“…In our model, there are two forces that influence incentive contracts: (i) the downstream firms' input prices in mutual outsourcing and (ii) the supplier's input price. In the fourth stage, when the decision-8 Several papers also show asymmetric managerial structures in different contexts (Vroom, 2006;Mujumdar and Pal, 2007;Löffler, 2008, 2012;Pan et al, 2020). We explain the difference between those papers and ours in Section 2.…”