We study two electricity markets connected by a fixed amount of crossborder capacity. The total amount of capacity is known to all electricity traders and allocated via an auction. The capacity allocated to each bidder in the auction remains private information. We assume that traders are faced with a demand function reflecting the relationship between electricity transmitted between the markets and the spot price difference. Therefore, traders act like Bayesian-Cournot oligopolists in exercising their transmission rights when presented with incomplete information about the competitors’ capacities. Our analysis breaks down the welfare effect into three different components: Cournot behavior, capacity constraints, and incomplete information. We find that social welfare increases with the level of information with which traders are endowed.