Strategic Capacity Planning Problems in Revenue Sharing Joint Ventures
40 Pages Posted: 24 Mar 2017 Last revised: 30 Jun 2019
Date Written: Feburary 12, 2018
We study strategic capacity investment problems in joint ventures (JVs) with fixed-rate revenue sharing contracts. We distinguish two types of JVs, depending on how individual resources determine the effective capacity of a JV. Despite its popularity across many industries, JVs tend to suffer from high failure rates and studies suggested misaligned incentives among JV participants as one of the leading causes. To investigate this phenomenon, we propose a game-theoretical approach that allows asymmetric players and nonlinear convex costs to model the strategic behavior of JV participants. 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. On the other hand, with substitutable resources, 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 also consider an extension with spillover effect which results from the knowledge and technology transfer among the JV participants. From a practical perspective, we show that for complementary resource sharing, there is an efficient and fair fixed-rate revenue sharing contract which induces the system optimal outcome in the Strong Nash equilibrium. With substitutable resources, we propose provably-good revenue sharing contracts with performance guarantees. Lastly, we also fit our model with historical data to shed some insights on two JV examples in the motion picture industry.
Keywords: capacity planning; joint venture; revenue sharing; game theory; efficiency; coordination
JEL Classification: C70
Suggested Citation: Suggested Citation