A Dynamic Duopoly Investment Game under Uncertain Market Growth

We model investments in capacity in a homogeneous product duopoly facing uncertain demand growth. Capacity building is achieved through adding production units that are durable and lumpy and whose cost is irreversible. There is no exogenous order of moves, no first-mover or second-mover advantage, no commitment, and no finite horizon; while building their capacity over time, firms compete `a la Cournot in the product market. We investigate Markov Perfect Equilibrium (MPE) paths of the investment game, which may include preemption episodes and tacit collusion episodes. However, when firms have not yet invested in capacity, the sole pattern that is MPEcompatible is a preemption episode with firms investing at different times, but both have equal value. The first such investment may occur earlier, and therefore be riskier, than socially optimal. When both firms hold capacity, tacit collusion episodes may be MPE-compatible with firms investing simultaneously at a postponed time (generating an investment wave in the industry). We show that the emergence of such episodes is favored by higher demand volatility, faster market growth, and lower discount rate (cost of capital).