Strategic capacity investment with common ownership or cross holdings

Strategic capacity investment with common ownership or cross holdings

We study how overlapping ownership affects the timing and size of capacity investments in duopoly. In addition to standard accommodation and delay strategies, internalization allows a leader to block follower entry. Follower timing and capacity reactions are less aggressive, making outcomes less competitive ex-post. Positional competition is more intense, and entry occurs earlier in equilibrium. Internalization raises a leader's incentive to delay follower entry rather than accommodate, and we show with an example that this strategic shift can benefit consumers.

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Horizontal ownership concentration, where a small number of institutional investors hold significant minority stakes in competing firms, is an increasingly pervasive phenomenon which has raised regulatory concern because of its potential to foster anticompetitive behavior (Backus et al. 2021, Posner et al. 2016). Horizontal minority shareholding, where firms take non-controlling stakes in product market rivals, has also been a growing concern since the turn of the millennium. Such forms of overlapping ownership have attracted a wave of academic interest, kindled notably by evidence of pricing distortions in the airline industry due to common ownership (Azar et al. 2018). New forms of evidence such as natural and laboratory experiments continue to emerge (Heim et al. 2022, Hariskos et al. 2022), altogether lending broad credence to the thesis that managers account for ownership structure in their decision-making by internalizing some of the effects they exert on rival firms. 

In the discussion surrounding common ownership, the causal mechanism linking owners to the managerial decisions that determine product market outcomes is a central theme (Hemphill and Kahan 2019, Anton et al. 2021). Institutional investors regularly engage with the management of their portfolio firms (Shekita 2022), and chief among the strategic decisions that top management makes is the exercise of a firm’s real options (Smit and Trigeorgis 2017). So far the study of strategic effects of common ownership has centered mostly around R&D investments, but in many of the industries concerned by common ownership firms hold other options, like the option to build production capacity, which are equally important. We propose therefore to examine how increased internalization modifies the timing and size of irreversible capacity investments under uncertainty, and ultimately find a variety of effects whose product-market consequences can be either anti or pro-competitive.

Our model extends the framework for strategic capacity investment in Huisman and Kort (2015) to incorporate overlapping ownership. We thus study two firms holding competing projects in a market which evolves over time. These firms have ownership structures which overlap (either because of common shareholders or because of cross-holdings) so their management internalizes rival value when making investment decisions. Other than this, the firms determine when and how much capacity to install in the standard way. In equilibrium, one of the firms acts as a leader and invests first, whereas the second firm is a follower and reacts to the leader’s timing and capacity decision. 

We find first of all that internalization invariably exerts an anticompetitive effect on the follower firm, in contrast with prior work involving fixed-size investments where the follower entered earlier if product market profits were very sensitive to internalization (Zormpas and Ruble 2021). In the present model, the weight attributed to leader profit effectively magnifies its capacity from the follower’s perspective, driving the follower to enter at a higher demand threshold and to choose a smaller capacity upon entry. 

The follower’s less aggressive timing and quantity reactions benefit the leader firm, which enjoys a protracted monopoly period followed by less intense duopoly competition. With internalization the leader has the novel possibility of blocking the follower entirely, though it ultimately prefers to either just delay the follower’s entry or to accommodate it. The leader prefers to delay (deter) the follower by investing in relatively larger capacities than it otherwise would at low demand states, but shifts to accommodation at higher demand states at which delaying the follower this way becomes prohibitively expensive. Because the leader benefits from both less aggressive capacity and timing reactions if it induces delay strategically, internalization strengthens leader preference for deterrence relative to accommodation. Overall we find that the leader’s optimal investment behavior resembles the case without internalization if the level of internalization is not too high, but also that qualitative differences otherwise arise, e.g. accommodation can fail to ever be optimal with sufficient internalization. 

If firms compete for the leadership role, we find that the follower’s less aggressive reaction makes leading relatively more attractive. Internalization therefore has a procompetitive effect on entry timing in preemption equilibrium. Entry occurs at a low enough demand state that the leader chooses a capacity which delays follower entry. The pro-competitive effect of internalization on entry timing is offset however by a lower leader capacity. Introducing endogenous capacities therefore leads us to nuance the results obtained in prior work with fixed investment size. 

Beyond these effects at the preemption threshold, we also find that if leader investment occurs at an intermediate demand state, a moderate degree of internalization can exert a procompetitive effect through an altogether different channel pertaining to the leader’s strategy choice. Specifically the leader’s increased preference for delay with internalization can push it to shift from accommodation to deterrence. Delaying the follower requires a sharp increase in capacity, and we find that this capacity increase can be substantial enough that consumers ultimately benefit, despite the detrimental effect on follower entry. 

We complement our analytical results with a numerical analysis which bears out these insights, i.e. that internalization is anticompetitive for the follower but also has a procompetitive effect on the timing of investment in preemption equilibrium. We show moreover that the second procompetitive effect mentioned above due to procompetitive shift in the leader’s strategy effectively occurs, and that the resulting increase in capacity can be large enough that overall consumer surplus increases.

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