Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities: A limit theorem

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. In the original spirit of Cournot (1838), we partially replicate the mixed exchange economy by increasing the number of atoms, without affecting the atomless part, and ensuring that the measure space of agents remains finite. 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 Walras 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 endogenous price-taking behavior.