Free riding in noncooperative entry deterrence with differentiated products.

• Author: Kovenock, Dan
• Position: Gilbert and Vives

1. Introduction

   This paper reexamines the phenomenon of free riding in entry deterrence when established firms in an oligopoly are unable to coordinate their entry preventing activities. Previous authors (e.g., Bernheim 1984; Gilbert and Vives 1986; Waldman 1987, 1991; Appelbaum and Weber 1992) have highlighted the public good aspect of noncooperative entry prevention--if costly entry deterring actions are successfully undertaken by a proper subset of the incumbents, then incumbents outside of that subset cannot be excluded from the benefits of deterred entry. It is in this sense that entry deterrence acquires the nature of a public good. This observation has prompted previous researchers to raise the "free rider" question (with its associated welfare implications): Can there occur underinvestment in entry deterrence due to the incentive for each firm to free ride on the others' (costly) entry preventing activities?

   The free rider problem in entry deterrence is first mentioned in the sequential entry model of Bernheim (1984). However, though Bernheim discusses the possibility of free riding in his model, the free rider problem is not the main focus of his paper. In fact, as pointed out by Waldman (1987, p. 309, footnote 2), the author's discussion of the role of the free rider problem is "... somewhat vague as regards whether Bernheim feels the free rider problem would ever be important in a noncooperative entry deterrence setting." (1)

   Gilbert and Vives (1986) is the first paper in which the underinvestment issue is explicitly addressed. The authors define underinvestment in entry deterrence to be associated with one or more of the following:

   "(a) Incumbents' total profits are higher preventing than allowing entry, but the (unique) industry equilibrium allows entry.

   (b) Either entry prevention or entry may be an industry equilibrium, but incumbents' profits are higher when entry is prevented.

   (c) An established monopoly (or colluding incumbents) prevents entry in more situations than an established, noncooperating oligopoly." (p. 77)

   Label (a), (b), and (c) as underinvestment of type 1, 2, and 3, respectively. Gilbert and Vives (G&V) go on to show that in none of these respects is there underinvestment in their quantity setting homogeneous product model. On the contrary, they demonstrate a strong possibility of overinvestment.

   G&V consider a situation where symmetric noncooperative incumbents with constant marginal costs of production make credible commitments to outputs in the preentry stage. (2) The entrant incurs a fixed entry cost if it enters the industry and makes its entry and output decision after observing the incumbents' output choices. Consequently, there exists a "limit output," which if jointly produced by the oligopoly, deters entry. (3) G&V find that entry is prevented when limit outputs are small, while entry is allowed for larger limit outputs. For limit outputs in an intermediate range, both allowing entry and preventing entry are equilibria. They prove that in this intermediate range where both entry accommodating and entry preventing equilibria coexist, the unique entry equilibrium Pareto dominates every deterrence equilibrium. In other words, compared with any deterrence equilibrium (there is typically a continuum of such equilibria) the accommodation equilibrium

   yields strictly higher profits to every incumbent. Hence, if the industry settles on an entry preventing equilibrium, the implication is that overinvestment exists because, by jointly reducing incumbents' outputs and allowing entry, every incumbent can be made better off.

   This paper introduces product differentiation into the G&V model and shows that sufficiently large amounts of product differentiation can generate underinvestment in entry prevention. The intuition is straightforward. Consider an incumbent's profit in any entry deterring equilibrium where exactly the limit output is produced by the oligopoly. In the homogeneous good model, the price of the product is always the (constant) price that clears the limit output, regardless of how the limit output is distributed among the incumbents. This, coupled with constant marginal costs, implies that each incumbent's profit is continuously increasing in its own output or, equivalently, decreasing in rival's output. (4) Consequently, each firm wants the largest share in the limit output--an incentive that rules out the possibility of underinvestment. However, with differentiated products, the larger an incumbent's share of the limit output is, the smaller the price is. There are, then, two opposing forces at work: An increase in an incumbent's share of the limit output has a positive influence on its profit, but the resultant fall in price has a negative effect on profit. When the second effect outweighs the first, the incumbent's deterrence profit need not be continuously increasing in own output, that is, it can be increasing in the other's quantity over some range and decreasing over other ranges. (5) This could weaken an incumbent's incentive to have the largest share in the entry deterring output and could generate underinvestment. Note that, starting from the homogenous good benchmark, increasing the degree of product differentiation strengthens the second effect, that is, for sufficiently differentiated products, an increase in rival output (and a consequent decrease in own output) raises own price to such an extent that its positive effect on profit more than compensates for the negative effect on profit of a lower own share of the limit output, thereby resulting in a deterrence profit that is increasing in rival output over the relevant range. (6)

   We formalize this intuition by incorporating the differentiated products demand structure of Vives (1985) into the G&V model. Using G&V's methodology, the equilibria of the game are characterized in terms of the limit output. Focusing on the region where both entry allowing and entry deterring equilibria exist, we show that underinvestment of type 2 is a distinct possibility, namely, the entry allowing equilibrium may be Pareto dominated by an entry deterring equilibrium. We call this type of underinvestment "coordination failure" underinvestment--there exists an equilibrium where entry is deterred, but coordination failure may lead to one that allows entry and yields lower payoffs to all incumbents. This sort of underinvestment can arise even when type 1 and type 3 underinvestment are absent and is more likely with greater amounts of product differentiation. However, moderate amounts of product differentiation preserve the G&V overinvestment result. We demonstrate that coordination failure underinvestment, in our model, can occur only if each incumbent's entry deterring profit is increasing in its rival's output at the point at which it is indifferent between allowing entry and preventing entry. A numerical example of underinvestment is also provided.

   Bernheim (1984) is the first paper to recognize the possibility of coordination failure underinvestment by pointing out the existence of one type of equilibrium in which each incumbent firm makes a zero investment in entry deterrence and equilibria of a second type where investments are just sufficient to deter entry. However, since the second kind of equilibria exist if and only if entry deterrence is jointly profitable, Bernheim chooses to focus on the symmetric entry deterring equilibrium on the grounds that the possibility of "informal communication" would lead to the industry settling on the equilibrium that is not Pareto dominated by the entry allowing equilibrium.

   In similar vein, Waldman (1987, 1991) adopts Bernheim's equilibrium choice rule and sets out to investigate whether or not, given this equilibrium choice rule, the free rider problem is important. While the possibility of coordination failure underinvestment is clearly understood, as evidenced by the discussion in Waldman (1987) of Bernheim's paper, the author's adoption of Bernheim's equilibrium choice rule necessarily results in coordination failure underinvestment being ruled out. More specifically, Waldman (1987) considers uncertainty regarding the exact investment needed to deter entry and demonstrates that while such uncertainty causes underinvestment in the Bernheim framework, introducing uncertainty in the G&V model does not change their original conclusions and free riding remains nonexistent. However, he defines underinvestment as the situation where the aggregate investment at the noncooperative equilibrium is less than that which maximizes expected joint profits, that is, his results refer to underinvestment of type 3 only.

   On the other hand, in the sequential entry model of Waldman (1991), underinvestment is regarded as the situation where allowing entry is the unique noncooperative equilibrium even though deterring entry is mutually more profitable for all incumbents. Thus, his conclusion that the presence of multiple potential entrants is crucial for underinvestment in entry deterrence is valid for type 1 underinvestment only. In their externalities model, Appelbaum and Weber (1992, p. 474) consider precommitments that can be unambiguously classified as "public goods" or "public bads" and predict that "if precommitments constitute 'public goods' but make incumbents 'tough', we have under-investment." They use the same definition of underinvestment as Waldman (1987), and so their results must be similarly qualified. In other words, because of their approach, none of these later studies explore the possibility of type 2 underinvestment.

   This may be reconciled by pointing out that, owing to the methodology used, much of the later literature has overlooked an important feature of lumpy public goods models. Lumpy public goods such as entry deterrence, by their very nature, give rise to discontinuous payoffs and multiple equilibria along with the associated coordination failure problems...