We investigate whether and how competing retailers should transship to each other in overlapping markets where customers encountering stock-out at one retailer may switch to another. A two-stage game model is used to examine the inventory and end-of-season transshipment decisions. We find that the stage-2 optimal transshipment policy consists of no transshipment, partial transshipment, and full transshipment, determined by the interplay of switching probability, transshipment price, and remaining inventory. We identify a sufficient condition under which a unique Nash equilibrium exists for the stage-1 inventory competition, and find that there exists a threshold such that transshipment dampens or intensifies the inventory competition when the transshipment price is below or above it. In addition to its (weakly) positive inventory pooling effect, transshipment under competition also has a competition effect which is positive when transshipment dampens inventory competition but not too strongly. The competing retailers always have an ex-ante incentive to transship when the competition effect is positive; but, even when the competition effect is negative, the retailers may still have an incentive to transship for a wider transshipment price range in which the combined pooling and competition effect is positive. We identify explicitly the necessary and sufficient conditions for the existence of a unique pair of coordinating transshipment prices and provide formulas to compute them. We also provide a complete solution for the ex-ante endogenous transshipment prices between symmetric retailers.
