Silviase/jgov_v1.4_full_ann huggingface dataset:
the essential component is the more efficient supplier of systems, technological tying can increase welfare in some instances by eliminating an equilibrium in which the less efficient system supplier invests and wins the market.

Economides (1998) shows that a price-regulated upstream monopolist participating in a downstream Cournot (quantity-setting) oligopoly has an incentive for non-price discrimination. $ ^{7} $ Our analysis develops this theme by analyzing the incentives for and consequences of technological tying for product improvement in a downstream systems market when firms compete on quality and price. $ ^{8} $ We consider the case of homogeneous consumer preferences over vertically differentiated products. More specifically, we study markets for systems as duopoly games. In our basic “product improvement game”, two firms sell systems comprised of two components: A and B. Firm 1 offers a system comprised of one unit of component A and one unit of its version of component B. Firm 2 purchases component A from Firm 1 at a price w and offers consumers a system that consists of component A and its version of component B. Conditional on the wholesale price of component A, rival firms invest in quality improvements of component B (or equivalently, improvements of their systems) and subsequently compete on the price of systems. Firm 2 is assumed to have an initial quality advantage and is the more efficient supplier of systems for the same level of investment in product improvement. In the companion “technological tying game” there is also an intermediate stage in which Firm 1 can act to degrade the quality of Firm 2’s system.

Given that consumers have homogeneous preferences, the market has a winner-take-all character and multiple equilibria of the product improvement game are possible. There always exists an efficient equilibrium of the product improvement game in which Firm 2 improves its product optimally and captures the entire market. If the initial quality advantage of Firm 2 is sufficiently small, then there also exists an inefficient equilibrium in which Firm 1 invests in product improvement and wins the market. In these equilibria, consumers enjoy a positive surplus as long as the losing firm exerts some competitive price pressure on the winner.

In the technological tying game, if the wholesale price is not too large, there is a unique equilibrium in which Firm 1 forecloses competition with an actual, or
perhaps merely threatened, technological tie, $ ^{9} $ improves its product efficiently, and sets a price that fully extracts consumer surplus. In this case, technological tying distorts market structure and reduces consumer welfare by eliminating competition from the more efficient Firm 2. The technological tying game has multiple equilibria for all higher prices of the essential component if the initial quality advantage of Firm 2 is sufficiently small. In one equilibrium, Firm 1 invests and forecloses competition with a technological tie. In the other equilibrium, Firm 2 invests and Firm 1 does not impose a tie. If Firm 2's initial quality advantage is large, then the technological tying game has multiple equilibria for intermediate values of the wholesale price and a unique equilibrium in which Firm 2 invests when the wholesale price is sufficiently close to the monopoly level. When the tying game has multiple equilibria, they are strictly ordered. Both firms are better off, and consumers are no worse off, in the equilibrium in which the more efficient Firm 2 invests.

Farrell and Katz (2000) also study incentives for product improvement in markets for vertically differentiated systems. In their model a monopolist supplies an essential component and competes with others to supply a complementary component to consumers who assemble a system. By “overinvesting” in product R&D for the complementary component, the integrated monopolist squeezes the rents of rival suppliers and is able to charge consumers more for the essential component. $ ^{10} $ Moreover, the firm prices the essential component to extract monopoly rents after observing the qualities and prices of the competitively supplied components. While Farrell and Katz (2000) do not explicitly address incentives for technological tying, their analysis generally supports the Chicago School insight that there is no reason for technological tying if the monopolist can extract rents effectively by adjusting the price of the essential component. In contrast, we assume that the wholesale price of the essential component is determined prior to systems market competition, and focus on cases in which the wholesale price fails to fully extract monopoly rents from the systems market.

Choi and Stefanadis (2001) also model competition in markets for systems. In their model an incumbent monopolist sells two complementary components and potential entrants invest under uncertainty to introduce new lower-cost versions of one or both of the components. Tying by the incumbent deters entry into both component markets and strengthens the incumbent's incentive to invest in cost reduction. As in Farrell and Katz (2000), component prices are determined after firms make their investment decisions, and the incumbent can price an essential component to extract rents if low-cost entry occurs in only one of the two markets. Thus, the incentive to
tie in Choi and Stefanadis (2001) depends on a risk of entry into both component markets. Moreover, in further contrast to our technological tying game, tying in their model requires a commitment to tie prior to firms' investment decisions.

Section 2 describes the structure of the market for systems and the technology for product improvement. This section introduces the assumptions that systems are vertically differentiated, Firm 2 is the higher quality supplier of systems when neither firm invests and that, by investing, Firm 1 can leapfrog Firm 2's initial quality advantage. These assumptions frame the policy issues by defining an environment in which Firm 1 can use its control over access to the essential component to influence investment incentives and thereby distort market outcomes. Section 3 introduces the product improvement game and identifies the pure strategy equilibria. Section 4 does the same for the technological tying game. Section 5 examines the welfare implications of the different equilibria, and Section 6 considers the competitive consequences of several variations on our basic theme, such as assigning the initial quality advantage to Firm 1, assuming that a firm exits the market if it cannot make any sales, and allowing network effects. Section 7 concludes.

## 2 Vertical Product Differentiation

There are two firms, indexed i = 1, 2. Consumers have a willingness-to-pay for systems that consist of an intermediate good supplied only by Firm 1 (component A) and another complementary good consumed in fixed proportions with the essential component (component B), which either firm can supply. For obvious reasons we call component A the essential component. Firm 2 must have access to the essential component to compete in the systems market. As explained further below, the essential component can be sold also on a stand-alone basis separately from systems.

Systems are differentiated in quality, which is partly exogenous and partly endogenous. Each of M identical consumers demands a single system. A consumer’s willingness-to-pay for a system consisting of components A and B from firm i is

$$ q_{i}=\gamma_{i}+q(r_{i}), $$

where $ \gamma_{i} $ is an exogenous quality parameter specific to systems sold by Firm i and the endogenous variable $ r_{i} $ is Firm i's investment in R&D to improve the quality of its system (or, equivalently, the quality of its component B). For analytical convenience, we assume that there are no additional variable costs of producing systems.

It is convenient to reinterpret equation (1) as Firm i choosing a level of quality improvement

$$ z_{i}=q_{i}-\gamma_{i} $$

by incurring an R&D cost

$$ r_{i}=r(z_{i}). $$
We maintain several assumptions.

A1: The symmetric R&D cost function $ r(z) $ is increasing, strictly convex, twice differentiable, and satisfies $ r(0) = r'(0) = 0 $ .

The first assumption implies that there is a unique $ z^{M} $ that maximizes the net benefits from quality improvement $ zM - r(z) $ and is the solution to $ r'(z^{M}) = M $ . Thus $ z^{M} $ is the efficient level of quality improvement for a firm selling to the entire market, yielding a net return $ z^{M}M - r(z^{M}) > 0 $ .

$$ A2:\gamma_{2}-\gamma_{1}>0. $$

The second assumption implies that Firm 2 is the more efficient supplier of systems for any given level of investment in quality improvement. $ ^{11} $ The maximum social surplus in this market is $ (\gamma_{2} + z^{M})M - r(z^{M}) $ , which corresponds to investment of $ z^{M} $ by Firm 2. $ ^{12} $ This surplus is fully extracted by Firm 1 with a monopoly wholesale price equal to

$$ \bar{w}\equiv\gamma_{2}+z^{M}-r(z^{M})/M. $$

$$ A3:(\gamma_{1}+z^{M})M-r(z^{M})>\gamma_{2}M. $$

The third assumption implies that Firm 1 can profitably leapfrog Firm 2’s initial quality advantage by investing efficiently in product improvement. Although this assumption is not necessary for some of our results, it describes an environment in which investment effects can dominate firm-specific efficiencies, which is the focus of our analysis.

The monopoly good that is an essential component of systems also has a separate stand-alone use that is valuable to a different group of consumers. While M consumers are willing to pay $ q_{i} $ for Firm i's system, another $ M' $ consumers are willing to pay w for the stand-alone product. The monopolist is unable to charge different prices to these two groups of consumers, and sets a profit-maximizing price equal to w if $ M' $ is sufficiently large relative to M. Moreover, if $ w < \bar{w} $ , then the profit-maximizing price fails to fully extract monopoly profits from the M consumers who demand systems. We make these additional assumptions, and hereafter treat w as the predetermined wholesale price of the monopoly component.

$$ W(x,z_{1},z_{2})=M\left[x\left(\gamma_{1}+z_{1}\right)+(1-x)\left(\gamma_{2}+z_{2}\right)\right]-r(z_{1})-r(z_{2}). $$
A4: $ \bar{w} \geq w $ and $ M' > (\frac{\bar{w} - w}{w}) M > 0. $

The fourth assumption states that the monopoly price of component A when used in a system $ (\bar{w}) $ weakly exceeds the monopoly price of the component when sold on a stand-alone basis $ (w) $ , and that the profit from selling in both submarkets exceeds the monopoly profit from the systems market alone. This implies that if Firm 1 cannot otherwise prevent arbitrage between the markets for systems and the stand-alone component, it would optimally commit to a wholesale price equal to w, earning a profit $ wM' $ from stand-alone sales of component A. The profit from stand-alone sales of the component plays no significant role in our analysis, and is ignored hereafter.

We compare the subgame perfect Nash equilibria of two different game forms. In the “product improvement game”, competition proceeds in two stages. In the first stage the firms simultaneously and independently choose quality improvements $ z_{i} $ at cost $ r(z_{i}) $ . In the second stage the firms simultaneously and independently set prices $ P_{i} \geq w $ after observing each other's quality. The “technological tying game” amends the product improvement game by introducing an additional stage in which the upstream monopolist can degrade the quality of its rival's system. In the first stage of the technological tying game the firms choose costly quality improvements $ z_{i} $ as in the product improvement game. In the second stage Firm 1 can degrade Firm 2's quality by a fixed amount $ \delta > 0 $ . A technological tie always forecloses competition if $ \delta $ is sufficiently large, which we assume to be the case. In the final stage the firms set prices. $ ^{13} $

The price subgame is the same in both game forms. Consumers observe prices and qualities and choose the product that offers the greatest net utility. Consumers have identical preferences, so Firm i makes sales to all M consumers if $ q_{i} - P_{i} > \max(q_{j} - P_{j}, 0) $ . When both products offer the same net utility, consumers are assumed to choose the higher quality product, and if both firms also have the same quality, then consumers are assumed to choose Firm 1.

Equilibrium prices and sales in the market for systems depend on the level of w and product qualities. In an equilibrium of the price subgame, only one firm sells to the entire market. If $ q_{1} > q_{2} $ and $ q_{2} \geq w $ , then Firm 2 sets price $ P_{2} = w $ and Firm 1 wins the market at price $ P_{1} = q_{1} - q_{2} + w $ . A similar result holds for Firm 2 if $ q_{2} > q_{1} $ and $ q_{1} \geq w $ . Then Firm 1 sets price $ P_{1} = w $ and Firm 2 wins the market at price $ P_{2} = q_{2} - q_{1} + w $ , because w is an opportunity cost of sales for Firm 1 and a direct cost for Firm 2. $ ^{14} $ If $ q_{2} < w $ , then Firm 1 wins the market at price $ P_{1} = q_{1} $ even if $ q_{1} < q_{2} $ . Furthermore, if $ q_{1} < w \leq q_{2} $ , then Firm 2 wins the market at price $ P_{2} = q_{2} $ . Thus,
the losing firm serves as a competitive check only when the quality of its system is above its opportunity cost. Summarizing, Firm 1 sells to all M customers at a price $ P_{1}=q_{1}-\max(q_{2}-w,0) $ if $ q_{1}\geq q_{2} $ or if $ w>q_{2} $ , and Firm 2 sells to all M customers at a price $ P_{2}=q_{2}-\max(q_{1}-w,0) $ if $ q_{2}>q_{1} $ and $ w\leq q_{2} $ .

We analyze the (pure strategy) equilibria of the product improvement and technological tying games. $ ^{15} $ The equilibria of the product improvement game show that a firm may win the market with a better product even when it would be more efficient for a rival to engage in product improvement. Thus, an ex post measure of product superiority can be a misleading indicator of market performance. The equilibria of the technological tying game illustrate the ability and incentives of a firm that controls an essential input to foreclose a more efficient downstream rival from participating in the market for systems. When technological tying is feasible and the wholesale price of the upstream good is insufficiently remunerative, the upstream monopolist has an incentive to foreclose rivals and substitute its own innovative efforts. Technological tying is potentially costly because it facilitates product improvement and market dominance by a less efficient firm. $ ^{16} $

## 3 The Product Improvement Game

In the product improvement game, firms invest in quality improvement at stage 1 anticipating a Bertrand-Nash equilibrium of the subsequent price subgame at stage 2. It is immediate that both firms do not make positive investments in equilibrium. One of the firms captures the entire market, leaving the other firm better off not investing. Given our maintained assumptions, there always exists an equilibrium in which the more efficient Firm 2 captures the entire market. A second equilibrium exists if the cost of efficient quality improvement is high relative to Firm 2's initial quality advantage.

Proposition 1 In the product improvement game:

(i) There exists an efficient equilibrium in which Firm 2 invests $ z^{M} $ and Firm 1 invests 0 in quality improvement. Firm 2 sets a price equal to $ P_{2} = \gamma_{2} + z^{M} - \max(\gamma_{1} - w, 0) $ , sells systems to all M customers, and earns $ \pi_{2} = (P_{2} - w)M - r(z^{M}) \geq 0 $ .
Firm 1 sets price $ P_{1} = w $ , sells M units of component A and no systems, and earns $ \pi_{1} = wM $ . $ ^{17} $

(ii) There exists a second equilibrium in which Firm 1 invests $ z_{1}=z^{M} $ and Firm 2 invests 0 in quality improvement if and only if $ r(z^{M})\geq(\gamma_{2}-\gamma_{1})M $ . Firm 1 sets price $ P_{1}=\gamma_{1}+z^{M}-\max(\gamma_{2}-w,0) $ , sells systems to all M customers, and earns $ \pi_{1}=P_{1}M-r(z^{M})\geq0 $ . Firm 2 sets price $ P_{2}=w $ , sells no systems, and earns $ \pi_{2}=0 $ .

## (iii) There are no other equilibria

We sketch the proof here. The payoffs to each firm depend on the firms' investment levels and the price of the essential component A. Table 1 below shows payoffs when the firms invest at the efficient level $ z^{M} $ or not at all and the price of component A is greater than $ \gamma_{2} $ and less than $ \gamma_{1} + z^{M} $ . The full proof in the Appendix shows that firms cannot profit by investing other than 0 or $ z^{M} $ . Each cell in the table shows the payoff to Firm 1 followed by the payoff to Firm 2. There are two possible equilibria, corresponding to investment by Firm 1 (and not by Firm 2) and investment by Firm 2 (and not by Firm 1). The first equilibrium exists if and only if $ r(z^{M}) \geq (\gamma_{2} - \gamma_{1})M $ , otherwise Firm 2 would leapfrog the less efficient Firm 1 even when Firm 1 invests. When $ r(z^{M}) \geq (\gamma_{2} - \gamma_{1})M $ , the differential quality $ (\gamma_{2} - \gamma_{1}) $ is not large enough to compensate Firm 2 for the cost of the quality improvement when both firms invest. $ ^{18} $

Table 1. Firm payoffs when $ \gamma_{1} < \gamma_{2} \leq w \leq \gamma_{1} + z^{M} $

$ z_{2}=z^{M} $	$ z_{2}=0 $
$ z_{1}=z^{M} $	$ wM-r(z^{M});(\gamma_{2}-\gamma_{1})M-r(z^{M}) $	$ (\gamma_{1}+z^{M})M-r(z^{M});0 $
$ z_{1}=0 $	$ wM;(\gamma_{2}+z^{M}-w)M-r(z^{M}) $	$ \gamma_{1}M;0 $

In the equilibrium in which Firm 1 invests, corresponding to $ r(z^{M}) \geq (\gamma_{2} - \gamma_{1})M $ , Firm 2 makes no sales even though it is able to produce systems more efficiently ex ante. By improving its system, Firm 1 endogenously becomes such a formidable competitor that Firm 2 cannot profitably compete once Firm 1's investment in quality improvement is sunk.

The equilibria of the product improvement game show that one cannot rely on ex post market structure to infer which firm is the more efficient supplier. Product
superiority is endogenous and in our model either firm can invest to become the market leader. In particular, the less efficient Firm 1 can overcome its disadvantage by investing to improve its quality. Having done so, if $ r(z^{M}) \geq (\gamma_{2} - \gamma_{1})M $ , the more efficient Firm 2 cannot profitably invest to win the market even though it can supply a better product than its rival. Thus the “wrong” firm can emerge as the market leader. This indeterminacy exists for any value of the component price, w, even when the vertically integrated firm does not engage in technological tying to impede access by its more efficient rival. $ ^{19} $ The next section explores equilibrium outcomes when such strategies are feasible.

## 4 The Technological Tying Game

Firm 1 can avoid competition from Firm 2 by foreclosing Firm 2's access to component A, which we assume is available only from Firm 1. Foreclosure strategies that are based on a contractual tie, pure system sales, or refusals to deal in the upstream product may be counterproductive for Firm 1 if, as we suppose, there is a separate demand for component A that the upstream monopolist wishes to serve and price discrimination is difficult. In contrast, a technological tie that obstructs the ability of Firm 2 to offer a competitive system, or makes it expensive for consumers to assemble a system using component B from Firm 2, does not limit the ability of the upstream monopolist to pursue a mixed bundling strategy in which the firm both sells systems and makes separate sales of component A in a different market. For simplicity, we assume that a technological tie lowers the quality of a system made with component B from Firm 2 by a fixed amount $ \delta $ . That is, $ q_{2} = \gamma_{2} + z_{2} - \delta $ , while $ q_{1} = \gamma_{1} + z_{1} $ is unaffected by the tie. We assume that technological tying is costless for Firm 1 (other than the indirect cost of lost revenues from sales of component A to Firm 2), and consider only Firm 1's incentives to engage in this activity. Foreclosure is clearly inefficient because it eliminates competition from a more efficient producer. Nonetheless, Firm 1 may profit by foreclosing sales by Firm 2 under some circumstances.

Consider the following three-stage “technological tying game”, which amends the basic product improvement game studied in the previous subsection. In stage one the firms choose costly quality improvements $ z_{i} $ as before. In stage two Firm 1 is able to impose a technological tie that degrades Firm 2’s quality by an amount $ \delta \geq 0 $ .
In stage three the firms set prices $ P_{i} \geq w $ . Because the tie is costless to Firm 1, the game can have multiple equilibria when Firm 1 is indifferent to imposing a tie in the second stage. To avoid these trivial outcomes, we assume that Firm 1 does not impose a tie when it is indifferent, which would be the case if technological tying incurred an arbitrarily small cost. Similarly, we assume that Firm 2 sets $ P_{2} = w $ when it is indifferent to setting w or a higher price.

With vertical product differentiation, Firm 1 may profit by degrading Firm 2's quality only if it wins the system competition; i.e., only if $ q_{1} \geq q_{2} - \delta $ . Thus, it is sufficient to focus on technological tying strategies in which the parameter $ \delta $ is sufficiently large that technological tying always forecloses competition. A sufficient condition is

$$ A5:\delta>\bar{w}-\gamma_{1}. $$

Firm 2 can make sales in the third stage of the technological tying game only if $ q_{2}(\delta) > q_{1} $ . Firm 1's quality is no less than $ \gamma_{1} $ and its price is no less than w. If Firm 2 is to make sales, it can charge no more than $ P_{2} = q_{2}(\delta) - \gamma_{1} + w $ and its profit can be no greater than $ (\gamma_{2} + z - \delta - \gamma_{1})M - r(z) $ . This is negative if $ \delta > \bar{w} - \gamma_{1} $ . Thus Assumption 5 guarantees that there cannot be an equilibrium in which Firm 2 wins the market.

The following proposition establishes the existence of a unique equilibrium outcome of the technological tying game for sufficiently low values of the component price. When $ w < \gamma_{1} + z^{M} - r(z^{M})/M $ , Firm 1 invests $ z^{M} $ and Firm 2 is foreclosed from the systems market by either an actual or threatened technological tie. For low values of $ w \left(w < \gamma_{2}\right) $ , Firm 1 forecloses Firm 2 with a technological tie, in order to eliminate Firm 2's unimproved system as a competitive constraint. For intermediate values of w, Firm 1 does not impose a technological tie in equilibrium because Firm 2 poses no competitive threat unless it invests in product improvement, and Firm 2 is deterred from investing by the credible threat of a technological tie if it were to become a competitive constraint for Firm 1. Although the threat of a technological tie is critical to the equilibrium outcome, whether or not Firm 1 actually imposes a technological tie in equilibrium in this case is irrelevant for profits or welfare if the tie is costless. Finally, note that multiple equilibria can exist when $ w \geq \gamma_{1} + z^{M} - r(z^{M})/M $ . These equilibria are strictly ranked, with both firms better off, and consumers no worse off, when Firm 2 invests.

Figure 1 shows the possible equilibria for each value of the essential component price, w. The possible equilibria depend in general on the firms' initial quality asymmetry and are shown for $ r(z^{M}) \geq (\gamma_{2} - \gamma_{1})M $ and $ r(z^{M}) < (\gamma_{2} - \gamma_{1})M $ . The following proposition characterizes the equilibria more formally.

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