Efficiency Loss in Cournot Games

We consider Cournot models of competition, where market participants choose the quantities they demand or supply. We study the loss of aggregate surplus due to the exercise of market power in Cournot competition, for both oligopsony and oligopoly models. We observe that efficiency loss is generally arbitrarily high in Cournot games, but also prove bounds on efficiency loss in several cases of interest. In particular, we show that if multiple consumers with concave utility functions face an affine market supply curve, or if multiple producers with convex cost functions face an affine market demand curve, the aggregate surplus at a Nash equilibrium of the Cournot game is at least 2/3 of the maximal aggregate surplus; i.e., the efficiency loss is again no more than 33%. We also show that if a monopsonist with concave utility faces a convex market supply curve, or a monopolist with convex cost faces a concave market demand curve, the efficiency loss is again no more than 33%.