This article investigates 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 show that, instead of unconditional full-transshipment for the case of non-competing retailers, 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 find that transshipment dampens (respectively, intensifies) the inventory competition when the transshipment price is viable and below (respectively, above) a threshold. In addition to its inventory pooling effect, transshipment under competition also has a competition effect which is positive when transshipment dampens inventory competition but not too strongly. The option of bilateral transshipment leads to a Pareto improvement for competing retailers, when the competition effect is positive; but even when it is negative, Pareto improvement is still achievable 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.