In ternary complex formation, cooperativity (of the ligand) is an asymmetric quantity describing how binding of a ligand to a first protein facilitates binding of a second protein. In addition to the binary ligand-protein binding affinities, cooperativity stands out as the third factor determining the efficiency of ternary complexation by the three partners. While high ligand-protein binding affinities can lead to an unwanted hook effect, cooperativity monotonically increases ternary complex formation. Increasing cooperativity at the cost of binary binding affinity can lead to an equally high fraction of ternary complex formation while alleviating the hook effect. To provide a physical interpretation of cooperativity, we introduced cooperative free energy, which is the sum of the protein-protein binding free energy and all non-pairwise additive effects during a three-body complex-forming process.