Effects of asymmetric knowledge spillovers on the stability of horizontal and vertical R&D cooperation

Abstract

In order to investigate the role of asymmetric spillovers in the stability of R&D cooperation, this paper distinguishes two different types of cooperative partners, and uses a game theory approach to reveal the relationship between asymmetric spillovers and R&D investment in the horizontally and vertically related R&D cooperation. In the horizontal R&D cooperation, higher incoming spillovers and lower outgoing spillovers induce firms to invest on R&D efforts as agreed. However, it is the contradiction between horizontal firms’ attitudes towards asymmetric spillovers that leads to the inherent instability of the cooperation. In the vertical R&D cooperation, our results question the usually held opinion about the effects of asymmetric spillovers on the decision of R&D investment. The incoming spillovers are less important in the innovation process for vertically related R&D cooperation. A firm tends to under-invest on the arranged level of R&D efforts when its incoming spillovers increase. Our results also show that efficient mechanisms to restrain firms’ non-cooperative behavior are essential to improve the stability of horizontal and vertical R&D cooperation.

Appendix

1. Numerical experiments of Firm B’s net expected payoffs with the variation of influencing factors in the horizontal R&D cooperation.

As shown in Fig. 10, Firm B’s higher level of incoming spillovers increases its net expected payoff gained from the cooperation, and a higher level of outgoing spillovers decreases its net expected payoff. The variation of outgoing spillovers has a greater significance on the net expected payoff.

Fig. 10

Net expected payoffs of Firm B under different levels of asymmetric spillovers in the horizontal R&D cooperation

From Fig. 11 we learn that the changing values of $n$ do not alter the curvilinear trends. But when the value of $n$ grows up, Firm B’s net expected payoff declines in the mass. The negative relationship is clearly shown in Fig. 12. Meanwhile, the slopes of the curves both decrease when the value of $n$ grows up. The impacts of asymmetric spillovers on the firms’ willingness to cooperate weaken as the R&D efforts of non-cooperative behavior grow up. We also verify that the changing values of $m$ and $p$ do not alter the positive or negative curvilinear trend between the net expected payoff and asymmetric spillovers. The effects of the variation of $m$ and $p$ on the net expected payoff are not significant. Their mediating effects on the relationship between asymmetric spillovers and the willingness to cooperate are also less significant.

Fig. 11

Relationship between Firm B’s net expected payoffs and asymmetric spillovers under different values of $n$ in the horizontal R&D cooperation

Fig. 12

Net expected payoffs of Firm B under different values of $n$ in the horizontal R&D cooperation

2. Numerical experiments of Firm B’s net expected payoffs with the variation of influencing factors in the vertical R&D cooperation.

As shown in Fig. 13, Firm B’s increasing levels of incoming spillovers and outgoing spillovers decrease its net expected payoff. The impact of outgoing spillovers on the net expected payoff is more significant than that of incoming spillovers.

Fig. 13

Net expected payoffs of Firm B under different levels of asymmetric spillovers in the vertical R&D cooperation

In the following, sensitivity analyses are presented to strengthen the above findings. From Fig. 14 we learn that the changing values of $n$ do not alter the negative curvilinear trends. Firm B’s net expected payoff first declines then increases with the value of $n$ growing up as shown in Fig. 15. It is notable that the changing trend could not be inferred from Fig. 14 because of the numerical value of $n$.

Fig. 14

Relationship between Firm B’s net expected payoffs and asymmetric spillovers under different values of $n$ in the vertical R&D cooperation

Fig. 15

Net expected payoffs of Firm B under different values of $n$ in the vertical R&D cooperation

In the vertically related R&D cooperation, the impact of the value of $m$ on the net expected payoff also does not affect the negative curvilinear trends, as shown in Fig. 16. As the value of $m$ grows up, the net expected payoff improves to some extent. In Fig. 17, the variation of $p$ also does not change the negative curvilinear trends, and its impact on the net expected payoff is less significant than that of $m$ and $n$.

Fig. 16

Relationship between Firm B’s net expected payoffs and asymmetric spillovers under different values of $m$ in the vertical R&D cooperation

Fig. 17

Relationship between Firm B’s net expected payoffs and asymmetric spillovers under different values of p in the vertical R&D cooperation