During the last decades the production of electrical energy has been liberalized. This paper studies the effect of using a market mechanism to allocate scarce transmission capacity when the incumbent producers remain dominant. We show that granting exclusive use to an incumbent producer is preferred to trading access to this essential facility if interregional production-cost differences are significant and transmission capacity is scarce. This result counters the intuition on third degree price-discrimination, that arbitrage will improve the social surplus when there is no output contraction. The reason is that with arbitrage the incumbent can still charge different regional prices as long as it creates congestion on the transmission lines. As a consequence, welfare will be lower, since the incumbent distorts production decisions to congest the lines. We recommend that a market-oriented access to scarce transmission capacity should be accompanied by additional regulatory or structural measures to address market power.