Strategic Capacity Planning Problems in Revenue-Sharing Joint Ventures

Abstract

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.