Exact equilibrium quantities in spatially separated markets under production constraints

Abstract

We deal with the Cournot game with production constraints, where the competing firms deliver an homogeneous product to spatially separated markets, linear demand functions may be different at each market, and linear production costs are non-identical. Despite the simplicity of this setting and although the existence and uniqueness of a Nash equilibrium have been proved, the problem of finding the exact equilibrium quantities has not been solved in the literature yet. In this paper, we analytically determine the unique equilibrium quantities for the constrained game when some conditions are verified. The equilibrium quantities and profits are compared with those obtained for the traditional Cournot game.