Efficiency Loss in Cournot Oligopoly with Convex Market Demand

Abstract:

We consider a Cournot oligopoly 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 market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria, which depends only on a one-dimensional parameter extracted from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium, to the slope of the line which connects the Cournot equilibrium and the social optimum. Our results provide nontrivial quantitative efficiency bounds for many convex inverse demand functions that have been widely used in the economics literature.

Biography:

Yunjian Xu is a third year PhD student at LIDS, under the supervision of Prof. Tsitsiklis. His research interests lie in the efficiency (Price of Anarchy) analysis for static and dynamic resource allocation games.