This paper studies Cournot competition with two generators who share one transmission line with a limited capacity to supply price-taking consumers. In such a game the network operator needs a rule to allocate transmission capacity. Three rules are studied: all-or-nothing, proportional, and efficient rationing. The first result is that if the network operator taxes the whole congestion rent, the generators strategically change their production quantities, such that the network operator obtains no congestion rent. This gives poor incentives for investment in transmission capacity. The second result is that the network operator can create competition among the generators, which can increase welfare. Marginal nodal congestion pricing, which is optimal under perfect competition, is sub-optimal when generators can set their production quantities freely. It does not generate revenue for the network operator, nor does it increase competition among the generators.