This essay examines strategic behaviour in network markets with particular attention to compatibility choice and the ability of a dominant firm to control that choice. A model of porting is developed that addresses this particular issue and allows us to analyze welfare outcomes and draw conclusions on policy. It also provides a novel interpretation of integration in a network market.
We also survey the activity of Microsoft in order to put flesh on the bones of theory and to provide motivation for the model. The behaviour of Microsoft has now, in consequence of the antitrust suit, been the subject of voluminous comment
We deal with markets displaying a Network Effect (NE). Network effects can be usefully divided into two direct and indirect forms. Network effects, particularly when they are direct, are also called network externality. The externality aspect of network effects will be the subject of further comment below.
A network effect is complementarity between my adoption of a good and yours: network effects stem from a consumer's desire for compatibility with other consumers' choices. Additional adoption both makes existing adopters better off (a total effect) and increases the incentive to adopt (a marginal effect).
Most prominent among these critics are Liebowitz and Margolis who have been particularly vocal in their opposition to the treatment of direct and indirect effects in the same way, particularly, when the talk is of networks externalities with all the implications of market failure [[#liebowitz_ea_1994#]] [[#liebowitz_ea_1999#]].
They suggest that in the case of indirect effects these externalities are in fact pecuniary: In fact, the pecuniary externalities that so perplexed Pigou walk and quack very much like the indirect network externalities that are waddling through the literature today
.
Liebowitz and Margolis are certainly right to point out the dangers of confusing pecuniary externalities and 'real' externalities. Pecuniary externalities are mediated via the price mechanism and therefore have no implications for welfare or of market failure, while 'real' externalities do have such implications. Nevertheless their strong conclusions such as the claim Many of the external effects of network size are pecuniary
) are not justified.
The distinction that needs to be introduced is between effects that operate through price and those that do not. In the first case there will be no externality but in the second there will. And as Church et al. [[#church_ea_2003#]] show in a wide variety of circumstances indirect network effects do give rise to 'real' externalities - precisely because the indirect network effects operate through the provision of greater variety or other similar non-price mechanisms.
Thus, it is safe to say that network effects of either type may give rise to real externalities and market failure. Nevertheless, as will be discussed below, ignoring the micro-foundations of the network effects can still be problematic in establishing welfare effects and understanding strategic behaviour.
This section provides summarizes some of the evidence of the PC Software market and the behaviour of Microsoft into a set of 'stylized' facts. Familiarity with some computing knowledge and terminology is assumed as is a grasp of basic history of the PC and associated software though some terms of relevance are defined below.
The history of computing in the modern era (from approximately 1970) can be seen as the provision of every higher level interfaces that provide ever greater levels of abstraction of the underlying system. This increase in abstraction is heavily tied to the increase in computing power. Every time a lower level system is encapsulated in an API, speed is reduced by the need to translate between this extra layer. Thus in the early days even a basic OS that would provide an interface to low level hardware was considered a luxury that represented a profligate use of system resources. Yet by the late 1990s systems such as Java had been developed that provide a whole other interface layer again on top of the underlying OS.
The ABE is has a close relation to the control of interfaces. Applications are written against the API of the underlying OS. If that API is open it will make it much easier to clone that API on another platform. This in turn will allow applications to be easily ported and an ABE to be easily overcome. Conversely a semi-open or closed API will make it much harder to overcome the ABE.
DOS/Windows 70% Windows 95 15% Windows NT 2% Other 13%
A new competitor 'born' on the Internet is Netscape. Their browser is dominant, with 70% usage share, allowing them to determine which network extensions will catch on. They are pursuing a multi-platform strategy where they move the key API into the client [browser] to commoditize the underlying operating system. They have attracted a number of public network operators to use their platform to offer information and directory services. We have to match and beat their offerings including working with MCI, newspapers, and others who are considering their products.
One scary possibility being discussed by Internet fans is whether they should get together and create something far less expensive than a PC which is powerful enough for Web browsing. This new platform would optimize for the datatypes on the Web. Gordon Bell and others approached Intel on this and decided Intel didn't care about a low cost device so they started suggesting that General Magic or another operating system with an non-Intel chip is the best solution
Before proceeding it will be necessary to establish some terminology and a basic framework.
There exist two complementary types of good. For simplicity they are denoted by: H ('Hardware'), S ('Software'). We take H as representing a complete system or platform and it need not be encapsulated in a single good. A piece of 'software' only work with a single H system. Hardware and software are purchased by end users/consumers whom we denote, as a group, by C.
There will be only limited number of H systems, normally only one or two even. This will be due to a combination of network effects and economies of scale (large fixed costs). The S market contains a large number of firms competing directly or in a form of monopolistic competition.
There may be many or a single supplier of a particular H system. Many suppliers of a single H is competition within a standard. Many proprietary H (with a single supplier therefore) is competition for a standard (this is more along the lines of [[#katz_ea_1985#]], see also [[#augereay_ea_2004#]]). When there is a single supplier of an H system we will refer to that supplier as the monopolist M. It is important to keep in mind that S1 and H1 do not refer to firms but to systems. The structure of the market within these systems is not yet specified. We may have anything from monopoly to something very close to perfect competition operating in each market
Diagram 1 C / | \ S1 S2 .... | | H1 H2 ....
Examples of such systems include:
The model I introduce is designed to focus on the ability to 'port'. That is the ability for an S firm to convert its product to run on a different H system from the one for which it was originally designed. Thus we are less interested here in the traditional concerns with the establishment of market share in the network market and the methods by which consumers form expectations
The ability to port is analogous to the question of compatibility. Adapting the diagram from above we have:
Diagram 2 C / | \ / A | \ S1 <-> S2 .... | B | H1 <-> H2 ....
Porting is indicated by the arrows at A is parallel to the issue of compatibility indicated by arrows at B.
Thus we can see the question of porting as analogous in an S/H market to direct compatibility in a simpler model with direct network effects. Given this close analogy it will be worth summarizing the conclusions reached in the general literature on compatibility and converters. The main points made by the literature are as follows:
A firm with a large installed base, or that would have a big expectations advantage, will thus tend to prefer incompatibility. A firm might most prefer in compatibility when (as a practical matter) any competition for expectations is all but over and it controls expectations.
The model shares some common inspiration with that of Farrell and Saloner [[#farrell_ea_1992#]], and that of Church and Gandal [[#church_ea_1992#]] but differs from either of them in important respects. The model of Farrell and Saloner investigates the consequences of the use of 'converters' in a market with (direct) network effects. Porting can be seen as similar to the provision of converters. However a porting model relates to a market where network effects are indirect and we have a two tier industry with S sitting on top of H. As we shall see this has important consequences for the model and for the focus of our analysis.
Church and Gandal meanwhile have a model with an industry structure more similar to our setup but their focus is on the behaviour of the S market and the equilibrium distribution of S firms across H systems. In their model the behaviour of H firms is not at issue and is not examined. Given that our particular interest is in the behaviour of M, the controller of a particular H system, this leads us again to have a markedly different approach. Nevertheless the framework, and some of the background results of the Church and Gandal model remain relevant.
A crucial point to our analysis is that network lock-in and its associated monopoly, even when well-entrenched, is not unassailable. As Bresnahan notes
... the theory [of networks] is sometimes
written so that there is permanent lock-in -- entry never overcomes the very high barriers
of the installed base effects. This is simply theory’s habit of rounding “difficult” up to
“impossible” for expositional clarity.
This elision of difficult and impossible, while useful for analytical ease, creates a crucial lacuna in understanding the behaviour of a firm such as Microsoft whose monopoly derives from (indirect) network effects. This is because it ignores - and thereby obscures - the primary motivation for much of such a firm's activities: the preservation and extension of the indirect network effects - the barriers to entry - that create its monopoly
... a mechanism existed to lower the entry barriers and make entry possible. That mechanism was divided technical leadership.
However, in practice, even in the case of a highly entrenched firm with a very large installed base, actual or potential competition will exist. Moreover technological change will not be entry agnostic - it can be used either to increase or decrease the barrier to entry. Given this fact, technological change and innovation takes on a strategic character and an incumbent firm may well have very large incentives to engage in activities that enhance its own position and reduce the possibility of the entry by competing firms and platforms.
There exist two types of complementary good: a 'Hardware' (H) good and a 'Software' (S) good
For a relevant example consider the PC OS market. Here, despite increasing returns to scale due to large up front fixed costs, the open Linux platform has many suppliers: at present count there are over 40 different Linux 'distributions' (distros) of which at least 5 have a major following (including the well-known commercial ones such as RedHat and Suse). Thus the Linux OS is a dramatic demonstration of competition within a standard (and in this case it results in a $$gamma$$ that is, in fact, zero).
Let us define:
We solve the model by a process of backward induction
Formally we have (proofs in the Appendix):
Where for convenience of notation we define:
(for convenience take $$x_1 = 2 mu^2 delta (m + 1), x_2 = mu^2 delta n$$). Substituting and rearranging gives:
In the simplest case $$m = 1, n =0$$ this yields:
Take $$x_i = delta mu^2 (y_i)/i, i = 1,3$$ and $$x_i = delta mu^2 (y_i -4) / i, i = 2$$ then
An explicit welfare analysis of the basic model is straightforward. It will be useful to distinguish between efficiency (relating to overall surplus) and surplus going to particular groups (e.g. consumer surplus). Intuitively the argument for welfare goes as follows:
Formally we have (full details in the Appendix):
Remark: Dead-weight costs for Welfare come from three distinct sources in this model:
The effects all operate in the same direction: lower cost of porting is associated with lower expenditure and lower prices from M. We therefore obtain very unambiguous and clearcut welfare results.
The cost of porting and providing converters is something that is readily acknowledged
Integration by M, and M's motivations for doing so, is an issue that arises frequently in the literature. The above model provides several reasons for M entry into the S market:
We will consider the different incentives of an integrated vs. an unintegrated S firm. In order to make the point as starkly as possible assume that basic profits are zero in the S market on H1 (e.g. just cover fixed costs). So M has no motivation to enter S for the profits in the S market.
Now an unintegrated S firm (of type $$beta$$) ports if and only:
Incentive for an integrated firm of type $$beta$$ differs because it takes account of effect on profits of hardware of a decision to port. Let an integrated firm control a mass of dx of S firms. Define $$Pi_p^i(beta)$$ as the net profits from porting of an integrated firm. Then we have the following result (details in the Appendix):
So an integrated firm is less likely to port. Moreover the corollary of this is that integration is allowing M to make more profits in its hardware business. Or, rather, the ability to prevent porting is allowing it to prevent erosion of its profits. In the marginal case, where an integrated S is indifferent between porting and not porting, the net profits in the S business from porting precisely equal (in absolute terms) the cost to M in the H business from the porting:
Moreover what this analysis shows is that there can be a gain to M of integrating above those that would obtain to its S division on its own. By this it is meant that in the case where M does not port M will be making more money than it would simply from porting. The net gain for M above that for an unintegrated S firm is the difference (when positive):
Thus M has incentives to integrate that go beyond the simple financial incentives of profits in the S sector, or even that relate (as in traditional analyses) to promoting the market for its complementary H system.
Furthermore in doing this initial calculation we have kept $$e$$ constant and have thus underestimated the benefits to M of not porting. Suppose that $$text(NGNP) >= 0$$ then we have the following ordering on profits:
where the superscript $$i$$ denotes profits in the integrated case, $$e^{**}$$ and $$e^{****}$$ denotes the optimal level of $$e$$ in the unintegrated case and integrated case respectively and $$p, bar(p)$$ represent the choice to port and not port respectively.
For M, integration with S firms is an alternative way by offering a unilateral method of reducing $$alpha$$ (by a decision simply not to port) in addition to the indirect route through $$c(e)$$. It therefore provides a way for M to make even greater profits than without integration
These 'extra' profits provide another motive for tying behaviour by M beyond those usually found in the literature. Normally anti-competitive behaviour is taken to occur when M leverages its monopoly in one market (H) into a monopoly in another, complementary, market (S) by tying the complement to its monopoly good
This was a substantial issue
For example Church and Gandal [[#church_ea_1992#]] (itself strongly based on [[#dixit_ea_1977#]]) starting from a CES utility function (NB: N is finite):
where $$y$$ is the consumer's wealth. They also show that in this case $$p_s = beta * s$$ where $$s$$ is marginal cost and hence is not a strategic variable as it is defined in terms of constants that are exogenous. This provides some justification for the treatment of $$p_s$$ in the model above.
Finally Church and Gandal's approach demonstrates that a more complete set of micro-foundations can be provided. This in itself would be an important extension to the model
Interpret cost $$e$$ as affecting quality of software. (perhaps change term in consumer welfare function for quality q from $$q = n_s$$ to $$q = n_s *(f(e)$$ where $$f(e)$$ measures degree of 'obfuscation' and $$f(0) = 1, f'(e) lt 0$$. This leads onto the M entry into S market story to make up for poorer quality of software that is now available. Story is: M 'obfuscates' interface to make porting harder but this also reduces quality of software written for H1 itself. So M itself has to start writing the software (as obfuscation does not affect it).
The structure of competition and the behaviour of M (via its effect on competition) may have an important impact on innovationThe third and final type of harm is the most familiar and fundamental. Microsoft has harmed the innovative process because it has limited competition, and competitive markets are, on balance, the best mechanism for guiding technology down a path that benefits consumers.
.
See also [[#gilbert_ea_2001:38#]] for a discussion of innovation in relation to the antitrust case
Information processing is a pervasive activity in our economy. Even small changes in the rate of innovation in this area can, over time, lead to large productivity gains and big improvements in the standard of living.
However innovation is often overlooked. There are several reasons for this. First innovation is 'hidden' since it is only affected indirectly via competition. Hence if one only looks at direct consequences the impact on innovation will be overlooked. Second, and more importantly, innovation is hard to analyze. How competition affects innovation is disputed
Nevertheless recent papers such as Farrell and Katz's [[#farrell_ea_2000#]] and [[#farrell_2003#]] have examined innovation in network markets explicitly. It would be interesting to add such an analysis to this model and the implications for welfare might be dramatic.
Consider the impact of innovation on $$c$$, the cost of porting. The motivation for such an investigation is provided by technologies such as Java (see section stylized facts section above) and the arrival of Web browser into the PC market in the mid 90s. Java, in particular, by inserting another layer of interface between the software application and the underlying OS would have radically reduced the cost of porting - practically to zero (though potentially at the cost of some extra initial development cost).
A reduction in the cost of porting could be modelled in framework used above as being reflected in an increase in $$e(c)$$ - the expenditure that M must make to achieve a particular level of porting cost. Attention would focus on a) the welfare effects of such an innovation b) the loss in profits suffered by M and the consequent incentive M would have to prevent or undermine such an innovation
In this paper we have presented a model of porting that providers new insights into the behaviour of a dominant firm in a network industry. The model illuminates several of the stylized facts presented earlier in the paper, in particular the significant level of integration by Microsoft. It demonstrates that a dominant firm may engage in considerable expenditure to maintain its position and the welfare consequences of so doing may be considerable. While we have focused on the case of Microsoft, there are many other areas that possess similar indirect network effects, for example payment card networks, to which the results of this paper would be relevant.
In the model the focus is on porting. Porting is the analogous activity in an INE market to compatibility choice in a DNE market. It has been shown how a dominant firm will attempt to raise the costs of porting to a competing platform.
Much of the literature - and much of the debate surrounding the Microsoft case - is hampered by the difficulty of establishing the welfare costs and competitive effects of the behaviour of a dominant firm
Attention is drawn to the implications for antitrust policy and enforcement. The results suggest that the major costs of monopoly behaviour may not arise through monopoly pricing. Rather they arise via costs a monopolist imposes on itself and others in pursuit of maintaining its monopoly and the consequences for innovation that arise from the chilling of competition.
$$t_2$$ is simultaneously the number of consumers on network H1 and the index of the marginal consumer - the consumer indifferent between the two networks. Noting that the number of software firms on H1 in period 1 and 2 = 1 we have $$t_2$$ defined by the following equation:
Profits for M in period 2 are $$P_2 = t_2 * p_2$$ so maximising gives:
We note for later reference that for plausibility we would want $$p_2 >= gamma$$. A sufficient condition is $$gamma \leq 1$$. So we have:
Assumption 1: $$gamma \leq 1$$.
Now marginal software firm (that is the firm indifferent between porting and not porting) has $$z = z^*$$ given by:
Now we can equate $$z^*$$ with $$alpha$$ here since all $$z$$ with $$z \leq z^*$$ will port. So combining this with the value for $$t_2$$ gives:
Imposing rational expectations ($$alpha^e = alpha$$ - actual number porting) gives
To ensure differentiability for $$c >= 0$$ we will assume $$(p_s * (2 + gamma)) / (4 + p_s) \leq 1$$.
So M's problem becomes $$max_(c,p_1) P_1(c) + delta * P_2(c)$$ where:
Because of the separable nature of the profit function maximising with respect to $$p_1$$ and $$e$$ can be performed individually. Maximising wrt $$p_1$$ is standard Monopolist profit maximization problem ($$q_1 = max(1,C - p_1) text(where) C = a + 2 - p_s$$) and yields $$p_1 = max(C - 1, C // 2)$$. Assuming $$a$$ sufficiently large this yields $$p_1 = C - 1 = a - p_s + 1$$.
What about $$c$$? Differentiating gives the FOC:
For an interior solution to be a maximum require:
Otherwise have maximum value at a boundary, either
Let total welfare/surplus be denoted by $$W$$ and consumer welfare/surplus by $$C$$. Let indices be used to indicate period.
Now $${:del alpha:} / {:del c:} lt 0$$. Combining this with the assumption (see Assumption 1) that $$gamma >= 1$$ we have:
Proposition 3: Assumption 1, $$gamma \leq 1$$ is a sufficient condition for $${:del W:} / {:del c:} lt 0$$ and therefore total welfare $$W$$ is maximized when $$e = c = 0$$.
Turning to consumer welfare we have:
Again using $${:del alpha:} / {:del c:} lt 0$$ we have:
Proposition 4: $$gamma \leq 4$$ is a sufficient condition for $${:del D:}/{:del c:} \lt 0$$ which in turn implies that consumer welfare is maximised with $$e = c = 0$$.
Incentive for an integrated firm of type $$beta$$ differs because it takes account of effect on profits of hardware of a decision to port. Specifically the incentive of a firm (or rather a mass of firms of measure dx) to port is:
Dividing through by $$dx$$ gives:
Since $${:d P_2:}/{:d alpha:} \lt 0$$ and $${:d alpha:}/{:d x:} > 0$$ we have $${:dP_2:}/{:dx:} \lt 0$$. Hence