For nearly two decades, ocean carriers have been locked in an arms race for capacity, which has led to huge losses for many and even bankruptcy for some. We investigate the nature of this investment race by studying a long-term capacity investment problem in a duopoly under demand uncertainty. In our model, two firms make sequential capacity decisions, responding to each other’s current and future capacity. We consider two types of strategies which differ in terms of how a firm considers the opponent’s future capacity in its own strategy: a proactive strategy where the firm assumes that the opponent will respond using a certain strategy, or a reactive strategy where the firm assumes that the opponent’s future capacity remains unchanged. In the proactive case, we allow the firm to have different assumptions on the opponent’s strategy, representing different amounts of information the firm has on the opponent. For each type of strategies, we derive the firm’s optimal decisions on both the timing and size of capacity adjustments, specified by an array of intervals for the optimal capacity in a given capacity space in each period. Using detailed data from the container shipping market (2000–2015), we illustrate how to plan competitive capacity investments, following our model. By comparing the optimal decisions specified by our model with the reality, we show that the realized capacity decisions of the leading carriers, which were often questioned as irrational, are close to optimal, assuming these carriers follow proactive strategies. By revealing the underlying structures of different strategies, that is, the stayput intervals, we show how a specific strategy brings value to firms under competition. Based on our results, we provide practical guidelines to carriers and firms which operate in a similar competitive market for implementing an effective competitive capacity strategy.