A Dynamic Duopoly Investment Game without Commitment under Uncertain Market Expansion

We model capacity-building investments in a homogeneous product duopoly facing uncertain demand growth. Capacity building is achieved through the addition of production units that are durable and lumpy and whose cost is irreversible. While building their capacity over time, firms compete à la Cournot in the product market given their installed capacity. There is no exogenous order of moves, no commitment regarding future decisions, and no finite horizon. We investigate Markov Perfect Equilibrium (MPE) paths of the investment game, which may include episodes during which firms invest at different times, a preemption pattern, and episodes in which firms invest simultaneously, a tacit collusion pattern. These episodes may alternate and are typically several. When firms have yet to invest in capacity, the sole pattern that is MPE-compatible is a preemption episode: firms invest at different times but 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: firms invest simultaneously at a postponed time (hence holding back production in the meantime), thereby generating an investment wave in the industry. Such investment episodes are more likely with higher demand volatility, faster market growth, and lower cost of capital (discount rate).