The competitive newsboy

We consider a competitive version of the classical newsboy problem – in which a firm must choose an inventory or production level for a perishable good with random demand, and the optimal solution is a fraction of the demand distribution. A splitting rule specifies how initial industry demand is allocated among competing firms and how any excess demand is allocated among firms with remaining inventory. We examine the relation between equilibrium inventory levels and the splitting rule and provide conditions under which there is a unique equilibrium. Our most general result is that if all excess demand is reallocated, i.e., there is perfect substitutability, then competition never leads to a decrease in industry inventory.