A Note on Bertrand and Cournot Competition in a Vertically Related Duopoly

Abstract

We revisit the classic discussion on the endogenous choice of a price or a quantity contract in a vertically related duopoly with a monopolistic upstream firm. We show, from the perspective of the upstream firm, choosing the price contract is a dominant strategy regardless of the nature of goods. We also show, from the perspective of the downstream firms, that the ranking of profits between Cournot and Bertrand competition in Singh and Vives (1984) is reversed. Thus, in equilibrium, downstream firms face a prisoners’ dilemma regardless of the nature of goods.