Efficiency loss in a Cournot oligopoly with convex market demand
Author(s)Tsitsiklis, John N.; Xu, Yunjian
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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, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature. © 2014 Elsevier B.V.
DepartmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systems
Journal of Mathematical Economics
Tsitsiklis, John N. and Yunjian Xu. "Efficiency loss in a Cournot oligopoly with convex market demand." Journal of Mathematical Economics 53 (August 2014): 46-58 © 2014 Elsevier B.V.