Earlier studies for mixed markets have established a series of socalled irrelevance results. While previous results relate to the attainment of the firstbestallocation for welfare, we provide a new irrelevance result in terms of the choice of strategic variable in the product market. We show that regardless of whether a public or private firm is the market leader, the leader always chooses the price contract whereas the follower is indifferent between the price contract and the quantity contract. The identity of the leader and the follower firm is therefore irrelevant for the equilibrium mode of competition. Implications for economic models in mixed market settings emerge, which arealso discussed.