Efficiency Loss in a Cournot Oligopoly with Convex Market Demand

We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function. Our results provide nontrivial quantitative bounds on the loss of social welfare and aggregate profit for several convex inverse demand functions that appear in the economics literature.

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