On the role of demand and strategic uncertainty in capacity investment and disinvestment dynamics

Abstract

Even mature industries seldom settle down into a long-run steady state. Fluctuations in demand disrupt the status quo and call for firms to adjust their capacities on an ongoing basis. We construct a fully dynamic model of an oligopolistic industry with lumpy capacity and lumpy investment/disinvestment decisions. In addition to uncertainty about the evolution of demand, a firm faces strategic uncertainty concerning the decisions of its rivals. We numerically solve the model for its Markov-perfect equilibria. For one set of parameter values, three equilibria exist, and while all of them have simple, intuitive structures, they exhibit widely varying patterns of response to demand shocks. At one extreme, one firm dominates the industry almost as a monopolist and changes its capacity to accommodate demand. At the other extreme, the larger firm keeps its capacity nearly constant while the smaller firm acts as the swing producer.

Introduction

In oligopolistic industries firms face at least two types of uncertainty. First, there is uncertainty about the evolution of demand and possibly also production technology. This type of uncertainty is typically exogenous to the industry. Second, there is uncertainty that emerges endogenously from the strategic decisions of firms. This strategic uncertainty often arises because a firm does not know the exact cost structure of its rivals and therefore cannot perfectly predict their decisions. It matters because a firm's decision regarding capacity addition and withdrawal has both an immediate impact on the profitability of its rivals and the potential to shape the evolution of the industry for years to come.

In practice demand uncertainty and strategic uncertainty are important, and the strategic management literature on capacity decisions exhorts managers to think carefully about both. For example, in his classic work Competitive Strategy, Michael Porter writes: “Because capacity additions can involve lead times measured in years and capacity is often long lasting, capacity decisions require the firm to commit resources based on expectations about conditions far into the future. Two types of expectations are crucial: those about future demand and those about competitors' behavior. The importance of the former in capacity decisions is obvious. Accurate expectations about competitors' behavior is essential as well, because if too many competitors add capacity, no firm is likely to escape the adverse consequences” (Porter, 1980, p. 324). Highlighting how strategic uncertainty can complicate the formation of expectations about competitors' behavior, Porter goes on to state, “If firms have differing perceptions of each other's relative strengths, resources, and staying power, they tend to destabilize the capacity expansion process” (pp. 332–333).

Demand uncertainty has received much attention in the literature, and there is by now a large body of research about investment under this type of uncertainty (see Dixit and Pindyck, 1994). This real options theory mainly considers monopolistic or perfectly competitive settings. There are but a few papers combining real options theory with the strategic interactions that arise in dynamic games played by multiple firms. Most study simple games that end once the option has been exercised (e.g., Smets, 1991, Grenadier, 1996, Lambert and Perraudin, 2003, Boyer et al., 2004, Huisman and Kort, 2004, Pawlina and Kort, 2006, Mason and Weeds, forthcoming). Examples include adopting a new technology or entering a new market.¹ It is not possible to partially recover the investment or to follow up on it with additional investments.

In Besanko et al. (forthcoming) we consider a setting that is flexible enough to characterize fully or partially sunk investment. Our model of an oligopolistic industry is fully dynamic in that a firm can in each period decide to add or withdraw capacity. While we abstract from demand uncertainty, we capture the strategic uncertainty that firms face about their rivals' investment/disinvestment decisions by assuming that a firm is privately informed about its own cost/benefit of capacity addition/withdrawal. We show that, under certain conditions, the evolution of the industry takes the form of a race. Each firm invests aggressively to expand its capacity before its rivals can do so. The industry ultimately reaches an asymmetric structure dominated by the winner of the race. Pursuing an aggressive approach to investment in an attempt to preempt rivals is thus a deliberate competitive move that has a lasting effect on the structure of the industry. This is consistent with the dominance of DuPont of the North American titanium dioxide industry that can be traced back to the preemptive strategy of capacity accumulation that DuPont initiated in the early 1970's (Ghemawat, 1984, Ghemawat, 1997, Hall, 1990). Indeed, in 2008, more than thirty-five years after launching its strategy of capacity preemption, DuPont's share of capacity in the U.S titanium dioxide market is over 50 percent (the next largest competitor Tronox has 20 percent), and DuPont's 21 percent global market share makes it the largest titanium dioxide seller in the world.

In this paper, we build on Besanko et al. (forthcoming) to explore capacity investment and disinvestment dynamics under both demand and strategic uncertainty. Without demand uncertainty, the case studied by Besanko et al. (forthcoming), the role of strategic uncertainty is bound to diminish over time: Once the industry has reached a “steady state,” investment activity comes to a halt, except possibly to make up for depreciation. Hence, it may not matter much that a firm does not know the exact cost structure of its rivals and therefore cannot perfectly predict their decisions to add or withdraw capacity. Fluctuations in demand call for firms to adjust their capacities on an ongoing basis and therefore ensure the continued importance of strategic uncertainty. Moreover, a sufficiently large swing in demand may upset the established structure of the industry. Combing the two types of uncertainty in one model allows us to answer questions regarding the identity of the swing producer and whether a firm is able to maintain—or perhaps even improve—its competitive position in the face of demand uncertainty.