Strategic capacity choice with risk-averse firms

Abstract

We study the joint effect of uncertainty, competition, and risk-aversion on the optimal time and size of firms in a duopoly. As risk-aversion increases, the leader’s alternatives between deterring and accommodating the follower’s entry become equivalent. When the leader’s role is assigned exogenously, risk-aversion reduces equilibrium investment sizes and timing. In equilibrium, the leader is always the largest firm in the market. When the leader’s role is determined in equilibrium, risk-aversion delays the rent equalization point. At high levels of risk-aversion, both firms invest in the same capacity.

Keywords:

• Real options games
• risk aversion
• capacity investments
• preemptive games

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 $E_x\left[g(X_t)\right]=E\left[g(X_t)|X_0=x\right].$

2 Chronopoulos et al. (2013), the first to document this effect, show that the more risk-averse the monopolist, the lower the investment size. Due to the increased concern about risk, the monopolist adjusts the risk profile of the investment by investing less. This reduces the value of the option of waiting since a lower amount invested requires a lower level of market size to maximize the investment’s profitability.

3 The kink observed in Figure 6 falls in a region in which accommodation is not feasible, and thus it does not affect the equilibrium. The existence of the kink is related to equation (52), which describes the optimal capacity of the follower when the leader accommodates her entry. Before the kink, the leader’s optimal capacity and the state variable are too low, and the follower’s optimal capacity is null. After the kink, the follower installs a positive capacity, which implies that the leader must reduce her capacity to accommodate the follower’s entry.

4 Due to space limitation, we present only one example of this phenomenon. However, we have run an extensive set of numerical experiments, all confirming the robustness of this result.