Strategic Capacity Planning Problems in Revenue‐Sharing Joint Ventures

We study strategic capacity investment problems in joint ventures (JVs) with fixed‐rate revenue‐sharing contracts. We adopt a game‐theoretical approach to study two types of JVs depending on how individual resources determine the effective capacity of a JV. With complementary resources, the effective capacity of a JV is constrained by the most scarce resource. We show that multiple Nash equilibria could exist. Nevertheless, there exists a unique Strong Nash equilibrium. We show that there is an efficient and fair fixed‐rate revenue‐sharing contract which induces the system optimal outcome in the Strong Nash equilibrium. On the other hand, with substitutable a resource, the effective capacity of a JV is measured by aggregating individual contributions. We show that there does not exist a fixed‐rate revenue‐sharing contract that induces the system optimum. We quantify that the efficiency of a JV which decreases with the number of participants, the cost asymmetry and the cost margin of the JV. We propose provably‐good fixed‐rate revenue‐sharing contracts with performance guarantees. We also propose a simple modified contract to achieve the channel coordination. Finally, we fit our model with historical data to shed some insights on two JV examples in the motion picture industry.