Bundling of RAND-committed Patents

Anne Layne-Farrar*

Michael A. Salinger**

June 2015

Abstract: We extend a simplified version of the Gilbert-Katz (GK) model of patent bundling to

incorporate RAND commitments and then use the model to consider whether a patent holder violates a

RAND commitment if it ties a license to its RAND-encumbered patents to licenses for patents on which it

has not made a RAND commitment. In the GK model, the ability to engage in patent tying makes a

patent-owner willing to engage in long term contracting that prevents it from charging “hold-up”

royalties. But a RAND commitment accomplishes the same objective; and the tying of licenses to patents

without RAND obligations to RAND-encumbered patents creates a risk of reneging on the RAND

commitment. Mixed bundling, where the licensor offers licensees the option of taking a license to

RAND-committed patents only or taking a license to the full portfolio honors the patent-holder’s RAND

commitment provided that the royalty for the RAND-encumbered patents is RAND (regardless of the

royalty for the larger portfolio of patent rights). (Pure) patent bundling/tying is, however, a common

practice that often has sound efficiency justifications. A patent-holder can engage in pure bundling/tying

of licenses to RAND-encumbered and non-RAND encumbered patents and still honor its RAND

commitments provided that it charges a royalty that would be RAND for the RAND-encumbered patents

alone. The patent owner cannot deduct the value of non-RAND committed patents from the license fee

for the bundle and argue that it has honored its RAND commitment as long as the difference is RAND for

the RAND-committed patents.

Key words: patents, licensing, bundling, tying, RAND, FRAND, intellectual property

JEL classifications: O3, K21

* Charles River Associates and Northwestern School of Law

** Boston University, Questrom School of Business

We thank Bernhard Ganglmair, John Harkrider, and Elizabeth Wang for helpful suggestions. We are also grateful to Google for financial support for this project. The opinions represent the views of the authors and not those of any organization.

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I. Introduction

In this paper, we address the inter-relationship between two common practices in the licensing

of intellectual property: RAND commitments and patent bundling. Patent bundling (or, more precisely,

pure patent bundling) is the practice of licensing patents only in bundles rather than offering licenses to

individual patents on an à la carte basis. A RAND commitment is a commitment to license technology on

“Reasonable and Non-Discriminatory” terms.1 The question we address is whether, once a patent owner

makes a general commitment to license its patents to all licensees on RAND terms, can it offer those

patents solely in a bundle with other patents? If it can, what are the implications of the RAND

commitment for the royalties it can charge for the bundle? Alternatively, does a RAND commitment on a

patent necessarily entail an obligation to offer it on an unbundled basis?

To address the general issue of bundling RAND-committed patents, one must first understand

why patent bundling is such a common phenomenon, what effect patent bundling has on licensing

terms, and why patent holders make RAND commitments. While there is a substantial and growing

economics literature on bundling in general and some of it specifically focuses on the bundling of

intellectual property (like computer software, music, and video entertainment), the formal literature on

patent bundling is remarkably thin. A notable exception is Gilbert and Katz (2006) (henceforth “GK”),

who discuss why the intrinsic features of patents differ from the assumptions of the existing economics

literature on bundling. They present a formal model of bundling based on assumptions designed to

capture some key features of patent licensing. As we explain in more detail below, their results seem to

suggest that patent bundling does not pose a public policy concern and that the case for forcing

companies to license patents on an à la carte basis is weak. Gilbert and Katz did not, however,

incorporate RAND commitments into their model. To assess whether tying RAND-committed and non-

RAND-committed patents violates the RAND commit, we incorporate a RAND commitment into a

simplified version of the GK model.

Many standards development organizations (SDOs) ask their members to first disclose any

patents that might be considered essential for compliance with a standard under development and

second to then promise to license any such essential patents on RAND terms and conditions to anyone

requesting a license. Thus, patent holders cannot refuse to license RAND-committed patents, nor can

they license them solely on an exclusive basis. In addition, the “reasonable” element of RAND caps

licensing rates to the value that the patented technology conveys to the licensee, again unlike patents

without RAND encumbrances where the patent holder can seek whatever the market will bear,

including rates that capture the licensee’s costs of switching to an alternative technology and that

capture the value of sunk costs that the licensee might have incurred to practice the patent prior to

obtaining a license.

1 As we understand the nomenclature, RAND is synonymous with “FRAND,” which is an acronym for “Fair,

Reasonable, And Non-Discriminatory.” Licensing terms that are both “reasonable” and “non-discriminatory” are necessarily “fair.”

3

Patent pledges are not limited to patents essential for cooperative SDO standards in large part

because SDOs are not the only way that standards emerge. In game theoretic terminology, standard

setting is an example of a “coordination game.” Multiple Nash equilibria exist (ex ante) for most industry

technology paths, and there are both private and social benefits from having the industry agree on one.

In this regard, the term “equilibrium” is misleading, as there is no reason to believe that the market will

naturally arrive at one of the so-called equilibria if all firms independently select which of the

alternatives to conform to.2 SDOs are a forum for explicit coordination, but standards can emerge

organically in the market as well. And coordination can sometimes occur without any explicit

coordination – either in SDOs or via organic evolution in the marketplace. A company might propose a

standard based on its proprietary technology hoping that the rest of the industry will coalesce around its

proposal. A well-known recent example is the standards competition with respect to DVD technology,

with Sony pressing its Blu-Ray laser technology and Toshiba promoting its HD-DVD technology. A RAND

(or other patent) commitment in such settings can have the same economic effect as in an SDO setting.

The patent owner makes the commitment in order to increase the likelihood that the industry will

coalesce around the technology rendering it an industry standard, and other industry participants then

rely on the patent owner’s commitment not to behave opportunistically before investing sunk costs to

develop products based on the standard. As a result, a commitment not to engage in patent hold-up can

be just as necessary for securing investment that results in licensed use of the patent outside of

cooperative standards as it is within SDOs for declared SEPs. Hence, firms often voluntarily commit

publicly to license certain of their patents that are not related to a standard established by an SDO on

RAND terms and conditions.3

The remainder of this paper is organized as follows. Section II discusses the economics of

bundling in general. Section III then turns to patent bundling with a focus on the GK model. In Section IV,

we present a model of the licensing of a single patent in a setting that otherwise reflects a simplified

version of the GK assumptions and show how to incorporate RAND commitments into that model. The

model brings out a key distinction between what we term “value-based royalties” and “cost-based

royalties.” The former captures the value created by the technology assuming that inventing around the

technology is not feasible. A cost-based royalty is one that is low enough to eliminate a patent-user’s

incentive to try to invent around the patent. The conditions when a patent owner would choose a value-

based as opposed to a cost-based royalty are more complicated than one might initially expect. In

Section V, we next extend that model to incorporate the licensing of two patents where the patent

holder has made a RAND commitment on just one. We do so in two ways. First, we assume that both

technologies are necessary to capture economic value (where the alternative ways to gain access to the

technology are (1) licensing the patents and (2) investing in R&D to invent around them). Then, we

consider the possibility that a licensee could capture value with just the technology obtainable through

2 A notable example in which the industry did not coordinate around a standard was the early generations

of cellular telephones in the United States. 3 The Program for Information Justice and Intellectual Property, at Washington College of Law, maintains

a database of more than 150 public such non-SDO patent pledges: http://www.pijip.org/non-sdo-patent-commitments/. Contreras (2014) and Elhauge (2015) discuss the legal basis for enforcing RAND commitments made outside an SDO setting, see. For other discussions of non-SDO patent pledges, see Layne-Farrar (2014) and Harkrider (2014).

4

the RAND-committed patent but could capture additional value with both technologies. Section VI

discusses policy implications.

Linking our analysis to the existing literature on tying, it is important to recognize that the

“single rent”4 principle lies at the heart of arguments economists tend to make for why tying is generally

not anticompetitive. However, a RAND commitment alters the key assumption underlying the single

rent principle and therefore makes tying of RAND-committed patents potentially problematic. In

particular, we find that tying RAND-committed patents to non-standard-essential patents, or even tying

RAND-committed patents across distinct standards, can provide a means to increase licensing rates and

thus side-step a RAND commitment.

As we explain below, our findings do not necessarily preclude bundling. To the contrary, the

patent holder can practice mixed bundling, offering licensees the option of taking a license to the RAND-

committed patents only or to a broader portfolio including non-RAND committed patents. Due to the

efficiency gains so common with portfolio licensing, we would expect to find lots of bundled licenses

even when all licensors offer the option of RAND-patent only licenses. Second, if the total royalty for the

bundle would be individually reasonable and non-discriminatory for each applicable RAND commitment

and each standard covered by such commitments, and the other terms of the license are similarly

reasonable and non-discriminatory, then bundling does not violate RAND or impose anticompetitive

harm on licensees. In other words, if the patent holder is willing to “throw in” the other patents – either

non-RAND committed patents or patents that are committed for separate and distinct standards – for

free, such that the licensing terms for the bundle would be RAND with or without the inclusion of the

additional patents, the mere inclusion of additional licenses would not necessarily harm consumers. If

that admittedly strict condition is not met, however, pure bundling (i.e., the absence of mixed bundling)

is the equivalent of supra-RAND pricing and is likely to harm consumers.

The above proposal has important policy implications. First, one cannot presume

anticompetitive harm simply from the fact that a licensor has tied its patents. An inquiry is required in

that case to determine whether or not the licensing terms meet our conditions above: is the rate RAND

for just the RAND-committed patents? Second, in disputes over RAND licensing, the patent holder

cannot deduct from the licensing terms the added value of the non-RAND-committed licenses to get an

implicit license fee for the RAND-committed licenses and then assert that this implicit license fee meets

the RAND obligation. Nor can it require licensees to license unrelated patents at a rate that aggregates

the RAND royalties for all of them. Symmetrically, licensees cannot demand a discount for RAND-only

licenses, as compared to RAND-plus licenses, without first establishing that the broader portfolio license

rates and terms are higher than the RAND-only rates and terms (e.g., without establishing that the

licensor has not thrown in the additional patents free of charge). The complexities of establishing that a

RAND-plus license has RAND terms and conditions may push licensors, as a practical matter, more

toward mixed bundling, but the door to RAND-committed patent tying should nonetheless remain open.

4 We explain below why we use this term rather than the related and more familiar term, “single

monopoly profit” principle.

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II. Bundling in General

Bundling is a long-standing antitrust issue that has attracted a great deal of attention in the

economics literature. The general concern with bundling is that a consumer is forced to obtain

something he does not want (“Good B”) in order to buy something he does want (“Good A”). In some

cases, the consumer might not want to buy Good B from the seller of Good A because he would prefer

to buy Good B from another firm. In other cases, he might simply have no use for Good B. Both

scenarios create the possibility for economic inefficiency and reduced consumer welfare. Despite the

increased acceptance of the principle that antitrust policy is to protect consumers rather than

competitors, the possibility that bundling (or, more precisely, tying) can violate the antitrust laws is

limited to the former case. The antitrust concern has been that competition in the market for Good B is

distorted when a seller with market power in the sale of Good A requires its customers to buy Good B in

conjunction with Good A. In other public policy contexts – with the bundling of channels in basic cable

television service being a prominent modern example – consumer harm from bundling has been a

concern.5

A. The Single Rent Principle

To those unfamiliar with economic reasoning, both the rationale for tying and the potential

harm from it might seem obvious. The consumer is harmed because he pays for an item he does not

want and the seller benefits because it gets the profits from selling the additional item. But that

argument is incomplete. It rests on the implicit assumption that the seller can attach B to A and charge a

price increment above the marginal cost of B without lowering demand. In general, such an assumption

is not warranted.

In particular, it is not warranted when B is available in a competitive market. To illustrate with a

numerical example, suppose the profit-maximizing price for A is $10/unit and B is available in a

competitive market for $5/unit. Since perfect competition drives price down to marginal cost, $5 is also

the marginal cost of B. For tying to be profitable, the firm must be able to charge more than $15 for the

A-B bundle. However, because consumers can already buy A and B for a combined price of $15 (the

monopoly price of $10 for A and the competitive price of $5 for B), a price of $16 for the A-B bundle is a

price increase and will generally lower demand. Moreover, the $10 price for A was chosen by the

monopoly seller of A, presumably to maximize its profits. It had the option of charging $11 for stand-

alone A sales, but decided not to do so. Yet, given the availability of B on the market for $5, selling the

bundle of A and B for $16 is in effect charging $11 for A. To the extent that selling A on a stand-alone

basis for $11 yields lower profits than selling it for $10, then we should expect the $16 price for the

bundle (which entails a an implicit price of $11 for A) also to result in lower profits. Indeed, this is the

case even if everyone who would purchase A would also want to buy B. If some people who want A

would not purchase B for $5, then the bundling strategy would be even less profitable.

5 But see Brantley v. NBC Universal, Inc., 675 F. 3d 1192 (9

th Cir. 2012) (tying “must have” cable channels

to less desirable channels did not state a cause of action under the Sherman Act).

6

The argument above is known in economics as the “single monopoly profit” principle.6 The

theory rests on the strong assumption that the market for the tied good is perfectly competitive.

Nonetheless, the principle is often taken to cast doubt on claims that a firm with market power over one

good (or, in the case of vertical integration, one stage of production) can profitably leverage that market

power into adjacent competitive stages.

While economists (as well as lawyers and courts) refer to the argument above as the single

monopoly profit principle, we prefer the term “single rent” principle because the argument applies to

rents of any kind, including patent royalties.

A patent is a property right that does not by itself confer a monopoly any more than other forms

of ownership do. By way of analogy, an apartment building is also a property right that might appear to

give the owner a “monopoly” over the rental of apartments in that particular building. But the fact that

there is a single seller of a specific asset does not constitute a monopoly unless that asset constitutes a

well-defined market. If other apartment buildings (or other forms of housing) are competitive

alternatives to the apartments in a particular building, the owner of the building has a property right but

not a monopoly. Some patents might well constitute well-defined markets, but not all patents do, and in

practice most patents do not. Regardless of whether or not a patent right is a monopoly, there are still

circumstances when the royalty a patent-owner can obtain from a single patent is just as great as the

royalty it could obtain from two.

As we discuss below, there is an extensive economics literature on how bundling and tying

might increase a firm’s profits. That entire literature is about exceptions to the single rent principle.

Nevertheless, the emphasis in the literature on the exceptions should not obscure the general rule. The

intuition that the objective of tying is to leverage market power from one good to another usually fails

to withstand rigorous economic scrutiny. As a result, whenever one argues that tying is a form of

leveraging, in addition to establishing market power one also needs to be able to explain why the single

rent principle does not apply.7 Indeed, since we argue below that it does not apply to the tying of a

license for RAND-committed patents to a license for non-RAND committed patents (or unrelated RAND-

committed patents), we are obligated to answer that question (as we will).

6 As evidenced by the title to Elhauge (2009) the term is widely recognized. However, we have not been

able to document the source of the term. Whinston (1990) attributes the arguments to a Chicago oral tradition. Bowman (1957) recognizes the strong assumptions underlying the principle and a set of exceptions to it when those assumptions do not apply.

7 Elhauge (2009) and, in a related context, Krattenmaker and Salop (1986) in effect argue that the

assumptions underlying the single monopoly profit principle are so restrictive that it should be considered the exception rather than the rule.

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B. The Economics Literature on Exceptions to the Principle

In broad terms, the literature on exceptions to the single rent principle in assessments of

bundling and tying has two main themes: price discrimination and entry deterrence through

foreclosure.8

1. Price Discrimination

The “price discrimination” strand of the literature on bundling started with George Stigler’s

analysis of block booking practices for movies.9 The argument rested on a very simple numerical

example. A firm sells two products, A and B, to two customers, I and II. (Specifically in the article, the

seller was a movie distributor, the products were films, and the customers were movie theaters.)

Customer I is willing to pay 10 for movie A and 2 for movie B. Customer II is willing to pay 2 for movie A

and 11 for movie B. If the seller does not bundle, it charges 10 for good A and 11 for good B. Only

customer I buys good A. To get customer II to buy good A, the seller would have to lower its price to 2,

but selling two units at 2 generates less profit than selling one unit at 10 (even assuming that marginal

cost is 0). Similarly, only customer II buys good B. Stigler’s insight was that the seller could offer the two

products only as a bundle and charge 12. Both customers would then buy both products. In this

example, bundling is “Pareto superior” – meaning that no party is harmed and some receive a positive

benefit – to selling the goods separately. The seller earns a profit of 24 instead of 21. Consumer surplus

goes up as well (from 0 to 1).10

While much of the subsequent literature has focused on extending the Stigler model to more

general distributions, arguably the most important insight for tying policy from this follow-on literature

is due to the early contribution by Adams and Yellin (1976). Like Stigler’s model, their analysis was based

on assumptions about the willingness to pay among a discrete number of customers. Adams and Yellin’s

insight was that in this framework, mixed bundling yields higher profits than pure bundling. Pure

bundling means that the firm sells only the bundle. Mixed bundling means that the firm sells both the

bundle and the individual goods separately, with the price of the bundle being different (typically less

than) the sum of the individual prices. Adams and Yellin’s insight on mixed bundling is important for

competition policy because mixed bundling is not tying: customers are still free to obtain the individual

goods should they so desire.11 Thus, while the price discrimination strand of the literature might explain

8 See Klein (1998).

9 See Stigler (1963).

10 The single rent principle does not apply in the Stigler setting because the monopolist has two

monopolies rather than one. Moreover, the model rules out price discrimination in selling the goods separately. As a result, simple pricing of the two goods leaves a “deadweight loss.” Customer A values good II at more than marginal cost but less than the simple monopoly price. The same point applies to customer B and good I. Thus, the bundling in this example does not force on each customer a good that he values at less than marginal cost. The standard interpretation of the Stigler model is that bundling is a substitute for price discrimination.

11 The distinction between pure bundling and mixed bundling can be blurry when the price of the bundle

is so close to the price of the individual goods that the seller engages in what is called a “virtual tie.”

8

why a firm offers bundles, it generally is insufficient to explain why firms choose not to offer the

individual goods separately as well.12

2. Foreclosure

The foreclosure strand of the literature has developed formal economic analysis to establish the

assumptions under which traditional concerns about tying as a form of monopoly leveraging make

sense. Whinston (1990) is the seminal paper in this area. He analyzed the possible strategies for a firm

that initially has a monopoly over two products. Its position in one (A) is protected but it faces potential

entry with respect to the other (B). In Winston’s model, tying B to A is a form of commitment to price

aggressively in response to entry. By refusing to sell A without B, the incumbent places itself in a

position in which losing sales of B after rival entry into the B market not only reduces the incumbent’s

profits from sales of B but also reduces its profits from sales of A. With tying, a lost B sale also means a

lost A sale, so tying gives the incumbent an incentive to price more aggressively in the face of potential

entry than it otherwise would.

An essential element of the Whinston model is that there are economies of scale in B. Thus,

even if the incumbent’s aggressive pricing for A remains above marginal cost (and thereby would

generally not run afoul of the prohibition against predatory pricing), the lower bundle pricing might

make the difference between whether the entrant can achieve the combination of price and scale to

make entry in B profitable.

In game-theoretic analysis, commitment to a strategy means sticking with it even when it would

be profitable to do otherwise. In the Whinston model, the incumbent would sell A separately (at the

monopoly price) after rival entry occurs in B if it could. However, as is often the case in game theoretic

results, committing not to act in one’s own interest can have strategic value. When the incumbent

commits not to act in its own interest by selling A separately, the entrant in B cannot exploit the

incumbent’s incentive to accommodate entry by unbundling.

When the United States Department of Justice sued Microsoft for tying its browser to its

Windows operating system, Carlton and Waldman (2002) adapted the basic insight of Whinston’s model

to assumptions that more nearly matched the facts of that case. Others have pursued different

extensions. Of them, Choi and Stefanadis (2001) is of particular note. In their model, an incumbent

monopolist sells two products (A and B) that consumers combine in fixed proportions. Entry into both

products is possible, but both require R&D expense with a random outcome that includes a chance of

failure. Because the two goods are only useful in combination (such as a computer and an operating

12

As noted above, much of the subsequent price discrimination strand of the literature extends the Stigler and Adams-Yellin insights to more general distributions with notable contributions by Schmalensee (1984) and McAfee, McMillan, and Whinston (1989). McAfee, McMillan and Whinston show that for completely general continuous distributions of reservation values, mixed bundling almost always yields higher profits for the seller than pure bundling. It is possible that the optimal mixed bundle might entail charging a premium for the bundle, which would only be a practical policy if the seller can prevent those who want both goods from buying them separately. However, we are not aware of anyone who has seriously suggested that tying can occur because it is not feasible to charge a premium for the bundle.

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system software program), a firm that successfully innovates in A can only sell its product if consumers

can purchase B as well, so innovation in B must also be successful. Alternatively, consumers might buy A

from a successful entrant if they can combine it with B from the incumbent. If the incumbent sells A and

B only in bundled form, it denies this possible path to market because it forecloses B innovators. With a

reduced prospect for successful entry, potential innovators might choose not to attempt entry.

A general theme of all these models is that when a monopolist over a product A ties a second

product B to it, some customers will buy B from the incumbent because they want A. Absent the tie,

they might not buy B alone from the A monopolist. A potential entrant in B then faces a tougher market

if it does enter. If entry into selling B entails scale economies, then the foreclosure of customers who get

B from the incumbent in order to get A can tilt the balance in the entry decision and convince the

potential entrant to stay out of the market altogether.

However plausible this effect might seem as a matter of theory, it is appropriate to assess

critically claims that it applies in any particular instance. One must always pose the question, “Why does

the seller of A refuse to sell it on a stand-alone basis to people who want to buy it but not buy B?”

In the foreclosure literature, the answer to the question is that the seller generally does have an

incentive to sell its monopolized good separately. 13 As a result, its decision not to do so comes from a

commitment that is difficult to break. The monopolists in the leveraging literature are imposing on

themselves the cost of not selling the good separately. They do so to influence the actions of potential

entrants.

The challenge for inferring policy conclusions from this literature is assessing whether the

conditions ever apply in practice. In any real case, there needs to be a presumption that the

commitment not to sell goods separately imposes a cost on the firm accused of tying to exclude

competitors. To apply the argument in a specific case, one would have to present compelling evidence

that the commitment is credible and that the benefit obtained from the commitment exceeds the cost.

3. A simpler and more compelling answer to the key question

As we have argued, any allegation about anticompetitive effects from tying must include a

compelling answer to the following question: “If a firm is selling A only in combination with B, why does

the firm refuse to sell A on a stand-alone basis to people who want just A?”

It is impossible to overstate how common this phenomenon is. Many times every day people

buy bundles of goods that include components they do not want. Virtually no one wants every section

of a newspaper. Whenever the purchase of something includes something else “at no extra charge,” the

term “no extra charge” is marketing lingo for “tied.” The thirteenth item in a “baker’s dozen” is not free.

13

The model in Nalebuff (2004) is similar to Choi and Stefanadis (2001) in that the incumbent initially has a monopoly over two goods and faces random entry in both. Nalebuff argues that in addition to its entry-deterring effects, bundling increases profits relative to selling the goods separately and therefore is not costly. The argument draws on the price discrimination strand of the literature. But that argument ignores the possibility of mixed bundling, which would be even more profitable than pure bundling.

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The baker who purports to be setting the price of a “dozen” knows very well that he is setting the price

for 13 with the thirteenth item tied to the first 12. Ironically, the modern economics literature on

“shrouded attributes”14 treats untying as a potentially deceptive practice. The advent of separate

baggage charges on airlines has engendered complaints, and Southwest Airlines has engaged in an

extensive advertising campaign to tout its business practice of tying the right to check two pieces of

luggage to its passenger service (although it of course does not explain its policy in precisely those

terms.)

The explanation for this very common practice, which occurs in competitive markets (like

bakeries) as well as those in which firms have market power, has to be simpler than the leveraging and

price discrimination models that dominate the economics literature.

Evans and Salinger (2005, 2008) provide such an explanation. They argue that one cannot

understand the vast majority of instances of tying without recognizing the cost of product offering

complexity. Before a firm decides on how much to produce (or try to sell) and how much to charge, it

first has to decide exactly what it sells. Even after deciding on its general line of business, the products a

firm offers are typically a small subset of the products and product combinations it could conceivably

offer. Dell revolutionized the personal computer industry by putting in place systems to customize

orders to consumer specifications to a degree that had previously been unimaginable. But even Dell’s

highly customized offerings did not include every conceivable configuration and, more importantly, Dell

and the personal computer industry are the exception. In general, companies do not and indeed cannot

customize their offerings to the precise desires of every (or, for that matter, any) customer.

The accounting literature on “activity-based costing”15 provides evidence for the cost of product

offering complexity. Evans and Salinger also provide evidence in their study comparing how United

States and Japanese automobile companies offered optional features and how the relative practices

changed over time.16 But the most compelling evidence for the importance of the phenomenon is not

14

See Gabaix and Laibson (2006). 15

See Cooper and Kaplan (1988). 16 When Japanese automobile companies first started their substantial penetration into the United States

markets, each model came with only a small number – possibly only two – bundles of options. The Honda Accord

might, for example, have a base model that did not have air conditioning or any sound system other than an FM

radio, a middle model that included air conditioning, power windows, and a few more extra features, and a top

model that also included leather seats, an upgraded sound system, a moon roof, and better tires. The original

rationale was that the Japanese companies had longer supply lines and did not have the ability to supply cars with

exactly the features customers wanted (to the relevant location). In contrast, US automobile companies were

selling options on an a la carte basis. In some cases, even the AM/FM radio was effectively optional. (Ford listed it

as standard, but a buyer could get a credit for not having it.) Over time, one might have expected competition to

compel Japanese companies to adopt policies more like the US policy. In fact, the US car companies came to

recognize that there were hidden costs to their more complex set of offerings and started emulating the Japanese

companies by offering options only on a bundled basis. Thus, the tying strategy won out over the unbundling

strategy in market competition.

11

published: it is the common experience of purchases that are bundles of items that are not available

separately for sale.

While Evans and Salinger did not address the issue of the tying of patents, the framework they

suggest provides a plausible – indeed, obvious – explanation for why patent tying is such a common

phenomenon. Whenever someone buys a bundle that contains items he does not want, there is a

temptation to ask to purchase just the wanted components at a discount to the bundle price. A cable

television subscriber who does not watch sports might want to purchase a basic package that excludes

ESPN and other sports channels and pay a lower rate.

The key question to ask with respect to such a request (as well as a legal mandate to honor it) is,

“What is the limiting principle?” Some large innovative companies that license their technology have

thousands of patents. Yet, they might offer them in only a handful of bundles, and they might not offer

any of them individually. For a company with 1,000 patents, the number of possible combinations of

patents is on the order of 10301, which is about googol cubed! The notion that the licensor is obligated to

unbundle any arbitrary bundle and offer a discount means that it would have to set 10301 different

possible prices and then monitor and enforce compliance for all those different configurations. As a

practical matter, the number of different combinations that licensees might demand would obviously be

much smaller, but there is nonetheless a cost of having more complex product offerings. As a result,

patent licensors necessarily offer a small subset of the patent bundles that they could conceivably offer;

and it should come as no surprise (and should not necessarily be a public policy concern) if many

licensees only use a subset of the patents they license.

It also should not be surprising if licensees want bundles to be inclusive. A licensee takes a

license to avoid being sued for patent infringement. A company that licenses just a subset of the patents

that it needs to implement a technology risks a patent-infringement suit even if it pays the royalties due

on the patents it does license. As a result, licensees might demand patents in an inclusive bundle that

completely protects them from the threat of a suit. To the extent that such bundles cover both RAND-

committed patents and non-RAND committed patents, then including all the patents that a licensee

might conceivably use in conjunction with one or more of a licensor’s patents is itself a form of

commitment on the part of a patent owner not to behave opportunistically by suing for patent

infringement on a non-RAND committed patent that the licensor of its RAND-committed patents ends

up infringing.

4. Reprise

The existing economics literature on bundling and tying generally does not specifically address

the bundling and tying of patents, which have unique features as intangible goods. Nonetheless, the

existing literature offers important insights for analyzing the bundling and tying of RAND-committed

patents.

We glean two main lessons from the general literature on bundling and tying that we believe

inform the analysis of bundling and tying of patents. First, any explanation for why firms find it

12

profitable to tie must take due account of the single rent principle. Second, one must take due account

of transactions costs.

We now turn to the one article on tying in the economics literature that focuses specifically on

patent tying.

III. The Gilbert-Katz (GK) Model

The Gilbert-Katz (GK) model addresses two enduring issues with respect to patent licensing,

along with the possible interaction between the two: patent bundling and patent hold up.

In the formal set up of the model, the owner of two complementary patents (“the IP owner”)

can license to a single licensee (the “manufacturer”). The patents are strongly complementary in the

sense that the manufacturer needs access to both technologies in order to capture any value in the

goods market. The IP owner does not have manufacturing capability, so it must license its technology to

the manufacturer to capture any value from it. The value that can be realized from the technology is a

function of the level of complementary investment, which only the manufacturer can make. The

potential hold-up problem derives from the fact that if the manufacturer does not obtain a license to

the technology prior to investing in complementary assets, the IP owner might be able to expropriate

the contribution of the manufacturer’s investment. In other words, if the manufacturer does not obtain

an early license, the IP holder can practice hold up.

A simple numerical example illustrates the point. Suppose that without any investment by the

manufacturer, the patented technology yields a value of 20 (unrealizable by the patent holder, by

assumption, as explained above). With efficient investment in complementary assets by the

manufacturer, however, the technology embodied in an end product yields gross (i.e., before taking

account of the cost of the manufacturer’s investments) benefits of 100 (unrealizable by the

manufacturer absent the initial contribution by the patent holder). But the investments needed to

generate the additional value (the end product) have a cost. Suppose that cost is 30, so that the

potential net value of the combined technology (patent plus manufacture) embodied in the end product

is 70.

Given these assumptions, the manufacturer would be foolish to invest in the complementary

assets before obtaining a license for the patented technology. If it did so, the IP owner could insist on a

license fee of 100 (or just below it). After the fact, the manufacturer would rationally accept this offer, in

which case it would lose its sunk investment of 30. In anticipation of this possibility, the manufacturer

would not invest in complementary assets and the most the IP owner could charge as a license fee

would be 20, the value created by the patented technology without any complementary manufacturing

investment. The IP owner has an incentive to commit up front to a license fee of 70 for the bundle,

which allows the manufacturer to recover its investment cost (and also to choose the most efficient

13

level of complementary investment).17 GK refer to licenses entered into before the manufacturer invests

as “long term” licenses and licenses signed after the manufacturer invests as “short term” licenses.

Up to this point, whether the technology is based on one patent or two is irrelevant. The

manufacturer needs both. Similarly, whether the IP owner offers the patents separately or in a bundle is

also irrelevant. It can offer the patents as a bundle at a license fee of 70. Alternatively, it can offer them

à la carte with individual prices that add to a cumulative license of 70. Profits and consumer welfare

(and, therefore, total surplus) are all the same under the various options for charging a total of 70. The

irrelevance of bundling under these conditions is an application of the single rent principle that we

discussed above. One patent that is essential for a product gives the patent holder the ability to extract

the same total license fee as it can with two such patents given that the manufacturer needs a license to

both patents to create the end product.

An additional feature of the GK model that makes bundling potentially relevant is that the

manufacturer can invest in R&D to invent around one or both patents. The outcome of the

manufacturer’s R&D is random. Thus, for a given level of investment, the manufacturer might invent

around just “patent A,” just “patent B,” both, or neither.18 The manufacturer’s incentive to invest in R&D

depends on whether it has licensed the patents on a bundled or an à la carte basis. If it licenses the

bundle, it only earns a return on its R&D if it succeeds in inventing around both patents. If it licenses on

an à la carte basis, then successfully inventing around just one of the patents will lower the license fees

it owes the IP owner. Thus, holding the total license fee constant, the manufacturer has more of an

incentive to invest in R&D under à la carte licensing than under bundled licensing. As a result, the IP

owner can limit the manufacturer’s incentive to invest in R&D to invent around its patents by licensing

its patents solely as a bundle. This effect is often stated as a reason for why patent bundling is

problematic. In the GK model, however, the manufacturer’s innovative efforts are assumed to be

duplicative, working only to replace the existing patented technology as opposed to extending it. The

benefit R&D potentially yields for the manufacturer is a private one (if successful, it enables the

manufacturer to avoid license fees), but it provides no social benefit. Furthermore, since the GK model

assumes patent license fees are lump sums, there is no distortion in the product market that could be

corrected by invent-around patents licensed at lower per unit fees.

Suppose the manufacturer waits until it learns the outcome of its R&D before obtaining a license.

That is, within the GK model, suppose the manufacturer decides to rely on short term contracting in

hope of being able to avoid a license for one of the patents. From the perspective of reaping additional

rewards from its R&D (by getting value when it successfully invents around just one of the patents), the

17

A simplifying assumption in GK is that the IP owner makes take-it-or-leave-it offers to the manufacturer, which implies that the IP owner is able to capture the entire available surplus. As they explain, the model would be more complicated if the IP owner and manufacturer bargained over the available surplus, but the risk would remain that the IP owner would expropriate part of the manufacturer’s investment if the manufacture invested prior to obtaining a license.

18 The assumptions and the phenomenon that the GK model examines are similar to those explored by

Choi and Stefanadis (2001), discussed above.

14

strategy does not provide the manufacturer with any benefits. (This point is yet another implication of

the single rent principle.)

Our numerical example from above clarifies the options – absent any R&D by the manufacturer –

that the IP owner has. Namely, the IP owner could 1) charge 70 for a bundle of the two patents, 2)

charge 35 per patent for each technology, 3) charge 70 for “patent A” and 0 for “patent B,” or 4) charge

70 for “patent B” and 0 for “patent A.” The options yield the patent holder the ability to earn the same

profit of 70, regardless of whether the manufacturer takes a long term contract or not. If the

manufacturer gets to wait to see which patent it needs (e.g., under short term licensing), then the IP

owner will know which patent the manufacturer requests19 and will choose its licensing terms

accordingly. So, if the manufacturer innovates around “patent A” and requests a license for “patent B,”

then the IP owner can charge 70 for a license to “patent B” and 0 for “patent A.” If, on the other hand,

the manufacturer innovates around “patent B” and requests a license for “patent A” only, then the IP

owner can charge 70 for a license to “patent A” and 0 for “patent B.”

In combination, GK interpret their results to suggest that many of the concerns with patent

bundling are misplaced. In their model, there is a benefit to “long term” (or ex ante) licenses because

such licenses prevent the IP owner from expropriating the manufacturer’s returns to complementary

investments (which are socially beneficial). But a ban on patent bundling acts as a deterrent to long-

term license agreements because the IP owner can accomplish with short term licensing some of what it

could accomplish by bundling. Allowing patent bundling in long-term licenses does allow the IP owner to

discourage “invent-around” innovation by the manufacturer, but such innovative effort is socially

wasteful by assumption under the GK model.

IV. RAND Commitments

The intent of the GK model was to assess whether there is any reason to be concerned with the

bundled licensing of patents. They conclude that there is not. The question we need to consider is

whether the model justifies a conclusion that there is no reason to be concerned about the tying of

patents that are not RAND-committed to patents that are.

The possibility of RAND commitments is an important consideration in assessing the policy

conclusions GK infer from their results. In their model, bundling facilitates long-term contracts which are

in turn necessary to protect patent users against the risk that the patent-owner will try to expropriate

the value of their sunk investments in complementary assets. RAND commitments are, however, an

alternative mechanism to accomplish the same ultimate objective of preventing hold-up. The premise

behind RAND commitments is that potential patent users will sometimes wait until they have sunk

investments into the use of a particular technology before seeking a license.20 Within the context of the

GK model, short-term contracting occurs in practice. We interpret RAND commitments as commitments

19

Within the GK model, the outcome of the manufacturer’s R&D is common knowledge. 20

See Swanson and Baumol (2005).

15

not to seek terms in short-term contracts that are more favorable to the patent-owner than it could

have obtained with long-term contracts.

Before incorporating a RAND commitment into the GK model of the bundling of two patents, we

first need to formalize what RAND means for the licensing of a single patent. Here, we assume a

simplified version of the GK model. Consider a patent owner where use of the patent yields net benefits

of B but requires expenditure of a sunk cost, S.21 With expenditure R, the licensee can invent around the

patent with probability p.22

Given how we interpret RAND, we need to analyze what terms the licensor and manufacturer

would agree to before the manufacturer incurs sunk costs in complementary assets and decides

whether to invest in R&D. If R is sufficiently high or p is sufficiently low (in a sense that we will be more

specific about below), then trying to invent around the patent is not a viable option. As a result, the

licensor would demand a royalty of B – S (analogous to the 70 in the numeric example above). If the

manufacturer waits until after it has incurred its sunk cost to seek a license, then the patent owner

would rationally charge a license fee of B, but that would violate the RAND commitment as the patent

owner would not agree to such a license fee before incurring sunk costs.

The possibility of inventing around the patent complicates matters. We assume a three-stage

game in which the licensor announces a licensing fee in the first stage, the manufacturer decides

whether to invest in R&D in the second stage. In the third stage, the manufacturer decides whether to

invest in complementary assets after it has observed the outcome of its R&D.

In principle, the manufacturer has four options. It can accept the license and invest in R&D,

accept the license and not invest in R&D, reject the license and invest in R&D, or reject the license and

not invest in R&D. We assume, however, that the manufacturer only owes a royalty if it uses the

patented technology and that successful R&D therefore allows the manufacturer to avoid the royalty

payment.23 As a result, the manufacturer has no reason to refuse the license as long as the royalty does

not exceed B – S. The patent holder has no reason to charge more than B – S, which the manufacturer

would refuse, so the patent holder charges B – S and the manufacturer accepts this license.

The manufacturer still has to decide whether to invest in R&D. That choice affects the patent

holder’s decision about what royalty to charge, as it has to decide whether to set a license fee that

eliminates the incentive to invest in R&D. One option for the patent holder is to charge a high license fee

(LH ) = B – S, which extracts the full value of the patent when the manufacturer needs it, but which can

provide the manufacturer with an incentive to invest in R&D. The alternative is to charge a low enough

21

GK allow for different levels of S and for B to be a function of S. The levels of sunk cost that are optimal for both the licensee and society are then part of the model solution.

22 GK allow for a range of R and let p be an increasing function of R.

23 GK allow for the possibility of licenses that require payment regardless of whether the manufacturer

uses the technology. But such licenses do not emerge in equilibrium when the patent owner has superior information about the quality of the intellectual property, and there are a variety of other practical reasons for not considering this possibility.

16

license fee (LL) to eliminate the manufacturer’s incentive to invest around the patent. (We refer to the

former strategy as a “value-based royalty” and the latter as a “cost-based royalty.”)

The condition that defines LL is:

(1) LL ≤ R/p

For p < R/(B – S), R/p > B – S. But the potential licensee would never accept a royalty greater than B – S.

As a result, whenever R/p > B – S, the licensor chooses value-based licensing as the potential licensees

would not try to invent around a value-based royalty.

For p < R/(B – S), the licensor will prefer the lower license fee if:

(2) R/p ≥ (1 – p)(B – S).

If we let p* be a probability that makes the patent owner indifferent between the high and low

license fee, then the condition for p* is quadratic with roots:

(3) 𝑝∗ = 1 ±√1−4

𝑅

𝐵−𝑆

2

When 4R < B – S, the equation has no real roots because cost-based licensing yields higher expected

profits than does value-based licensing. This leads to our first proposition:

Proposition 1: If R > (B – S)/4, the ex ante royalty that yields the highest expected return for the

licensor is the minimum of (B – S) and R/p.

A consequence of Proposition 1 is that when R > (B – S)/4, the licensor always chooses a royalty that

eliminates the incentive to develop an alternative to the patent.

Matters are more complicated when R ≤ (B – S)/4, in which case equation (3) has two real roots.

Again, for p < R/(B – S), the possibility of inventing an alternative to technology 2 does not constrain

value-based royalties. Between p = R/(B – S), inequality (2) holds, meaning that a cost-based royalty

generates a higher expected yield than a value-based royalty. Between the two roots, inequality (2) is

reversed; a value-based royalty of B – S has a higher expected yield than the cost-based royalty of R/p.

For probabilities greater the higher of the two roots, inequality (2) holds, implying that a cost-based

royalty gives higher expected yield than a value-based royalty. Summarizing these results, we get:

Proposition 2: If R ≤ (B – S)/4, the ex ante royalty that yields the highest expected return for the

licensor is:

(i) B – S if p < R/(B – S) or if 1−√1−4

𝑅

𝐵−𝑆

2 ≤ 𝑝 <

1+√1−4 𝑅

𝐵−𝑆

2

(ii) and R/p otherwise.

17

These results are of independent interest with respect to the meaning of a RAND commitment.

If the “reasonable” component of RAND commits the patent-owner to not seeking a royalty that is

greater than it could negotiate ex ante, then a RAND commitment implies value-based royalties in some

cases and cost-based royalties in others.24 Even if this qualitative point is not surprising, these results

suggest that distinguishing the two cases might be even more complicated in practice than one might

expect. If Proposition 1 applied to all parameter values, then the distinction would at least be simple

conceptually. The RAND commitment would be the lesser of the two possibilities. This conceptual

simplicity in no way implies that measuring the relevant parameters would be also be simple, but the

parameters reflect factors that everyone would recognize as being relevant: the underlying value of the

technology and the cost and risk associated with trying to circumvent it.

Proposition 2 adds two conceptual complications. As a practical matter, one might be a mere

theoretical curiosity, but the second is not.

The first complication is that for given values of R and B – S, one might expect the royalty that

the patent-holder would choose to be a non-increasing function of p. That is, one would not expect an

increase in the possibility of inventing around the patent to increase the royalty that the incumbent

would charge.25 If one were to incorporate this result into legal proceedings, then it is possible that

patent-holders would argue for a value-based royalty on the grounds that the patent would be easier to

invent around than the potential patent user claims and the patent user arguing for a lower cost-based

royalty on the grounds that inventing around the patent would be harder than the patent-holder claims.

Even if one were to restrict the legal standard to one in which the maximum royalty implied by a

RAND commitment is a non-decreasing function of the expected cost of inventing around the patent,

there remains the question of what that threshold should be. Patent-users might like to argue that the

cost-based license royalty should always place an upper bound on RAND and that RAND should

accordingly be the minimum of (B – S) and R/p. Proposition 1 provides support for such an argument

given parameter values underlying that proposition. But proposition 2 suggests that the argument is not

24

Here, “cost-based” means the patent user’s ex ante expected costs of developing a successful work-around technology. This differs from the original cost of developing the patent for two reasons. First, the cost of developing a second technology need not be the same as the cost of developing the first. (It can be either higher or lower.) Second, the expected cost entails a scaling of the actual costs to reflect the probability of success. That is, within the model, cost-based means R/p rather than R.

25 As a matter of mathematics, the result arises for the following reason. When p ≤ R/(B – S), the potential

patent-user has no incentive to invent around the patent even if the incumbent charges a value-based royalty. Thus, in the relationship between the probability that an R&D would succeed (if attempted) and the probability that the potential patent-user actually invents around the patent, there is a discontinuous jump at p = R/(B – S). At this point, the value-based and cost-based royalties equal each other; and, for probabilities slightly above the threshold, the cost-based royalty is only slightly less than the value-based royalty. As a result, the cost to the patent holder of dissuading the potential patent user from trying to develop an alternative technology is small and therefore worth incurring to avoid a positive probability of getting no royalties at all. For higher probabilities of success, however, the cost of getting the potential patent user to forego R&D is much greater. For a range of probabilities (i.e., the probabilities between the two real roots of the quadratic), that cost is large enough that the patent holder can get a higher expected return with a value-based license that induces the potential patent user to try to invent around the patent even though and thereby exposes the patent holder to the risk that the potential patent user will succeed.

18

sufficient in all cases. Such a position ignores that “reasonable” must apply equally to both the patent-

user and patent-holder. Ex post, it is attractive for the patent-user to argue that a value-based royalty

would not be RAND because, if it had known that the patent owner would charge value-based pricing, it

would have tried to invent around the patent. The model suggests, though, that the risk that the patent-

user would have tried to invent around the patent and might have succeeded would not have prevented

the patent holder from choosing value-based licensing.

V. Incorporating RAND Commitments into the GK Model

Having formalized the meaning of a RAND commitment on a single patent, we can now analyze

the tying of a RAND-committed patent to a non-RAND committed patent within our simplified version of

the GK model. Assume that the patent-owner owns two patents (as in GK). Let R1 and R2 be the R&D

expenses needed to invent around each patent and p1 and p2 be the respective probabilities of success.

Suppose the patent-owner makes a RAND commitment on patent 1 but not patent 2.

The issue of whether tying patents 1 and 2 together might violate a RAND commitment is only

of substantive interest if a patent user might make commercial use of patent 1 without patent 2. This

possibility arises in the GK model if the patent user can invent around patent 2. Below, we analyze this

case. We also consider the possibility that the net value can be captured by exercising patent 1 without

technology 2. In each case, we evaluate what limits the RAND commitment places (and does not place)

on the patent holder, including the maximum license fee it can charge for a bundle of the two patents

depending on whether it offers patent 1 separately (i.e., depending on whether it engages in pure

bundling/patent tying as opposed to whether it engages in mixed bundling.)

A. Both Technologies Necessary

Extend the model from Section IV so that, as in GK, two technologies are necessary to capture

value B. A single firm has a patent for both technologies, but it makes a RAND commitment only on one

of them (patent 1).

Absent a RAND commitment on patent 2, a firm seeking to exercise patent 1 would be foolish to

invest in sunk complementary assets without investing in R&D to develop the second technology itself.

Otherwise, it would be subject to hold-up on the royalty for patent 2.

Given that the potential licensee needs to invest in R&D on technology 2, it would not agree to a

royalty of B – S for patent 1, even before sinking costs into complementary assets. In effect, the

investment in R&D on technology 2 is another sunk cost in complementary assets. As a result, a value-

based RAND royalty for patent 1 would be B – S – R2/p2 and a cost-based royalty would be R1/p1. The

analysis in Section IV would apply as to which strategy the patent-holder would choose ex ante as the

19

RAND rate, with B – S – R2/p2 substituting for B – S and R1/p1 substituting for R/p. That is, the maximum

RAND royalty for patent 1 is:26

i) min{R1/p1, B – S – R2/p2} if R1 > (B – S – R2/p2)/4

ii) B – S – R2/p2 if 𝑝1 ≤

1−√1−4 𝑅1

𝐵−𝑆−𝑅2

𝑝2⁄

2

iii) R1/p1 if 𝑝1 >

1−√1−4 𝑅1

𝐵−𝑆−𝑅2

𝑝2⁄

2

Having made a RAND commitment just on patent 1, the patent holder is not limited on the

royalty it can charge for patent 2. Nothing prevents it from patent hold-up, which would entail a

combined royalty of B for the two patents. It could implement this licensing strategy either by offering

the bundle of the two patents for B or by offering patent 2 separately for a royalty equal to the

difference between B and the RAND royalty on patent 1.

Note that if the patent-holder had made a RAND commitment on patent 2 as well as patent 1, it

could offer two RAND-committed patents in a bundle and, for some parameters, charge a royalty of B –

S. As a result, one might consider whether only offering the two patents in a bundle at a royalty of B – S

would honor the RAND commitment. The problem with this argument is that absent a RAND

commitment on patent 2, the potential licensee for patent 1 would only consider putting itself in a

position of licensing patent 1 (which would require incurring the sunk investment S) if it also invested in

R&D to develop technology 2. Offering the patents only in a bundle and charging B – S expropriates the

potential licensee’s investment in (successful) R&D which was necessitated by the patent holder’s

decision not to make a RAND commitment on patent 2.

If the patent holder wants to license the two patents only in a bundle, it can still honor its RAND

commitment by charging a royalty that would equal the RAND royalty for patent 1 alone. In effect, it

would be including patent 2 for free. Absent transaction cost considerations, it is hard to see why it

would choose to do so; but, particularly if R2/p2 is low enough, then transaction cost savings from pure

bundling might induce it to do so.

B. One Patent Necessary

We now consider an extension to the GK model in which it is possible to capture value from

patent 1 but a license to patent 2 makes it possible to extract more value. To expand the notation, let B1

and S1 be the gross benefits and necessary sunk cost in complementary assets from patent 1 alone. Let

B2 and S2 be the incremental gross benefit and sunk costs associated with practicing patent 2 in addition

to patent 1 with B2 - S2 > 0. Assume that B2 - S2 is independent of whether anyone practices just patent

26

This standard embodies our judgment that the RAND royalty should be cost-based when the probability of R&D success exceeds the higher root of the quadratic equation that determines whether the patent-holder would choose cost-based or value-based licensing.

20

1.27 As above, let R1 and R2 be a potential licensee’s R&D costs associated with attempting to develop

their own technology and p1 and p2 be the respective probabilities of success.

One might argue that to the extent that the patent holder has made a RAND commitment on

patent 1 and it is possible to reap value by exercising patent 1 alone, then the analysis of the maximum

RAND royalty for patent 1 should follow the analysis in Section IV. If this argument were valid, then

propositions 1 and 2 above would characterize the maximum RAND royalty (with the substitution of p1,

B1, S1, and R1 for p, B, S, and R). Suppose, however, that B1 – S1 is much smaller than B2 – S2. In that case,

there are two alternative ways of exercising patent 1, either separately or in conjunction with patent 2,

and the latter is the more valuable strategy. The RAND commitment on patent 1 does not oblige the

patent holder to license its technology at a rate that allows a licensee to exercise it “profitably” but

inefficiently.28 That said, even if the patent holder is entitled to set a RAND rate premised on the use of

patent 1 in conjunction with the second technology, the patent holder has not made a RAND

commitment on patent 2, nor is patent 2 essential for creating a product compliant with the standard.

Thus, even if the patent holder can honor its RAND commitment with a royalty that presumes the use of

technology 2 as well, the analysis from Section V(B) applies. That is, the RAND rate would be:

i) min{R1/p1, B1 + B2 – S1 – S2 - R2/p2} if R1 > (B1 + B2 – S1 – S2 - R2/p2)/4

ii) B1 + B2 – S1 – S2 - R2/p2 if 𝑝1 ≤ 1−√1−4

𝑅1𝐵1 + 𝐵2 – 𝑆1 – 𝑆2 − 𝑅2/𝑝2

2

iii) R1/p1 if 𝑝1 > 1−√1−4

𝑅1𝐵1 + 𝐵2 – 𝑆1 – 𝑆2 − 𝑅2/𝑝2

2

Provided that the patent holder honors the RAND commitment with a license to patent 1 alone,

it can then also offer the bundle of patents 1 and 2 at the hold-up rate of B1 + B2 (i.e., it can achieve the

higher rate through mixed bundling). However, if it does pursue a pure bundling/patent licensing

27

One might also consider the possibility that the value from exercising patent 2 depends on whether there is competition from one or more firms exercising patent 1. Doing so raises a complicated set of issues. One of the simplifying assumptions of the GK model is that there is a single possible licensee. (A related assumption is that the royalty is a fixed fee). Absent the possibility of R&D to invent around a patent, one could interpret the royalties could be the per unit charges to a perfectly competitive industry that cause the competitive price to equal the monopoly price (provided that the sunk costs reflect constant long run marginal costs). The possibility of R&D by each firm would strain this interpretation, although one might assume that the source of the R&D would be another technology developer without the capacity to exercise the technology itself.

28 In our simplification of the GK model, we have assumed a single value for the benefits from exercising

the patent and for the sunk costs in complementary assets. GK assume that the gross benefit is an increasing function of the investment in complementary assets and obtain the results that the long run royalty would be based on the assumption that the licensee makes optimal complementary investments. Our point that the RAND rate can reflect efficient investment in R&D in technology 2 is similar in spirit to this more general feature of the GK model.

21

strategy by offering only the bundle, then the RAND rate for the bundle would be limited to the RAND

rate for patent 1 alone.29

VI. Conclusions and Policy Implications

The question we address in this paper is whether a patent holder that has made a RAND

commitment on a patent violates that commitment by offering a license to that patent only in a bundle

of patents that include patents that are not RAND-committed.

The starting point of our formal modeling is the GK model of patent bundling. That model

captures a key element of the problem we are addressing – the desirability of patent licenses that

protect patent users against hold up that effectively expropriates the value of the patent user’s sunk

investments in assets needed to capture the value of the technology. In the GK model, patent tying is

socially desirable because it is necessary to induce patent holders to enter into what they call long-term

licenses, i.e., licenses that the patent users can enter into prior to incurring sunk costs.

The desirability of bundling within the GK model does not, however, fully resolve the policy issue

that we address. One cannot use an economic model to analyze the implications of tying patents

without RAND-commitments to patents with RAND commitments unless RAND commitments are

explicitly addressed within the model, and the GK model does not take RAND commitments into

account. Incorporating RAND commitments into the GK model turns out to be important for two

reasons. First, the purpose of RAND commitments is to solve precisely the same problem that patent

bundling solves in the GK model: they are a commitment not to expropriate sunk costs (not to practice

hold-up). The possibility of making a RAND commitment at least weakens and potentially eviscerates the

argument that the primary effect of patent bundling is to prevent hold-up. Second, one of the reasons

that patent bundling is benign in the GK model is that the single rent principle applies for long run

contracting. The patents in the GK model are perfect complements, so the patent owner only needs one

patent to extract the full rent. But a RAND commitment necessarily implies a limit on the royalty for the

RAND-committed patent. Just as the single rent principle does not apply to a good that is subject to

price regulation, it does not apply to the combination of RAND-committed and non-RAND-committed

patents.

In the concern with licensing RAND-committed patents only in bundles with non-RAND

committed patents, the word “only” is key. As long as a patent owner offers a RAND-committed patent

(or a set of RAND-committed patents that are all necessary to implement a given standard) and charges

a RAND royalty, nothing precludes it from also offering a bundle that includes patents that are not

29

We have assumed that B2 – S2 is independent of whether or not one or more companies practice just patent 1. While it would be interesting to consider the possibility that competition from companies practicing just patent 1 reduces the value obtainable from practicing both patents, modeling this possibility raises complicated issues. A key simplifying assumption of the GK model is that there is only one potential licensee. (Related, they assume that the royalty is a fixed fee). Absent the possibility of undertaking R&D to invent around the patents, one could interpret the royalties as per unit rates offered to competitive users (with constant-returns-to-scale production) that induces them to charge the price that maximizes the value from the patents. But this alternative interpretation breaks down if R&D to invent around the patents is possible.

22

RAND-committed with those that are and the RAND commitment places no limit on the royalty for the

bundle. Using standard economic terminology, if the patent holder engages in mixed bundling, it honors

its RAND commitment by charging a RAND rate for the RAND-committed patent.30

The licensing practice that potentially gives rise to a concern is when the patent owner engages

in tying (not mixed bundling).31 While the GK results are not sufficient to dismiss concerns about tying

licenses for patents without RAND commitments to licenses of RAND-committed patents, the licensing

of patents only in bundles is a common practice with sound efficiency justifications. Thus, while there is

a legitimate concern that this type of tying might be a way to evade a RAND commitment, a ban on the

practice would ignore the significant transaction-cost justifications for the bundling of patents.

Importantly, the problem with offering RAND-committed patents only in bundles is not the bundling per

se but, rather, the terms on which the bundle is offered. A RAND commitment is a commitment to

make the RAND-committed patent(s) available for a reasonable rate. While that rate might not be

known when the patent-holder makes the RAND commitment, there is a process for determining a

RAND range and for assessing rates as RAND if the patent(s) were offered separately.32 As long as the

royalty rate for the bundle of patents would be considered RAND for the RAND-committed patent alone,

and the non-royalty terms of the license are similarly RAND, then the patent owner is honoring the

commitment even though it is including other patents in the bundle.

Determining a RAND rate is not a simple matter. Part of the complication stems from the

difficulty of measuring the factors that matter. As our model clarifies, part of the complication is

determining whether RAND implies value-based or cost-based royalties. But these complications are

inherent in any RAND determination. They do not alter and should not obscure the analysis of whether

offering a RAND-committed patent only in a bundle with other patents necessarily violates the RAND

commitment. It does not, but it only does not if the total license fee would be RAND for the RAND-

committed patents alone.

30

Strictly speaking, “mixed bundling” entails offering all the components of a bundle separately in addition to the bundle. In the GK model and our simplified version of it, mixed bundling would entail offering not only a license for the bundle and a stand-alone license for patent 1, but also a stand-alone license for patent 2. Moving away from these simple models, however, a practical application of mixed bundling would entail offering a license to the portfolio of RAND-patents alone, offering a second license to the non-RAND patents (either as a portfolio or in rational subsets), and offering a third license with a bundle of the RAND and non-RAND patents together, rather than having to offer individual licenses of each RAND-patent and each non-RAND patent, for the product offering cost reasons we explain above.

31 If the patent owner offers only the bundle, it engages in “pure bundling.” If, in addition to offering a

license to the bundle, it also offers a license to patent 2, it no longer engages in pure bundling but it is still tying patent 2 to patent 1.

32 While this process is still evolving, several court rulings offer frameworks for determining RAND rates.

See, e.g., Microsoft v. Motorola, 2013 WL 2111217 at *12 (W.D. Wash. Apr. 25, 2013); In re Innovatio IP Ventures, LLC Patent Litig., 2013 WL 5593609 at *8-10 (N.D. Ill. Oct. 3, 2013); Ericsson Inc. v. D-Link Systems, Inc., 773 F.3d 1201 (Fed. Cir. 2014); and In the Matter of Certain Wireless Devices with 3G and/or 4G Capabilities and Components Thereof, ITC Inv. No. 337-TA-868 at 123-24 (June 13, 2014), available at http://www.essentialpatentblog.com/wp-content/uploads/sites/234/2014/07/2014.06.26-Initial-Determination-on-Violation-PUBLIC-337-TA-868smMRC.pdf.

23

This principle limits the arguments that licensees and licensors can make. The limit on a licensee

is that it cannot argue that it necessarily deserves a discount from the bundled price if it only wants the

bundle in order to get access to the RAND-committed patents. As long as the licensor can show that its

royalty for the bundle would be RAND just for the RAND-committed patents, it is honoring its RAND

commitment. The limit on the licensor that engages in tying is that it cannot compute an implicit royalty

for licenses to the RAND-committed patents by subtracting the value of the licenses to the additional

patents in the bundle from the royalty for the bundle and then argue that this implicit royalty is RAND.

Allowing such an argument as a defense would create an obvious way for patent owners to avoid their

RAND commitments.

24

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