Incentives to Innovate, Compatibility and Welfare in Durable Goods Markets with Network Effects

Incentives to Innovate, Compatibility and Welfare in Durable Goods Markets with Network Eﬀects

Thanos Athanasopoulos∗

June 12 2017†

Abstract

This paper investigates the relation between ﬁrms’ R&D incentives and their atti-

tude toward the compatibility of their potentially innovative future network goods with

direct competitors. My work explains puzzling compatibility agreements that market

leaders sign with small rivals and challenges the view that compatible standards lead

to free-riding in terms of ﬁrms’ incentives to invest. The paper also explains evidence

from a natural experiment in the United States, where dominant ﬁrms decreased their

R&D spending despite the higher future value appropriated from being incompatible.

Regarding welfare, I ﬁnd that a policy of mandatory compatibility leads to welfare

losses when consumers coordinate on the Pareto optimum.

∗Leicester Castle Business School. E-mail address: [email protected] †This paper is a revised version of the third chapter of my PhD Thesis submitted to the University of Warwick. Helpful comments have been provided by Claudio Mezzetti, Luis Cabral, Michael Waterson, Dan Bernhardt, Kenneth Binmore, Brahim Herbane, Bhaskar Dutta, Jacob Glazer, John Morrow, Elias Carroni, Sinem Hidir, Kirill Pogorelskiy, Zheng Wang, Gertjan Lucas, Kassa Woldesenbet, Parmjit Kaur, Alessandro Iaria, Niall Hughes, Maria Garcia de la Vega, Daniel Sgroi and Udara Peiris. I am also indebted to participants’ comments in EARIE 2015 Conference participants’ comments (08/2015 in Munich, Germany), in the RES 2016 Conference (03/2016 in Sussex, UK), in the MACCI Conference for Competition and Innovation (03/2017 in Mannheim, Germany), in the Conference of the Scottish Economic Society (04/2017) and at the De Montfort University (09/2016 and 12/2016). All errors in this work are solely mine.

1 1 Introduction

Market R&D spending is imperative for economic growth and development and an important governments’ target. Thus, incentivizing firms to spend and overcome the problem of appropriability of intellectual property due to the public good nature of knowledge but with- out neglecting to support competition is of the first order of importance.1 In this respect, a crucial academic and policy question is how standardization and (in)compatible standards relate to firms’ incentives to invest. This paper is at the heart of this question. I focus on markets that entail physical networks – consumers’ utility increases with the number of users that use compatible products – such as the market application software, which is an important multi-billion-dollar industry.2 In these markets, technological progress is rapid and innovation is carried out either by the initially dominant – in terms of market shares or other traits – or smaller firms. Consumers are key actors whose utility depends on other customers’ choice and face a coordination problem related to their purchasing decision.3 This paper will highlight the crucial role that customers’ equilibrium purchasing rule plays in firms’ R&D and compatibility choices. In particular, my work adds to the literature on standards regulation and is close to Cabral and Salant (2014). The authors in that article assume that standardization increases firms’ revenues, and their main contribution is that incompatible standards are a necessary evil due to decreased firms’ R&D incentives under compatibility. By expanding the analysis in markets with direct network externalities and considering, unlike their paper, consumers who affect the equilibrium, I show novel results. More precisely, when consumers coordinate on the Pareto optimum – and are reluctant to change – in equilibrium, competition in the product market is fiercer under incompatibility. Thus, the winner of the R&D race can appropriate higher profits under compatible standards. This future benefit from compatibility affects current R&D incentives. In particular, if firms are symmetric in their potential to in-

1See Belleﬂamme (2006). 2See Gandal (1994) for an article that identiﬁes network externalities in software industries. 3See Ellison and Fudenberg (2000).

2 novative, they invest more under compatible standards and are also better off supporting the compatibility of their future products. These results challenge the view that compatible standards decrease firms’ R&D spending. Contrary to conventional wisdom, according to which dominant firms do not support compatibility in markets with network effects (Malueg and Schwartz, 2006; Chen, Doraszelski, and Harrington, 2009; Cremer, Rey, and Tirole, 2000), I explain puzzling agreements that dominant firms sign with smaller competitors regarding the compatibility of their future products through their interrelated R&D and compatibility decisions.4 When consumers follow the equilibrium rule that induces them to pay higher prices – Ellison and Fudenberg (2000) call this rule the “eager equilibrium” – compatible standards no longer benefit the winner of the R&D race like Cabral and Salant (2014) assume. I show that although the innovator can appropriate higher profit under incompatible standards (potentially via the use of a patent), dominant firms that are less likely innovators invest less in R&D compared to the economy operating under compatibility. This suggests that market leaders decrease their current R&D spending in the anticipation of getting a patent in the future. The result explains evidence from a natural experiment that took place in the software market industry in the United States during the 90s. In that period, the patent system both made it cheaper for an innovator to get a patent and decreased the standard above which a patent was granted. These changes should – according to the incentive theory – have a positive effect on established firms’ R&D intensity – R&D spending over either the number of sales or revenue – due to the higher appropriated profit upon the use of the patent. However, this theoretical prediction failed to match firms’ R&D choices in practice. Webbink (2005) showed that Microsoft’s – a dominant firm in the productivity suites market during the 90s – propensity to patent was negatively correlated with its R&D relative to revenue.5 Bessen and Hunt (2007) also found a negative correlation between established firms’ R&D

4One example is the 2007 Microsoft-Novell agreement regarding the compatibility of their future products. For more details regarding the agreement, see http://news.microsoft.com/2007/02/12/microsoft-and- novell- announce-collaboration-for-customers/. 5See Webbink (2005), page 14.

3 intensity and their propensity to get a patent. I show that competitors who are more likely innovators, and consumers that follow the “eager” equilibrium rule lead dominant firms to decrease their R&D spending in the anticipation of getting a patent. Thus, this argument challenges the alleged benefit from the use of patents in boosting firms’ R&D incentives, at least prior to innovation (Bessen and Maskin, 2009). Moreover, this paper contributes to the debate regarding consumer welfare: is it welfare- enhancing to have compatible or incompatible standards? I find that welfare depends on the equilibrium rule that consumers use in their purchasing decisions. If consumers follow the “eager” equilibrium, compatible standards lead to lower prices and higher consumer surplus. In contrast, incompatible standards increase competition and lower prices when consumers coordinate on the Pareto optimum. Thus, antitrust concerns from dominant firms’ refusals to support compatibility, such as the 2008 EU vs Microsoft case, depend on consumers’ equilibrium rule related to their coordination problem.6 This paper is organized as follows: Section 1 discusses the related literature. Section 2 presents the Model. Section 3 looks at firms’ R&D spending under compatible and incompatible standards as well as their compatibility decisions. Section 4 provides an answer to the question regarding which economy maximizes consumers welfare: an economy that mandates compatibility or the one that adopts a laissez-faire approach. Section 5 concludes.

6For details regarding this case, see http://europa.eu/rapid/press-release_MEMO-08-19_en.htm.

4 Related Literature

This paper aims to contribute to several lines of research. First, it relates to the literature regarding dominant firms’ attitude towards the compatibility of their products when network effects are present. Absent innovation, seminal articles, such as Katz and Shapiro (1985) and Farrell and Saloner (1985) show that firms with larger networks refuse to facilitate compatibility with competitors. Cremer, Rey, and Tirole (2000) analyze competition between Internet backbone providers with asymmetric installed bases and predict that a dominant firm may want to reduce the degree of compatibility with smaller market players. Malueg and Schwartz (2006) investigate a dominant firm’s incentives to support compatibility with smaller competitors who are themselves compatible. They find that a market leader with a very high market share is less likely to support compatibility. Similar results appear in Chen, Doraszelski, and Harrington (2009), who consider a dynamic setting with product compatibility and market dominance. This work differs in that it allows for product innovation in industries with network effects; I find that dominant firms facilitate compatibility when consumers coordinate on the Pareto optimum, and the market leader and a smaller competitor do not differ much in their innovative potential. I find this result after endogenizing firms’ investment decisions; in particular, I look at the interplay between firms’ compatibility choice and their investment spending.

This observation takes us to the second literature that this work contributes to, which looks at the relationship between R&D incentives and compatibility. In the absence of innovative products and network externalities, Cabral and Salant (2014) showed that dominant firms free-ride over a smaller competitor’s R&D effort when there is one standard; they argue that standardization, at least early standardization may deter the market leader from investing. Thus, they conclude that incompatible standards may be a necessary evil. This paper differs from Cabral and Salant (2014), as apart from the standardization choice that leads to (in)compatible networks, I consider product innovation in markets with network

5 effects and the role of consumers’ behavior in firms’ R&D and compatibility decisions. My results somewhat complement those in Cabral and Salant (2014). I also find that firms’ R&D efforts are strategic substitutes and the market leader invests less under compatible networks when it is less likely to be inventive and consumers coordinate on the Pareto optimum. In contrast, firms invest more under future compatible networks when consumers coordinate on the Pareto optimum, and competitors have similar innovative potential. Regarding welfare, this paper also relates to the debate regarding the economy that maximizes welfare: is compatibility desirable for consumers and society? In a static environment, Alexandrov (2015) shows that an economy mandating compatibility decreases welfare. Similarly, in an infinite horizon model with stochastic demand, Chen, Doraszelski, and Harrington (2009) show that in the absence of innovative activity, a laissez-faire market is preferable for consumers. These articles contrast the traditional view that compatibility is welfare-increasing, as in Economides (2006). I find that welfare depends on the equilibrium rule that consumers use to resolve the coordination problem related to their purchasing decisions. If consumers coordinate on the Pareto optimum, incompatible networks benefit all consumers because of the higher degree of competition that decreases equilibrium prices. Thus, dominant firms’ potential refusals to support compatibility may not be anticompetitive and instead, such refusals may be welfare-enhancing. In contrast, when consumers coordinate on the “eager” equilibrium, consumers benefit from lower prices under compatible networks.

2 The Model

I consider a two-period model – time is indexed by t – where at date t=1, both a dominant ﬁrm – in terms of market shares – and a smaller competitor decide simultaneously how much to invest in R&D in order to improve product quality from the level q1 sold by the dominant ﬁrm at date t=1 to a higher level in the future. Firms’ research lines are independent and

6 their R&D spending is quadratic in the probability of successfully improving quality, which is random – indexed by q2D, q2R for the dominant ﬁrm and the smaller competitor, respectively

– with exogenous, continuous densities φD and φR on (q1,q¯2]. Besides the investment decision, at t=1 the two firms also choose what stance to take regarding the compatibility of their future products that are introduced at date t=2 when firms compete a la Bertrand. As in Malueg and Schwartz (2006), I assume that compatibility between the competitors’ new products needs bilateral consent and is a binary decision, while I exclude inter-firm payments for compatibility as they may lead to collusion.7 Also, note that the dominant firm’s products are not perfectly compatible; although new products are backward compatible – and allow their users to open and edit files that are created with older versions – old products are partially forward compatible. This means that users of the old product versions open files that are created with newer products with errors.8

On the demand side, there is a mass λ1 of consumers who own the dominant ﬁrm’s old version q1, and they are its installed base. Customers have unit – or zero – demand and the same taste for quality. Their utility is linear and depends partially on network externalities. For example, a customer’s date t=2 utility from using a product of quality q is q +αx, where α captures the extent of network externalities, and x is the number of other customers that use compatible products. At date t=2, consumers observe the compatibility regime as well as the quality of the competitors’ products and their prices, and they make their purchasing decisions, aiming to maximize their net utility. If the competitors facilitate compatibility and both succeed in improving product quality at date t=2, a customer that purchases any new product at

7Even if I allow for partial compatibility, the basic trade-offs and results would be intact. 8This is consistent with software industries; Microsoft’s products have traditionally been backward compatible but old versions have been only partially forward compatible. Also see: https://support.office.com/en-us/article/Open-a-Word-2007-document-in-an-earlier-version-of- Word-8FE47805-64A9-4CC5-A115-B148625FE043 as well as https://answers.microsoft.com/en- us/msoffice/forum/msoffice_word-mso_other/docx-incompatible-between-word-2010-and-word- 2007/2764c5ac-4f7c-4a6d-9419-9e37bddf82d8 and https://support.office.com/en-gb/article/Worksheet- compatibility-issues-f9c80c5b-5afc-40da-a841-b888746abd40?ui=en-US&rs=en-GB&ad=GB for examples where forward compatibility is only partial.

7 t=2 enters a network of maximum size, and her net utility is q2i + αλ1 − p2i (i = D,R).

Note that she joins a network of size λ1 regardless of other consumers’ purchasing decisions due to the backward compatibility of the dominant ﬁrm’s new product, and D, R index the dominant ﬁrm and the rival, respectively. If the customer chooses to keep the product

0 0 of quality q1, her utility is q1 + ραλ1x1 + αλ1x1 (x1 + x1 = 1), where x1 is the number of

0 customers that purchase a new product at date t=2, and x1 is the fraction of consumers

that stick to the product of quality q1. Also note that the parameter ρ (0 ≤ ρ < 1) captures the degree of forward compatibility of the old dominant ﬁrm’s versions. Under incompatible standards, consumers join their seller’s network. More precisely, if a consumer purchases

the dominant ﬁrm’s new product of quality q2D, her utility net of the price charged p2D is

0 q2D + αλ1(x1 + x1) − p2D, while if she purchases the rival’s product of quality q2R or sticks to

0 the dominant ﬁrm’s old product of quality q1, her net utility is q2R + αλ1(1 − x1 − x1) − p2R

0 or q1 + ραλ1x1 + αλ1x1, respectively. If the smaller competitor fails to succeed in its R&D eﬀort, I assume that it can still

sell a product of quality q1 at date t=2. Thus, if the dominant ﬁrm is the sole inventor at

t=2, a customer that purchases the market leader’s product of quality q2D under compatible

standards enjoys net utility q2D + αλ1 − p2D, while if she purchases the smaller competitor’s

good of quality q1, her net utility is q1 + αλ1 − p1R because of the compatibility between

the competitors’ new products, where p1R is the rival’s price for its good of quality q1. If the

0 consumer sticks to the dominant ﬁrm’s product of quality q1, her utility is q1+αρλ1x1+αλ1x1,

0 0 where x1, x1(x1 + x1 = 1) are the customers’ fractions that purchase any new product and those that stick to the dominant ﬁrm’s old version, respectively. In contrast, under

0 incompatible networks, a customer’s net utility from purchasing q2D is q2D + αλ1x1 + αλ1x1,

0 where x1, x1 are the fractions of consumers that purchase q2D and stick to the dominant ﬁrm’s q1, respectively. If the consumer purchases the product q1 from the smaller competitor, her

0 utility is q1 + αλ1(1 − x1 − x1) − p1R, while if she sticks to the dominant ﬁrm’s product of

0 quality q1, her utility is q1 + ραλ1x1 + αλ1x1.

8 Similarly, if the smaller competitor is the only innovator, a customer’s net utility from

purchasing the high-quality product under compatible standards is q2R is q2R+αλ1 − p2R regardless of which product other customers purchase, while if she sticks to the dominant

ﬁrm’s old version of quality q1, her utility is q1 + αλ1 because of the compatibility between the competitors’ products. Under incompatible standards, the customer enjoys utility

0 q2R+αλ1(1 − x1) − p2R if she purchases the product of quality q2R, while her utility from

0 0 sticking to q1 is q1 + αλ1x1, where x1 is the consumers’ fraction that sticks to q1 at date t=2.

00 If both firms succeed in their R&D effort, and ∆q = |q2D − q2R| indexes the absolute value of the innovative step at date t=2, all consumers purchase the high-quality good if the difference between the competitors’ prices for their new products at date t=2 is lower than

∗ 00 ∗0 00 p2 = ∆q and p2 = ∆q −αλ1 under compatible and incompatible standards, respectively. In

0 00 contrast, if the price diﬀerence between the competitors is higher than p2u = ∆q +αλ1 under incompatibility, no consumer purchases the good of superior quality. Similarly, if only one ﬁrm manages to improve product quality at date t=2, all consumers purchase the high-quality good under compatible and incompatible standards when the price the winner of the R&D

∗ 0 ∗0 0 0 race sets at t=2 is lower than p2 = ∆q or p2 = ∆q − αλ1, respectively, where ∆q = q2i − q1 is the magnitude of the innovative step from the introduction of the new product from seller

0 0 i. If, instead, the price faced by consumers is higher than p2u = ∆q + αλ1 under incompatible standards, no consumer purchases the superior product, as customers are better off by sticking to the dominant firm’s product of quality q1. In the coordination problem in markets that entail network externalities, there are multiple equilibria. As in Ellison and Fudenberg (2000), I consider two equilibrium rules that consumers may follow when coordinating their purchasing decisions under incompatible standards: First, consumers may coordinate on the Pareto optimum and purchase the high-quality product if the price difference between the

∗ ∗0 two sellers is at most p2 or p2 under compatible and incompatible standards, respectively – this equilibrium rule is the “reluctant” equilibrium in Ellison and Fudenberg (2000). Second, consumers may follow the “eager” equilibrium rule (Ellison and Fudenberg, 2000), and they

9 purchase the high-quality good if the price diﬀerence between the competitors is at most p2u

0 or p2u under compatible and incompatible networks, respectively. Firms aim to maximize the present value of their total expected profit; at t=1, both firms decide how much to invest and whether or not they will support the compatibility of their future products, while at t=2 they compete a la Bertrand. In particular, the dominant firm aims to maximize

2 maxsD δE[λ1p2D|Ai]P rob(Ai) − sD/2, (2.1)

where E[λ1p2D|Ai] is the conditional expectation of the market leader’s future revenue – conditioned on the set of states Ai that the market leader’s revenue is positive. Also note that in consistence with software markets, the marginal cost of production for any product version is normalized to zero.

3 Market Outcome

There are two main points from the equilibrium analysis. The first is that dominant firms may invest more under compatible standards irrespective of how consumers resolve the coordination problem regarding their purchasing decisions. The second point is that there are conditions under which both market leaders and small competitors support compatibility, providing an explanation to compatibility agreements signed in reality. To understand these results, an important observation is that the equilibrium prices at date t=2 depend on whether compatible or incompatible networks arise. Under compatibility, the higher-quality seller typically sets a price that is equal to the quality differential between the competitors’ products (∆q00 or ∆q0 when either both firms or only one competitor succeed in their R&D efforts, respectively), and this leads the other firm to set a zero price. These prices arise in equilibrium except for one case when the smaller competitor wins the R&D race, and consumers coordinate on the eager equilibrium. This is because all consumers

10 enter a network of the same size if they purchase a new product regardless of their seller’s identity. When incompatible networks arise, the equilibrium rule that consumers use to resolve the coordination problem regarding their purchasing decisions aﬀects the equilibrium prices.

“Reluctant” Equilibrium

If consumers follow the “reluctant” equilibrium rule, and they are less willing to switch from the dominant firm’s old version and purchase a new product, the equilibrium date t=2 price the winner of the R&D sets is lower than the price under compatible standards. This is because under the Pareto rule, a consumer purchases a high-quality good even if all other customers either stick to the dominant firm’s old version or purchase the competitor’s new date t=2 good. For example, if the dominant firm is the R&D winner, a consumer that purchases its new

0 product of quality q2D under incompatible standards enjoys utility q2D +αλ1x1 +αλ1x1 −p2D, while her utility by purchasing either the competitor’s q2R or stick to q1 is q2R + αλ1(1 −

0 0 x1 − x1) − p2R and q1 + ραλ1x1 + αλ1x1, respectively. When consumers coordinate on the Pareto optimum, they purchase the dominant ﬁrm’s new product even if all other customers

0 0 make an alternative purchasing decision (1 − x1 − x1 = 1 or x1 = 1); the dominant ﬁrm’s optimal price choice is:

00 p2D = ∆q − αλ1, leading its competitor to set a zero price, and consumers purchase the higher-quality product

9 q2D. Similarly, if only one ﬁrm manages to succeed in its R&D eﬀort, the equilibrium price the R&D winner charges consumers – who purchase the new product even when all others

9The same equilibrium prices obtain when the smaller competitor wins the R&D race.

11 stick to the dominant ﬁrm’s old product of quality q1– is

0 p2D = ∆q − αλ1.

These findings are consistent with Cabral and Salant (2014), who assumed that compatibility increases industry profits absent network effects. When consumers coordinate on the Pareto optimum in markets with network externalities, compatible standards allow the winner of the R&D race to appropriate higher profits. This fact also affects firms’ R&D spending and their compatibility stance at date t=1.10 The next proposition summarizes firms’ R&D incentives as well as conditions under which compatibility is supported when consumers follow the “reluctant” equilibrium rule:

Proposition 1. When consumers coordinate on the Pareto optimum, both firms invest more under compatible standards when their innovative potential is not too different. In this case, firms sign the compatibility agreement.

Proof. See the Appendix

The proposition offers novel results regarding firms’ R&D incentives under compatible and incompatible standards. Dominant firms’ attitude toward investment depends on their relative innovativeness – compared to the competitor’s potential to be the future innovator. When consumers coordinate on the Pareto optimum and firms are symmetric – or not too different – regarding their innovative potential, firms invest more under compatible rather than incompatible standards. This happens because the innovators’ higher future appropriated profit under compatibility triggers higher incentives to invest for both competitors, who

10See the Appendix for the standard ﬁrst-order conditions that provide the competitors’ R&D optimal spending under future compatible and incompatible standards.

12 also benefit from supporting compatibility. Firms’ mutual support to compatibility stems from their expected benefit for those states they are both successful in their R&D effort – these states are reached with higher probability under compatible standards, as both firms invest more – that outweighs their loss for those states firms are the sole innovator. Moreover, firms that are more likely innovators tend to invest more under compatible standards, and although they would be better off if compatibility was supported, compatibility is blocked by less innovative firms. These results contrast with Cabral and Salant (2014), who showed that dominant firms free-ride on the competitor’s R&D effort under compatible standards. The proposition also rationalizes compatibility agreements that dominant firms sign with smaller competitors, such as the Microsoft-Novell agreement highlighted in the introduction.

“Eager” Equilibrium

When consumers follow the “eager” rule, the equilibrium date t=2 prices are higher under incompatible standards than when compatibility is supported. This is because consumers are willing to purchase a new product even if the innovative step from its introduction is not particularly high. In fact, under the “eager” equilibrium, customers are “eager” to purchase a new product and follow their peers – in equilibrium – by purchasing it at date t=2. This fact decreases the alternative payoﬀ from any other choice and thus, the equilibrium prices are higher under incompatible standards. In the example above where the dominant ﬁrm is

the R&D winner, consumers are eager to purchase the product of quality q2D (x1 = 1), and the dominant ﬁrm’s optimal price is:

00 0 p2D = min{∆q + αλ1, ∆q + αλ1(1 − ρ)},

13 11 forcing its competitor to set a zero price and consumers to purchase q2D. Note that if the dominant firm is the only firm that succeeds in its R&D effort, the equilibrium price it charges consumers is

0 p2D = ∆q + αλ1(1 − ρ).

12These equilibrium prices are always higher than the price charged by the R&D winner under compatible standards, and contrast with Cabral and Salant (2014), who assumed that compatibility increases industry profits. In markets with network effects, whether (in)compatible standards actually allow the winner of the R&D race to appropriate higher profits is endoge- nous to the equilibrium rule that consumers use, which also affects firms’ R&D spending and their compatibility stance at date t=1. The higher date t=2 equilibrium prices under incompatible networks affect the competitors’ R&D incentives at date t=1 as well as which stance to take regarding compatibility, and the next proposition analyzes firms’ choices:

Proposition 2. When customers coordinate on the “eager” equilibrium, incompatible networks arise; less innovative dominant ﬁrms invest more under compatible standards.

Proof. See the Appendix

When consumers coordinate on the “eager” equilibrium, firms do not find it optimal to facilitate future compatibility. This is due to the fact that the profits that the innovator can appropriate are now higher under incompatible standards compared to when compatibility is supported. Interestingly, less innovative dominant firms spend more under compatible standards, and the magnitude of the difference between their R&D investment under compatible and incompatible standards is decreasing in the probability of being more innovative than

11 00 Similarly, the smaller competitor’s optimal price at date t=2 if it is the R&D winner is p2R = ∆q +αλ1. 12Similarly, if the smaller competitor is the only ﬁrm that succeeds in its R&D, the equilibrium price it 0 charges consumers is p2R = ∆q + αλ1.

14 their rival. Thus, this paper offers new insights related to the natural experiment observed in the United States when firms decreased the intensity of their R&D spending in the anticipation of getting a patent. I argue that innovative competitors and the equilibrium rule that consumers follow drive this result in markets that entail network externalities. My findings also provide novel results in the literature on standards regulation that predicts that incompatibility increases firms’ R&D incentives at least prior to innovation (Cabral and Salant, 2014 and Bessen and Maskin, 2009).

4 Welfare

After investigating firms’ investment and compatibility decisions, it is important to understand the effects of the different economic structures on consumer surplus. The next proposition aims to contribute to the debate on whether compatible rather than incompatible standards lead to higher future degrees of innovation.

Proposition 3. Incompatibility is beneﬁcial for consumers when they coordinate on the Pareto optimum. Compatible standards beneﬁt consumers when they coordinate on the “eager” equilibrium.

Proof. See the Appendix

Consumers’ equilibrium behavior affects the degree of competition in the market and the welfare effects from (in)compatible standards. More precisely, when consumers coordinate on the “eager” equilibrium, competition under compatible networks becomes fiercer. This decreases the equilibrium prices and benefits all consumers. In contrast, when consumers

15 coordinate on the Pareto optimum, incompatible networks lead to more aggressive competition. This fact implies lower prices and higher consumer surplus for all groups compared to compatible standards. Thus, dominant ﬁrms’ refusals to support compatibility with smaller rivals, such as the EU vs. Microsoft case highlighted in the introduction do not necessarily decrease consumer surplus. Instead, incompatible standards may lead to a more competitive environment, which beneﬁts consumers rather than provides examples of anticompetitive practices and abuse of dominance.

5 Concluding Remarks/ Discussion

This paper offers new insights in how standards relate to firms’ incentives to invest in R&D. I find that when consumers coordinate on the “eager” equilibrium, market leaders decrease their current R&D spending in the face of innovative competitors despite the anticipation of being incompatible in future. This result explains why established firms decrease their expenditure in scenarios prior to innovation, such as the situation in the United States highlighted in the introduction. When consumers coordinate on the Pareto optimum, firms with similar innovative potential increase their R&D spending under compatible standards. This fact challenges the accepted role of incompatible standards of promoting innovation – at least in a static innovation scenario. Moreover, increased R&D spending leads competitors to facilitate compatibility regarding their future products. Thus, the paper explains compatibility agreements, such as the Microsoft-Novell agreement mentioned in the introduction. In addition to that, consumers benefit from incompatible standards when they coordinate on the Pareto optimum. Thus, a dominant firm’s refusal to facilitate compatibility is not necessarily anticompetitive, as the degree of competition may be greater under incompatibility. In contrast, if consumers coordinate on the “eager” equilibrium, they benefit from compatibility, as incompatible networks lead to a lower degree of competition and higher equilibrium prices.

16 Future work can look at the role of competition in this setting; what is the effect of more firms that can be potential innovators on investment/innovation and firms’ compatibility decisions? Moreover, it would be interesting to investigate how the investment/compatibility decisions would alter in the face of stochastic or endogenously evolving demand.

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6 Appendix

Optimal Prices

Compatible networks

If the consumer gets any of the competitors’ new products, her utility net of the price charged is:

q2i + αλ1 − p2i, i = D,R, where D,R denote the dominant ﬁrm and its competitor, respectively. Similarly, her utility by sticking to q1 is:

0 q1 + αλ1(ρx1 + x1),

where p2i is the equilibrium price at t=2 that induces consumers to purchase the higher quality product q2i. Thus, regardless of consumers’ coordination rule, the equilibrium date t=2 prices are:

00 p2i = ∆q , p2j = 0, and consumers purchase the high-quality product. If only one ﬁrm innovates, the date t=2 equilibrium price is:

0 p2i = ∆q .

21 Incompatible Networks

Consumers purchase the dominant ﬁrm’s higher quality good q2i if their utility surpasses their utility by purchasing either the competitor’s product or sticking to the dominant ﬁrm’s q1 :

0 0 0 q2i + α(λ1x1 + x1) − p2i ≥ max{q2j + αλ1(1 − x1 − x1) − p2j, q1 + αλ1x1 + ραλ1x1}.

When consumers coordinate on the “eager” equilibrium (x1 = 1), the dominant ﬁrm’s optimal price is:

00 0 p2D = min{∆q + αλ1, ∆q + αλ1(1 − ρ)}, p2R = 0, and consumers purchase the higher-quality product.13 In contrast, if consumers coordinate

0 0 on the Pareto optimum (1 − x1 − x1 = 1 or x1 = 1), the optimal dominant ﬁrm’s price is:

00 p2D = ∆q − αλ1, p2R = 0, and consumers purchase the dominant ﬁrm’s new product.14 If only the dominant ﬁrm innovates, consumers purchase its new product if:

0 0 0 q2D + α(λ1x1 + x1) − p2i ≥ max{q1 + αλ1(1 − x1 − x1) − p1, q1 + αλ1x1 + ραλ1x1}.

The equilibrium prices are

0 p2i = ∆q + αλ1(1 − ρ), p1 = 0,

13 00 If the smaller competitor is the winner of the R&D race, her optimal choice is ∆q + αλ1 if consumers coordinate on the “eager” equilibrium. 14 00 The same equilibrium price ∆q − αλ1 comes up when the smaller competitor is the winner of the R&D race, and consumers coordinate on the Pareto optimum.

22 0 p2i = ∆q − αλ1, p1 = 0,

if consumers coordinate on the “eager” equilibrium (x1 = 1) and the Pareto optimum (1 −

0 0 x1 −x1 = 1 or x1 = 1), respectively. Similarly, if the smaller competitor is the sole innovator, consumers purchase its new product if:

0 0 q2i + αλ1(1 − x1) − p2i ≥ q1 + αλ1x1.

Thus, the equilibrium prices are

0 ∆q + αλ1 when consumers coordinate on the eager equilibrium and

0 ∆q − αλ1 if consumers coordinate on the Pareto optimum. Firms’ Optimal R&D eﬀort Compatible Networks The dominant ﬁrm’s maximization problem is:

∗ 2 ∗ maxsD δsD(1 − sR )A + δsDsRP rob(q2D ≥ q2R)B − sD/2, where

0 A = λ1E(∆q ),

00 B = λ1E[∆q |q2D ≥ q2R],

∗ and sR is the smaller competitor’s optimal R&D effort. Standard first-order conditions provide us with the dominant firm’s reaction function:

∗ sD = δ[−A + P rob(q2D ≥ q2R)B]sR + δA. (6.1)

23 Similarly, the smaller competitor maximizes its expected proﬁts, taking into consideration that the market leader is doing the same:

∗ ∗ 2 maxsR δsR(1 − sD)A + δsRsDP rob(q2R ≥ q2D)B − sR/2.

Again, ﬁrst-order conditions provide us with the smaller competitor’s eﬀort as a function of the market leader’s optimal choice:

∗ sR = δ[−A + P rob(q2R ≥ q2D)B]sD + δA. (6.2)

After substituting the smaller competitor’s eﬀort in the dominant ﬁrm’s reaction function, one gets: 2 ∗ δA + δ [−A + P rob(q2D ≥ q2R)B]A sD = 2 . (6.3) 1 − δ [−A + P rob(q2D ≥ q2R)B][−A + P rob(q2R ≥ q2D)B]

Incompatible Networks Similarly to the case that networks are compatible, under incompatible networks, the two ﬁrms’ maximization problems are:

0 0∗ 0 0 0∗ 0 02 max 0 δsD(1 − sR )A + δsDsR P rob(q2D ≥ q2R)B − sD/2, (6.4) sD

0 ∗0 00 0 0∗ 0 02 max 0 δsR(1 − sD)A + δsRsDP rob(q2R ≥ q2D)B − sR /2, (6.5) sR

where the first and the second problem is the dominant firm’s and the competitor’s maximization problem, respectively. Standard first-order conditions provide us with the firms’ reaction functions:

0 0 0 0∗ 0 sD = δ[−A + P rob(q2D ≥ q2R)B ]sR + δA , (6.6)

0 00 0 0∗ 00 sR = δ[−A + P rob(q2R ≥ q2D)B ]sD + δA , (6.7)

24 where

0 0 A = E[λ1(∆q − αλ1)],

A00 = A0 ,

0 00 B = E[λ1(∆q − αλ1)|q2D ≥ q2R],

and consumers coordinate on the Pareto optimum, while

0 0 A = E[λ1[∆q + αλ1(1 − ρ)],

00 0 A = E[λ1(∆q + αλ1)]

0 00 B = E[(λ1(∆q + αλ1)|q2D ≥ q2R],

0 if customers coordinate on the “eager” equilibrium. After substituting sR to equation 6.6, one gets the dominant ﬁrm’s optimal eﬀort under incompatible networks:

0 2 0 0 0 ∗0 δA + δ [−A + P rob(q2D ≥ q2R)B ]A sD = 2 0 0 0 0 (6.8) 1 − δ [−A + P rob(q2D ≥ q2R)B ][−A + P rob(q2R ≥ q2D)B ] when consumer coordinate on the Pareto optimum. Similarly, the dominant ﬁrm’s optimal R&D eﬀort is:

0 2 0 0 00 ∗0 δA + δ [−A + P rob(q2D ≥ q2R)B ]A sD = 2 0 0 00 0 (6.9) 1 − δ [−A + P rob(q2D ≥ q2R)B ][−A + P rob(q2R ≥ q2D)B ] when consumers coordinate on the “eager” equilibrium. I will assume throughout that δ = 1, and ρ = 0 (but the results can be generalized for any discount factor and any degree of compatibility). If we observe that B0 = B + c,A0 = A+c (c is positive when consumers coordinate on the eager equilibrium and negative when consumers coordinate on the Pareto optimum), the dominant ﬁrm invests more under

25 compatible standards if and only if:

0 sD > sD ⇔

Π = −c(1 − 2A − c) − pc(B + c + A) + c[A2 − A(1 − p) − pBA + p(1 − p)B2](1 − 2A + 2pB)−

−c(2Ap − 2Bp2 + Bp − pBc − A − B + pB + pc)[A + c + (−A − c + pB + cp)(A + c)] > 0, where p is the probability that the dominant ﬁrm will be more innovative than its competitor

Prob(q2D ≥ q2R). The function Π is continuous with respect to the probability of the dominant firm being more innovative than the rival should both firms succeed in their R&D effort Prob(q2D ≥ q2R). The derivative of function Π with respect to the probability p is given by the following (after some algebraic manipulation): Π0 = K + Rp2 + Lp, where:

K = −c(B−B2)−c2−cA−2cBA(2B−A)+(−2Ac−2Bc+Bc2−c2)(−A2−2Ac)−c2+A+c)+

+c(AB + Ac + B2 + Bc)(A + c).

R = −4cB3 − 2cB3 + 4Bc(B + c)(A + c) + 2Bc(A + c)(B + c),

L = 4B3c − 2B2c + 4AB2 + 4ABC(1 − A) − 4ACB2+

26 +(−4ABc − 4Ac2 − 4B2c − 4Bc2 + 2B2c2 + 2Bc3 − 2c3)(A + c)

Proof of Proposition 1 When consumers coordinate on the Pareto optimum (c<0), one gets that:

R < 0, K < 0, L > 0, and Π0 (p) > 0 ⇐⇒ p > p∗.

For example, if the two ﬁrms are equally likely to be more innovative in the future, and A=1,

∗ ∗ B=0.8, c=-0.3, both ﬁrms invest more under compatible standards (sD = sR = 0.625 >

∗0 ∗0 0.482 = sD = sR ), while if the dominant ﬁrm is more likely to innovate (p = 0.8), the

∗ dominant ﬁrm invests more under compatible standards and the diﬀerence increases (sD =

∗0 0.917 > 0, 597 = sD). In contrast, the smaller competitor invests more under incompatible

∗0 ∗ standards when p = 0.8 (sR = 0.3821 > 0.2297 = sR). Note that when the innovative potential of the two firms is not too different, both firms sign the agreement. In the example above (p=0.5), firms’ profits are higher under compatible standards. When the two firms’ innovative potential differs (for example p = 0.8), incompatibility prevails although the firm that is a more likely innovator would be better off if compatibility was supported. Proof of Proposition 2 If consumers coordinate on the eager equilibrium:

R > 0, L < 0 and Π0 (p) < 0 ⇔ p < p∗.

It is straightforward to see that the dominant firm’s difference in spending between compatible and incompatible networks is decreasing in the probability it is a more likely innovator. For example, if p=0.4 (and the other values are as in Proposition 1), the dominant firm ∗ ∗0 invests sD = 0.495 under compatible networks, while it invests less (sD = 0.4615) under

27 incompatibility. In contrast, when the two ﬁrms are equally likely innovators, both ﬁrms in- ∗ ∗ ∗0 ∗0 vest more under incompatibility (sD = sR = 0.625

CS = q2i + αλ1 − [q2i − q2j] = q2j + αλ1,

0 CS = q2i + αλ1 − [q2i − q2j − αλ1] = q2j + 2αλ1, respectively. It is clear that consumers beneﬁt from incompatible networks. Similarly, if consumers coordinate on the “eager” equilibrium, their surplus under incompatible standards is:

0 E(CS) = q2i + αλ1 − [q2i − q2j + αλ1] = q2j, while their surplus under compatibility is:

CS = q2j + αλ1.

Thus, compatible networks are always beneﬁcial for consumers when they follow the “eager” equilibrium rule.