Bilateral Oligopoly with a Competitive Fringe

In this paper we consider a bilateral oligopoly on whose fringe there is a market comprising price taking buyers. The sellers in both markets are the same. The sellers and the buyers in the bilateral oligopoly behave strategically as in a Shapley-Shubik market game. We define the concept of an exact active equilibria and show that if the economy is replicated giving rise to a convergent sequence of (type) symmetric exact active equilibria (i.e. exact active equilibria where all replica of an agent in the original economy choose the same strategy) then the corresponding sequence of price-allocation pairs converge to a competitive equilibrium for the original economy. In a final section we discuss an example of an economy where all buyers have Cobb-Douglas utility functions and show that the concepts introduced in this paper (as also the convergence result) are non-vacuous.