The paper focuses on markets in which firms with different ownership structures compete with each other in a one-period Nash-Cournot setting. In particular the market outcome of a duopoly of one marketing cooperative and one private wholesaler (cooperative mixed duopoly) is compared to the outcomes of a public firm mixed duopoly and a pure private duopoly. None of these market arrangements are found to produce the first-best efficient outcome. However, both mixed markets improve efficiency compared to the private solution, and the overall welfare effects of the public firm mixed duopoly are superior to the cooperative mixed market. Finally, the distribution of surplus between the different producer groups and the different wholesaler firms is discussed.