-to-one correspondence between the solutions of an integer program de ned on this set and the set of all Arrovian social welfare functions - without restrictions on the range

Noncooperative oligopoly in economies with infinitely many commodities and traders

In this paper, we extend the noncooperative analysis of multilateral oligopoly to exchange economies with infinitely many commodities and trader types where exchange is modelled using a strategic market game with commodity money and trading posts. We prove the existence of an “active” Cournot-Nash equilibrium and its convergence to a Walras equilibrium when the economy is replicated.