Competition and Cooperation in Network Games

We consider games where agents are embedded in a network of bilateral relationships and have multivariate strategy sets. Some components of their strategies correspond to individual activities, while the other strategic components are related to joint activities and interaction with the partners. We introduce several new equilibrium concepts that account for the possibility that players act competitively in individual components of their strategy but cooperate on the components corresponding to joint activity or collaboration. We apply these concepts to the R&D collaboration networks model where firms engage in bilateral joint projects with other firms. The analysis shows that investments are highest under bilateral cooperation and lowest under full cooperation because the spillovers associated to bilateral collaboration are bound to the partnership. This leads to welfare being maximized under bilateral collaboration when there are a few firms in the market and under non-cooperation in markets with many firms; full cooperation is never social welfare maximizing. Investigating the issue of endogenous network formation, we find that bilateral cooperation increases (lowers) the profits of more (less) connected firms. However, this does not always lead to a denser stable network of R&D collaboration under bilateral cooperation.