Strategic Complements with First Mover Advantage

We show the existence of equilibrium and first mover advantage when two firms sequentially invest in quality improvement of their respective products. Although the actions (investment levels) of the firms are strategic complements, the second mover does not have an advantage. This is because, although firms are a priori identical, a change in rival investment can affect a firm differently, depending on whether the rival has a higher or lower level of investment. Thus, the marginal payoff with respect to rival action will differ for the first and second mover. We also show that the first mover may choose a higher level of investment than the second mover even though actions are strategic complements and the first mover's marginal payoff with respect to second mover action is negative.