Access to bottleneck inputs under oligopoly: a prisoners' dilemma?

• Author: Brito, Duarte
• Position: Company overview

1. Introduction

   As is well known, the monopolist owner of a bottleneck production factor, which is also present in the downstream market, may have the incentive and the ability to restrict access to the bottleneck production factor in order to limit competition in the downstream market. Examples include telecommunications, electricity, or railways incumbents, which may restrict access to their networks.

   In some industries, more than one vertically integrated firm owns a bottleneck production factor, to which they can sell access to downstream entrants. In mobile telephony, more than one firm owns a license to use the radio-electric spectrum and a mobile telecommunications network, to which they can give access to downstream entrants, such as mobile virtual network operators. In broadband access to the Internet, in some countries, both the telecommunications incumbent and cable television firms own local access networks capable of delivering telecommunications services, to which they can give access to downstream entrants, such as Internet service providers.

   In those industries there are at least three reasons to suspect that vertically integrated oligopolists have different incentives than a vertically integrated monopolist, to concede access to their bottleneck production factors to a downstream entrant. First, even if an incumbent denies access to his bottleneck production factor, there is no guarantee that the entrant will not obtain access elsewhere. Second, an incumbent that provides access to an entrant shares with the other incumbents the downstream revenue loss caused by entry. Third, if entry cannot be blocked, then it is probably better for each incumbent to be the access provider. This allows the incumbent to earn additional wholesale revenues that at least compensate partially any loss in retail revenues caused by entry. Altogether, this suggests that incumbents may face a prisoners' dilemma. They would be better off if entry did not occur. However, individually, they have incentives to be the one who gives access to the entrant.

   We develop a two-stage game to analyze these issues. In the first stage, two incumbents make access price offers to an entrant, which chooses which one to accept, if any. In the second stage, firms compete on retail prices. We model the industry as a horizontally differentiated product oligopoly on Salop's circle (Salop 1979). A distinguishing characteristic of our approach is that the firms may be asymmetrically located on the circle, with the degree of asymmetry captured by a single parameter. The varying relative location of firms on the loop captures differences in consumer shares.

   The model confirms our intuition. For some values of the asymmetry parameter, it is a dominant strategy for the incumbents to concede access to the entrant; although, they would be better off without entry. However, this intuition requires two qualifications. First, for some values of the asymmetry parameter, although entry occurs in equilibrium, the incumbents do not face a prisoners' dilemma. Second, for other values of the asymmetry parameter, the equilibrium of the first stage is for the incumbents to deny access to their bottleneck production factor. These results highlight the importance of product differentiation and firm asymmetry in the entry decision.

   As expected, entry may lead to lower retail prices. Interestingly, however, entry may also lead the retail prices of the access provider and of the entrant to rise above pre-entry levels. If the access provider is a direct rival of the entrant, by hiking his retail price he increases the sales of the entrant, and thereby his own wholesale revenues. Additionally, since the entrant will typically have higher marginal costs than the incumbents because of the access price, it may charge a retail price higher than those the incumbents charged prior to entry.

   Our article relates to (i) the literature on vertical foreclosure, (ii) the literature on raising rivals' costs, and (iii) the literature on access pricing. The first literature strand addresses the question of whether a vertically integrated firm can increase its profit by foreclosing the downstream market. Rey and Tirole (2006) review the case in which the upstream market is monopolized. (1) Ordover, Saloner, and Salop (1990) and Hart and Tirole (1990) analyze the case of an oligopolistic upstream market, focusing on the profitability of vertical mergers. We depart from this literature by assuming that several incumbents are vertically integrated from the beginning and focus on their incentives to allow the entry of downstream competitors. Ordover and Shaffer (2006) develop, independently, an approach similar to ours. The main difference between our articles resides on the demand model. The complete characterization of the equilibria in Ordover and Shaffer (2006) is hard because of the large number of parameters for the firms' baseline market shares and for the consumers' cross-price sensitivities. Some of their results are obtained by numerical methods. As Ordover and Shaffer (2006) acknowledge, an advantage of our model is that it has a closed form solution, which enables us to derive our results without resorting to numerical methods. Besides, our model allows us to derive various results in a unified way. The second literature strand (e.g., Krattenmaker and Salop 1986; Salop and Scheffman 1987; Vickers 1995; Economides 1998; Sibley and Weisman 1998) analyzes the incentives of an upstream monopolist to raise his rivals' costs, inducing them to contract their market share. (2) In our model, setting a high access price is the only way of raising rivals' costs. Regarding the third literature strand on access price regulation, Laffont and Tirole (1993) and Masmoudi and Prothais (1994) analyze Ramsey pricing, and Willig (1979), Baumol (1983), Baumol and Sidak (1994), and Armstrong, Cowan, and Vickers (1996) analyze the efficient component pricing rule. (3) Armstrong and Vickers (1998) and Lewis and Sappington (1999) study access pricing when the downstream market is not regulated. In these articles, the bottleneck input is controlled by a regulated monopolist. Our article differs from these by assuming that several incumbents own bottleneck inputs and compete to provide access to the entrant. Additionally, the access price is not regulated.

   The remainder of the article is organized as follows. In section 2, we present the model, whose equilibria we characterize in section 3. In section 4, we present two variations to the model. Section 5 concludes.

2. Model

   In this section, we develop a simple model that abstracts from many institutional details for three reasons: (i) to make the strategic interaction transparent, (ii) to broaden the applicability of the results, and (iii) for tractability.

   Environment

   Consider an industry where firms sell products horizontally differentiated on Salop's circle. (4) Initially there are two firms, the incumbents. A third firm, the entrant, wants to join the industry. Each incumbent owns a bottleneck input. To operate, the entrant has to buy access to the bottleneck input of one of the incumbents. We assume that both incumbents may sell the input, but the entrant buys access from only one of them. We also assume that the incumbents do not need to buy inputs from each other.

   The game has two stages. In stage 1, the incumbents make access price offers, and the entrant decides which one, if any, to accept. In stage 2, firms choose retail prices.

   Consumers

   There is a large number of consumers, formally a continuum, whose measure we normalize to 1. Consumers have unit demands, are uniformly distributed along a loop of unit length, and have quadratic transportation costs, where [ty.sup.2] measures the cost of traveling distance y. We further assume that consumer valuation is sufficiently high so that the entire Salop circle is served.

   [FIGURE 1 OMITTED]

   Firms We index firms with subscript i = 1, 2, e, where firms 1 and 2 are the incumbents and firm e is the entrant, and we index the access provider with superscript j = 1, 2.

   The production of one unit of the final good involves the consumption of one unit of the bottleneck input, whose cost we normalize to 0. Additionally, firms face a nonnegative downstream, or retail, marginal cost of c. Denote by [[alpha].sub.i], the access price of the bottleneck input of firm i = 1, 2, by [P.sub.i], the retail price of firm i = 1, 2, e, by [D.sub.i], the demand of firm i = 1, 2, e, and by [[pi].sup.j.sub.i], the profit of firm i when firm j is the access provider, with i = 1, 2, e, and j = 1, 2. Let [P.sub.i] : = [P.sub.i] - c. The demand function can be expressed as a function of [p.sub.i] instead of [P.sub.i] because only price differences matter. Thus, [[pi].sup.j.sub.e], = ([P.sub.e] - [[alpha].sub.j]) [D.sub.e], and

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

   As profit functions depend only on the [p.sub.i]s, we assume this is the firm's decision variable in the retail pricing stage.

   We assume that the locations of the incumbents and the entrant are exogenously defined. (5) We denote by [delta] and 1 - [delta] the distances between the two incumbents, and we assume, as illustrated in Figure 1, that the entrant locates at a distance of [delta]/2 from each incumbent. Parameter [delta] measures the degree of asymmetry between the incumbents, with maximum differentiation occurring when [delta] = 1/2. If [delta] [right arrow] 1, or if [delta] [right arrow] 0, there is pre-entry product homogeneity. (6) This specification encompasses other cases of interest with a single parameter: (i) if [delta] = 1/2 there is pre-entry symmetry, and (ii) if [delta] 2/3 there is post-entry symmetry.

   Product differentiation is captured by two parameters, t and [delta]. Global differentiation is measured by parameter I; whereas, local differentiation between the incumbents is measured by parameter [delta].

   The access...