Dynamically stable corporate joint ventures

doi:10.1016/j.automatica.2005.10.010

Automatica

Volume 42, Issue 3, March 2006, Pages 365-370

https://doi.org/10.1016/j.automatica.2005.10.010 Get rights and content

Abstract

As markets continue to become global and firms become more international, corporate joint ventures provide firms with opportunities to rapidly create economies of scale and learn new skills and technologies that would be very difficult for them to obtain on their own. However, it is often observed that after a certain time of cooperation, some firms may gain sufficient skills and technology that they would do better by breaking up from the joint venture. This is the well-known problem of time inconsistency. In this paper, we consider a dynamic joint venture which adopts the shapley value as its profit allocation scheme. A compensation mechanism distributing payments to participating firms at each instant of time is devised to ensure the realization of the shapley value imputation throughout the venture duration. Hence time-consistency is attained, and a dynamically stable joint venture results. Extension of the analysis to a stochastic environment is also made. It is the first time that stable joint venture is analyzed both deterministically and stochastically in a dynamic environment.

Introduction

As markets become increasingly globalized and firms become more multinational, corporate joint ventures are likely to yield opportunities to quickly create economies of scale and critical mass, incorporate new skills and technology, and facilitate rational resource sharing (see Bleeke & Ernst, 1993). With joint ventures becoming a powerful force shaping global corporate strategy, partnerships between firms have significantly increased. Despite their purported benefits, however, joint ventures are highly unstable and have a consistently high rate of failure (Blodgett, 1992, Parkhe, 1993). In addition, other adverse effects, such as uncompensated transfers of technology, operational difficulties, disagreements and anxiety over the loss of proprietary information have been found (Hamel et al., 1989; Gomes-Casseres, 1987). D’Aspremont and Jacquemin (1988), Kamien et al. (1992) and Suzumura (1992) have studied cooperative R&D with spillovers in joint ventures under a static framework. Cellini and Lambertini, 2002, Cellini and Lambertini, 2004 considered cooperative solutions to investment in product differentiation in a dynamic approach.

A fundamental premise is that joint ventures are formed primarily so that participating firms can readily gain core skills and technology which would be difficult for them to obtain on their own (Murray & Siehl, 1989). After a certain time of cooperation, some firms may gain sufficient managerial and technological expertise that they would do better by breaking away from the joint venture. Thus a major source of instability is the lack of dynamical stable or time consistent cooperative solutions to the joint venture. Time consistency is a fundamental element in dynamic cooperation, and it ensures that: (i) the extension of the solution policy to a later starting time and a state brought about by prior optimal behavior of the players would remain optimal, and (ii) all participating firms do not have incentive to deviate from the initial plan (see Yeung and Petrosyan, 2004, Yeung and Petrosyan, 2005). The absence of a formal mechanism to time-consistent cooperative solutions has precluded rigorous analysis of the problem of corporate joint ventures. Petrosyan and Zaccour (2003) provided a time-consistent solution to a class of differential games involving pollution cost reduction.

In this paper, we consider a joint venture which adopts the shapley value (1953) as its profit allocation scheme. Since joint venture is a continual arrangement, a dynamic specification of the shapley value is provided. To fulfill time consistency, the shapley value imputation has to hold throughout the venture duration. A compensation mechanism distributing payments to participating firms at each instant of time ensuring the realization of the shapley value imputation within the venture duration is devised.

Section snippets

A dynamic model of joint venture

In this section, we present a framework of a dynamic joint venture in which there are n firms. The venture horizon is $[t_{0}, T]$ . The state dynamics of the ith firm is characterized by the set of vector-valued differential equations: ${\dot{x}}_{i} (s) = f_{i}^{i} [s, x_{i} (s), u_{i} (s)],$ $x_{i} (t_{0}) = x_{i}^{0}, for i \in [1, 2, \dots, n] \equiv N,$ where $x_{i} (s) \in X_{i} \subset R^{m_{i} +}$ denotes the state variables of player i, $u_{i} \in U_{i} \subset R^{l_{i} +}$ is the control vector of firm i. The state of firm i include its capital stock, level of technology, special skills and productive resources.

Dynamical imputation

Consider a joint venture involving n firms. The member firms would maximize their joint profit and share their cooperative profits according to the shapley value (1953). The problem of profit sharing is inescapable in virtually every joint venture. The shapley value is one of the most commonly used sharing mechanism in static cooperation games with transferable payoffs. Besides being individually rational and group rational, the shapley value is also unique. Specifically, the shapley value

Transitory compensation

In this section, a profit distribution mechanism will be developed to compensate transitory changes so that the shapley value principle could be maintained throughout the venture horizon. First, an imputation distribution procedure (similar to those in Petrosyan & Zaccour, 2003; Yeung & Petrosyan, 2004) must be now formulated so that the imputation scheme in Condition 3 can be realized. Let the $B_{i}^{τ} (s)$ denote the payment received by firm $i \in N$ at time $τ \in [t_{0}, T]$ dictated by $v^{(τ)} (τ, x_{N}^{τ *})$ . In

Stochastic extension

The above analysis can be extended to the case where there are stochastic elements in the system. Consider the situation where the state dynamics of the ith firm is characterized by the set of vector-valued differential equations: $d x_{i} (s) = f_{i} [s, x_{i} (s), u_{i} (s)] d s + σ_{i} [s, x_{i} (s)] d z_{i} (s), x_{i} (t_{0}) = x_{i}^{0} for i \in N,$ where $σ_{i} [s, x_{i} (s)]$ is a $m_{i} \times k_{i}$ matrix and $z_{i} (s)$ is a $k_{i}$ -dimensional Wiener process and $z_{i} (s)$ and $z_{j} (s)$ are independent for $i \neq j$ . The stochastic nature of (18) reflects the uncertainty in the evolution of the

Concluding remarks

Despite all their purported benefits, however, joint ventures are highly unstable because of the lack of dynamical stable profit sharing schemes. In this paper, we consider a dynamic joint venture which adopts the shapley value as its profit allocation scheme. A compensation mechanism distributing payments to participating firms at each instant of time is devised to ensure the realization of the shapley value imputation throughout the venture duration. Hence time-consistency will be attained,

Acknowledgments

Invaluable suggestions from three anonymous referees and financial support from the Research Grant Council of Hong Kong (Grant HKBU2103/04H and Grant FRG/04-05/II-03) are gratefully acknowledged.

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David Yeung obtained his Ph.D. in economics from York University, studied D.Sc. program in applied mathematics at St. Petersburg State University, and was awarded the degree of Dr. h.c. for his contributions in differential game theory. He is the managing editor of the International Game Theory Review. His main research areas are differential games and control theory. His pioneering contributions in game theory include differential games with uncertain types and number of future players, the first stochastic differential game in financial speculation, the concept of subgame consistent and its solution techniques. He is currently Professor of Decision Sciences at Hong Kong Baptist University, Kantorovich Research Chair in Stochastic Differential Games and Co-director of the Centre for Game Theory at St. Petersburg State University, Distinguished Guest Professor of Qingdao University and Honorary Professor of the University of Hong Kong.

Leon Petrosyan obtained his Ph.D. and D.Sc. in mathematics from St. Petersburg State University. He is editor of the International Game Theory Review and Game Theory & Applications. His main research areas are cooperative differential games and control theory. His pioneering work in game theory include time-consistency solutions in cooperative differential games and subgame consistent solutions in cooperative stochastic differential games. He has published nine books and over one hundred and fifty papers, including the first ever book (co-authored with D. Yeung) on cooperative stochastic differential games. He is currently Dean of Applied Mathematics-Control Processes, Director of Center of Game Theory and Kantorovich Research Chair in Cooperative Dynamic Games at St. Petersburg State University.

^☆: This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Editor $BercRustum$ .

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Dynamically stable corporate joint ventures☆

Abstract

Introduction

Section snippets

A dynamic model of joint venture

Dynamical imputation

Transitory compensation

Stochastic extension

Concluding remarks

Acknowledgments

Journal of Economic Dynamics and Control

Collaborating to compete

Factors in the instability of international joint ventures: An event history analysis

Strategic Management Journal

Private and social incentives towards investment in product differentiation

International Game Theory Review

Cooperative and noncooperative R&D in duopoly with spillovers

The American Economic Review

Joint venture instabilityIs it a problem?

Columbia Journal of World Business

Collaborate with your competitors and win

Harvard Business Review