On the Relationship Between Quantity Precommitment and Cournot Games

Supply-then-price competition is common in settings in which capacity commitments precede pricing decisions. We provide a characterization of when and why equilibria of such games clear the market at the Cournot outcomes. The paper extends the seminal work of Kreps and Scheinkman (1983) to differentiated product settings with an arbitrary number of firms and general demand and spill functions. We identify two new fundamental properties that drive the result: independence from irrelevant supply and spill inertia. These properties are satisfied by common demand and spill models. Our result provides a shortcut approach to analyzing supply-then-price games and highlights the importance of demand specification, compared with spill specification, in determining the outcome of such games.