Strategic Capacity Planning Problems in Revenue Sharing Joint Ventures

40 Pages Posted: 24 Mar 2017 Last revised: 30 Jun 2019

See all articles by Retsef Levi

Retsef Levi

MIT Sloan School of Management - Operations Research Center

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Cong Shi

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering

Wei Sun

IBM Corporation - Thomas J. Watson Research Center

Date Written: Feburary 12, 2018

Abstract

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

Levi, Retsef and Perakis, Georgia and Shi, Cong and Sun, Wei, Strategic Capacity Planning Problems in Revenue Sharing Joint Ventures (Feburary 12, 2018). Available at SSRN: https://ssrn.com/abstract=2939664 or http://dx.doi.org/10.2139/ssrn.2939664

Retsef Levi

MIT Sloan School of Management - Operations Research Center ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-565
Cambridge, MA 02142
United States

Cong Shi (Contact Author)

University of Michigan at Ann Arbor - Department of Industrial and Operations Engineering ( email )

1205 Beal Avenue
Ann Arbor, MI 48109
United States

Wei Sun

IBM Corporation - Thomas J. Watson Research Center ( email )

Route 134
Kitchawan Road
Yorktown Heights, NY 10598
United States

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