Investment in Shared Suppliers: Effect of Learning, Spillover, and Competition

We investigate the optimal strategies for firms to invest in their suppliers when the benefits of such investments can spillover to other firms who also source from the same suppliers. We consider two Bayesian firms that can invest in improving the quality of their shared supplier; the firms do not have complete information on the true quality of the supplier, but they update their beliefs based on the supplier's performance. We formulate the problem as an investment game and obtain Markov perfect equilibria characterized by the investment thresholds of both firms. The equilibrium investment strategies of the two firms are characterized by a region of preemption and a region of war of attrition. We also examine how the interplay between spillover, competition, and returns from the investment at shared suppliers affect the investment threshold and the time to the leader's investment, and identify the conditions under which competition delays or hastens the first investment in a shared supplier.