Consider a supply chain with one supplier and multiple retailers. The supplier produces a single product and sells it to the retailers, who in turn sell the product to consumers. The supplier has limited production capacity, and the retailers are engaged in a Cournot competition at the consumer/market level. When the sum of the retailer orders exceeds the capacity, the supplier allocates her capacity according to a pre-announced allocation mechanism. Two mechanisms are considered: proportional allocation and lexicographic allocation. An extensive study of the two allocation mechanisms shows that the lexicographic mechanism has the ability to dampen the competition at the retail level, increasing the profits for both the supplier and the supply chain.