Collaborative innovation among competitors in a supply chain with cross shareholding

Many firms have transferred from independent innovations to engage in collaborative innovations with competitors to boost the synergy effects. However, such innovation mechanisms may involve conflicts of interest problems due to the existence of a co-opetition relationship. The cross-shareholding that allows enterprises to share partial profits of competitors by holding a certain proportion of shares in each other's business, can be used to counterbalance multi-agents' strategic decisions and thus improve benefits allocations. Nevertheless, its role in the innovation field has rarely been explored. Motivated by this, we incorporate cross shareholding into a supply chain with one supplier and two manufacturers, and investigate the incentives of competing manufacturers to adopt cross-shareholding in investments of innovation. A benchmark model without innovation and two innovation models are considered, including independent innovation and collaborative innovation with cross shareholding. By comparing the different innovation models, we find that cross shareholding may weaken manufacturers' innovation levels when technology spillover is small. However, it exerts a positive effect on manufacturers' profits if a significant technology spillover and shareholding ratio are achieved or the technology spillover is within a low range. Also, with the joint consideration of investment in innovation and crossshareholding, manufacturers have motivations to adopt collaborative innovation under certain conditions. Besides, the horizontal innovation of competing manufacturers may benefit or harm the suppliers' profits through a vertical channel, which depends on the difficulty level of innovation and shareholding ratio. Finally, our main results remain robust when considering manufacturers' asymmetric production costs, shareholding ratios, production scales and innovation capabilities, as well as the linear demand function and endogenous shareholding ratios.