Abstract: This paper contributes to the increasing literature on modelling R&D network formation among firms using game theory approach. What distinguishes this paper from existing ones is that it allows the firms to form or delete links with both their suppliers and their competitors simultaneously. In a benchmark model, we try to highlight the pair-wise stable networks among all the possible formations and to characterize the properties of the pair-wise stable networks. Moreover, we try to verify the impacts of R&D collaborations'spillover on the formation of pair-wise stable networks and the social welfares.
In a two-tier industry with one supplier S and two manufacturers M_i,(i=1,2), the four-step game proceeds as follows: at step 1, the supplier and the two manufacturers select their vertical and horizontal R&D links simultaneously. The R&D collaboration between the manufacturers and the supplier is called vertical links, and the one between two manufacturers is called horizontal link. At step 2, knowing the R&D network structure, the three firms (S, M₁, and M₂) choose the optimal R&D efforts to maximize their own profits. At step 3, the supplier S chooses to provide the quantity of inputs to two downstream manufacturers. At step 4, M₁ and M₂ compete in a Cournot market to choose the quantities of production simultaneously.
In this benchmark model, there are 8 possible networks and 6 of them have different results at equilibrium. Under each network structure, the model is solved by using backward induction. First, the quantity of each manufacturer at equilibrium is worked out. Then the optimal R&D efforts for the three firms is solved, and thereby their profits under each network are computed. Finally, pair-wise stable network under Goyal and Joshi's concept is verified.
The main finding is that the complete network is the unique pair-wise stable network if the R&D spillover rate between the two downstream competitors is not smaller than the one between the supplier and the manufactories. However, the unique pair-wise stable network may not always be the most efficient one from the social welfare point of view. Our results verify the empirical findings that R&D collaboration is ubiquitous in the industry and vertical collaboration is more prevalent than horizontal collaboration. Furthermore, a new perspective for further research on the R&D network of upstream and downstream firms is provided.

Key words: upstream and downstream firms, R&D networks, pair-wise stable network, social welfare