First-to-invent versus first-to-file:

Invention, and international patent law harmonization

Kaz Miyagiwa*

Osaka University and Emory University

Abstract:

The U.S. has been under pressure to abandon the unique first-to-invent feature of its patent lawfor awarding patents. The opposition to reform argues that switching to a first-to-file rule, theinternational norm, will undermine innovation. We evaluate this argument in a dynamicstochastic model of a patent race that captures the key features of the U.S. patent system. Themodel also explains the puzzle why there is much filing activity in the U.S., when in first-to-invent the inventor never has to file for a patent unless he must sue.

JEL Classification numbers: L3, O31, O34Keywords: first-to-file, first-to-invent, patent law harmonization, innovation, U.S. patent law

Please send correspondences to: Kaz Miyagiwa, The Institute of Social and EconomicResearch, Osaka University, Mihogaoka, Ibaraki, Osaka 567-0047, Japan. E-mail:kmiyagiwa@gmail.com

* The Institute of Social and Economic Research, Osaka University, and the Department of Economics, EmoryUniversity. I thank C.O.R.E. at the Unversite Catholique de Louvain at Louvain-la-neuve for the hospitality and theresearch environment. I also benefited from comments on earlier versions by Yuka Ohno, and seminar participantsat Hitotsubashi, Kobe, and Okayama Universities. A research grant from Microsoft’s Academic Research Programis gratefully acknowledged. Any opinions expressed as well as remaining errors are the author’s.

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1. Introduction

Despite recent successes in harmonizing patent law internationally, the U.S. patent law

still retains some unique and peculiar features. In this paper we focus on one such feature,

namely, the first-to-invent rule.1 When two people apply for a patent on the same invention, the

person who filed his application first gets the patent virtually everywhere else in the world.2 In

the U.S., however, determination is made as to priority of invention, and a patent is awarded to

the person who can demonstrate to have discovered the invention first. Although the U.S. has

repeatedly expressed its willingness to conform to the first-to-file rule, the international norm,

the opposition to reform remains strong.3

The opposition in the U.S. embraces two arguments. One is that the first-to-invent rule

protects small inventors who may take longer time to prepare patent applications and who

therefore would in a first-to-file system lose to major corporate inventors capable of hiring an

army of patent lawyers.4 However, Lerner (2003) asserts that this argument is spurious since

the recent patent law reform in the U.S. has created a new provisional patent application, which

is much simpler to file. Further, in the U.S., disputes over priority of invention are settled in a

legal proceeding called interference, which involves examining laboratory logbooks,

establishing dates for prototypes, and so on at a hearing before the USPTO (U.S. Patent and

1 Another prominent feature of the U.S. patent law was its confidential filing system. Until the Intellectual Propertyand Communications Omnibus Reform Act of 1999, all patent applications were kept secret until patents weregranted. This has since been changed and now applications are published 18 months after their filing dates, theinternational norm (see Aoki and Prusa 1996, and Aoki and Spiegel 2003). However, inventors choosing not to filefor a foreign patent can opt for non-publication of their applications, leaving open the possibility of notorious“submarine” patents; see Graham and Mowrey (2004).2 The exception is the Philippines, which uses a first-to-invent rule due to its colonial legacy with the U.S.3 A first-to-file rule is contained in the Patent Act of 2005, introduced by Rep. Lamar Smith, R-Texas. This billhowever, has not been approved, as of this writing. Also at the 2007 G8 Summit meeting in Germany, PresidentGeorge W. Bush formally stated his support for a first-to-file rule.4 See, e.g., Stephenson (2005).

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Trademark Office) Board.5 In one estimate the adjudication of the average interference costs

over one hundred thousand dollars (Kingston 1992). Since the costs of interferences are borne

equally by the parties involved, a first-to-invent rule does not necessarily protect financially

constrained small inventors. This point is confirmed in an empirical study of Cohen and Ishii

(2005), which finds that interference does not help small individual inventors against large

corporate inventors. Thus, concludes Lerner (2003), “the greatest beneficiary from the first-to-

invent system is the small subset of the patent bar that specializes in international law.”

This leads us to the opposition group’s second argument; that is, switching to a first-to-

file rule will undermine innovation because a patent issues not to the inventor but to the

individual who is fastest in filing a patent application. Although the precise mechanism by

which first-to-file undermines innovation is never spelled, the opposition often bolsters its

argument by adducing the undeniable fact that the U.S. has led the world in inventions for more

than a century, and attributing that remarkable record to the first-to-invent feature of the patent

law that the nation has had since 1836.6

The main objective of the present paper is to evaluate the opposition’s argument that a

first-to-file rule undermines innovation relative to a first-to-invent rule. In doing so, we focus

on two types of risks faced by an inventor. One is the risk of losing his invention to someone

who discovers it later. First-to-invent diminishes this risk, giving an inventor time and security

to experiment with and perfect his invention without the fear of losing it to later inventors. On

the other hand, first-to-invent exposes the inventor to the risk of duplication. Since the inventor

5 See Cohen and Ishii (2005) for a detailed study of the interference process.6 For example, “It should be understood that it is because the U.S. has a first to invent structure and the rest of theworld has a first to file structure that the U.S. is the production and employment machine that it is.” (Seehttp//www.piausa.org/layout/set/print/patent_reform_issue.)

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can establish his priority of invention at any time under the first-to-invent rule, he can delay

filing for a patent. In such an environment, the inventor in general bears the risk of reinventing

something that has already been discovered, wasting time and resources and being sued in the

end. Due to these two conflicting risks, it is not a priori clear whether first-to-invent is more

conducive to invention than first-to-file.

In addition, first-to-invent also poses a puzzle. Given that, in reality, filing for a patent is

costly in terms of legal fees and the time to write the patent application, it is not clear why

inventors should file for a patent at all in first-to-invent unless they must sue. And yet we see so

much filing activity in the U.S., even though only a small fraction of patentees end up suing for

patent infringements.

In this paper we examine these issues in a dynamic model of a patent race. The model

has two stages. In the first stage, each firm chooses a level of investment in R&D, which

determines its probability of discovery in the second-stage game. This assumption is consistent

with the finding of Cohen and Ishii (2005) that most patent races are among major corporate

research laboratories chasing well-defined research topics, where initial setups are of utmost

importance in conducting research.

The second stage consists of an infinite time horizon. At each instant, the firms

simultaneously decide whether to carry out R&D activity at a fixed cost c, representing, e.g.,

the cost of running the lab. If they proceed with R&D activity, nature chooses a “success” or a

“failure” for each firm according to the probability of discovery determined in stage 1. Each

firm learns what nature chose for it, but not what nature chose for the rival. Thus, there is an

informational asymmetry in the model.

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Once having made a discovery (at a stochastic date), a firm decides whether to file for a

patent immediately or improve the quality of the invention. The improvement process is not

stochastic but time-consuming. For simplicity we assume the process requires a fixed time.

After completing the improvement process, the firm again decides whether to file for a patent

or delay until it has to sue (this decision is irrelevant in first-to-file, because there the inventor

must establish his priority by filing). A strong novelty requirement or scope protection is

assumed, so the unimproved and the improved version cannot be patented separately.

Our results can now be summarized. The first-to-file rule yields two types of pure-

strategy equilibria, depending on the parameter values. In one, the firms file immediately, in

another, they improve the invention. There is also the mixed-strategy equilibrium. The first-to-

invent rule also yields these two pure-strategy equilibria. However, the equilibrium with firms

improving the invention is risk-dominant. The model possesses another equilibrium, in which

the inventor delays filing after the improvement. This equilibrium however exists only if the

cost of interferences being sufficiently low relative to the patent application fee, an unlikely

scenario, given the extremely high cost of interferences in reality, as we saw above. Thus, our

model explains why there is much filing activity in the U.S. when there is no need to file for a

patent.

Our analysis shows that the firms invest more in R&D when they improve the

invention. Since the firms always improve the invention in first-to-invent but not necessarily so

in first-to-file, our result suggests that first-to-invent is more conducive than first-to-file when

the improvement adds little to the value of the invention.

The paper contributes to the existing literature that examined various aspects of patent

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law; for example, patent length and breath (Nordhaus 1969, Gilbert and Shapiro 1990,

Klemperer 1990, O’Donoghue, Scotchmer and Thisse 1998), novelty requirements (Scotchmer

and Green 1990), patent renewal rules (Scotchmer 1999, Cornelli and Schankerman 1999), and

pre-grant patent publication (Aoki and Prusa 1996, Aoki and Spiegel 2003). However, there is,

to the best of the author’s knowledge, no formal analysis of the first-to-invent feature of the

U.S. patent law, with the exception of Scotchmer and Green (1990). Their work however

differs significantly from the work on hand both in focus and setup.

Scotchmer and Green (1990) consider the setup in which two firms races to improve

some base-level technology already patented to a third-party. There are two innovations:

intermediate and final. Two features set their work apart from the present study. First, there, the

probability of innovation is exogenous so the relative effect of the two rules on the levels of

R&D investment is unexamined. More importantly, in their model there is complete

information; the firm learn immediately when the rival discovered the innovation, whether it is

patented or not. So, unlike in this paper, firms do not face the risk of duplication.

As regards focus, Scotchmer and Green (1990) are more concerned with the varying

degrees of novelty requirements of patent law than with the patent awarding rules. In their

model, patenting the intermediate invention reveals its content to the rival firm, enabling the

rival to bypass the intermediate step, thereby accelerating discovery of the final innovation. If

the novelty requirement is so strong that the intermediate innovation infringes the existing

patent on the base-level technology, however, the intermediate innovation is not patented,

thereby retarding the discovery of the final innovation. Even with a weaker novelty

requirement, the inventor may forgo patenting the intermediate invention to force the rival out

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of competition. However, such a shakeout is less likely to arise in first-to-file because the rival

could get a patent on the intermediate innovation if the inventor does not. Scotchmer and Green

(1990) thus conclude that first-to-file accelerates discovery of the final innovation relative to

first-to-invent in a broader set of parameter values they consider.

The remainder of the paper is organized in five sections. The next section gives a more

detailed description of the model. Sections 3 and 4 are devoted to the study of first-to-file, and

first-to-invent, respectively. In Section 5 we compare the incentives to innovate under these two

rules. Section 6 concludes.

2. Environment

We consider an R&D race between two symmetric firms, i = A, B. The model has two

stages. In the first stage each firm simultaneously chooses a level ki of investment in R&D,

which determines the probability of discovery to be explained in detail below. The second stage

has an infinite time horizon, with time running continuously from t = 0. There, the first-stage

R&D investment generates a Poison process, with the cumulative probability of discovery by

time t given by

prob(τ > t) = 1− e−hi t ,

where the hazard rate hi = h(ki) is determined by the first-stage R&D investment.

The invention generates the flow m of revenues without the improvement and the flow

µ with the improvement. The improvement process is non-stochastic and takes a fixed length of

time Δ to complete. The premature abandonment of improvement adds nothing to the value of

the invention. A patent is issued immediately whenever the inventor files for it with the

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application fee f > 0. We assume strong novelty or scope requirements in patent law so that the

original and the improved invention cannot be patented separately been patented. Finally, not to

make the model trivial, we assume that

e-rΔ(µ/r – f) > m – f,

where r is the instantaneous rate of interest. The left-hand side of the inequality denotes the net

value of the improved invention. Thus, the above inequality says that the invention is worth

improving in the absence of rivalry. However, that need not be the case under rivalry.

In contrast to Scotchmer and Green (1990) this paper assumes incomplete information.

Nature reveals the outcomes of R&D activities to each firm but not to its rival. Thus, a firm

knows of the rival’s discovery only if the latter files for a patent.7 Since the firms play a game

of incomplete information, we look for a perfect Bayesian-Nash equilibrium, according to

which the equilibrium strategies are sequentially rational, given beliefs, while beliefs are

Bayes-consistent with the equilibrium strategies. In solving the models we focus on a stationary

equilibrium of the game, i.e., a strategy that specifies a time-independent action for all t ≥ 0.

3. First-to-file

Under the first-to-file rule, because priority of invention must be established by filing

for a patent, not filing (unless the inventor must sue) is never an equilibrium outcome. This

points to two symmetric pure-strategy equilibria: one in which both firms file for a patent

immediately, and one in which both improve the invention.

7 In contrast, we assume that the firm that already has the invention knows it when its rival makes a discovery, evenif neither invention is patented. That may be because the profits diminish when there are two competing inventions.This assumption is needed when we later discuss the possibility of the firms never filing for a patent under the first-to-invent rule.

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3.A. Equilibrium in which firms file immediately for a patent

In perfect Bayesian-Nash equilibrium, the firms form beliefs as to the probability that

the rival has made the discovery to date. The equilibrium under consideration implies the

following beliefs: when a patent has not been issued to the rival before t, the firm believes that

the rival has not discovered the invention yet. Using such beliefs, we proceed to describe the

equilibrium profit. Given the Poison process, R&D activity by firm A results in a discovery

with the probability (1 - e−haε ) during a brief time interval [t, t + ε), where ε > 0 is arbitrarily

short, and the hazard rate ha is pre-determined. It can be showed that the expected profit to firm

A approaches ha(m/r – f) – c when ε approaches zero. This profit of course is conditional on the

invention not having yet discovered before t. Given the independent Poison processes, neither

firm has discovered the invention before time t with the joint probability that exp[– (ha + hb)t].

Summing these conditional expected profits over time t ≥ 0, we obtain the total expected profit

for the second-stage game as

e−rte−(ha +hb )t[ha (m / r − f ) − c)0

∞

∫ dt .

Turning to the first stage, the exposition simplifies considerably if we let the firms

directly choose the hazard rate hi instead of the R&D investments ki. Evaluating the above

integral, and subtracting the cost of R&D investment, we obtain the expected net profit:

(1)ha (m / r − f ) − cr + ha + hb

− k(ha )

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where k(hi) denotes the cost of investment in R&D. In the first stage, firm A chooses ha to

maximize (1), given hb. The first term in (1) is concave in ha. To ensure an interior optimum,

assume that k(hi) satisfies the Inada conditions: i.e., k(0) = 0, k’ > 0, k” > 0, k’(0) = k(1) = ∞,

where primes denote differentiation.

The first-order condition can be arranged to yield the following equation:

(2) (m / r − f )(r + hb ) + c − k '(ha )(r + ha + hb )2 = 0 .

This implicitly defines A’s best response function r0(hb), where subscript “0” reminds us that

the firms file for a patent without no (zero) improvement on the invention. Firm B solves the

symmetric problem. The symmetric Nash equilibrium levels of investment (hazard rates)

obtain by putting ha = hb in (2). We denote this common equilibrium value by h0*.

In the equilibrium, no firms should have the unilateral incentive to deviate from it. If A

deviates, improving the invention would yield the profit exp(-rΔ)(µ/r – f) in the absence of

rivalry, but with rivalry that profit is realized only if B does not discover the invention while A

improves the invention. Should B make a discovery before A completes the improvement, B

will file immediately and get a patent. Since B fails to discover the invention during the interval

Δ with the probability exp(- hbΔ), the expected profit to A of a deviation equals

e−hbΔe−rΔ (µ / r − f ) .

A has no incentive to deviate if and only if this is less than the equilibrium profit; i.e.,

m / r − f ≥ e−h0 *Δ (µ / r − f )e−rΔ ,

where we replaced hb with the equilibrium hazard rate, h0*.

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Although the invention is worth improving, in first-to-file the inventor faces the risk of

losing the invention to the rival who discovers the invention second but files first. Thus, if the

probability of discovery during the improvement process is large, or exp(- h0*Δ) is small, then

the firms prefer to file immediately to minimize this risk

3.B. Equilibrium in which the invention is improved

We next consider the equilibrium in which each firm improves the invention. In this

case, at time t ≥ Δ, the firm does not know whether the rival has discovered the invention

during the preceding interval [t - Δ, t). However, the rival would have filed for a patent before t

if he made a discovery before t - Δ. Thus, the firm has incomplete information only over the

interval [t - Δ, t).

If B made the discovery during this interval, B will surely file for a patent before A

completes its improvement process. Therefore, A earns the revenue only if B did not make the

discovery during the preceding interval, which occurs with probability exp(-hbΔ). Thus, A’s net

profit from doing R&D at t ≥ Δ is

(3) hae−hbΔe−rΔ (µ / r − f ) − c

This of course is conditional on A not having made a discovery before t and B not having made

its discovery before t - Δ ≥ 0, which occurs with the joint probability exp(-hat)exp[-hb(t - Δ)].

Weighting the profit (3) with these probabilities and summing over t ≥ Δ, we obtain the

expected profit to A

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(4) e−rte−hate−hb (t−Δ )[hae−hbΔ (µ / r − f )e−rΔ − c]

Δ

∞

∫ dt

= e−(r+ha +hb )Δ[ha (µ / r − f )e−rΔ − cehbΔ ]

r + ha + hb. (t ≥ Δ)

For t < Δ, the situation is similar except that firm A is ignorant about the rival’s

discovery over the shorter interval [0, t) < Δ. As B fails to make the discovery with the

probability exp(- hbt) in this interval, the corresponding expected profit is given by

(5) e−rte−hat[hae−hbt (µ / r − f )e−rΔ − c]

0

Δ

∫ dt

= (1− e−(r+ha +hb )Δ )ha (µ / r − f )e−rΔ

r + ha + hb−c(1− e−(r+ha )Δ )

r + ha.

Adding up (4) and (5) and subtracting the cost of investment in R&D, we obtain the total net

profit for A in stage 1:

(6)ha (µ / r − f )e−rΔ

r + ha + hb−c(1− e−(r+hb )Δ )

r + ha−ce−(r+hb )Δ

r + ha + hb− k(ha )

The first-order condition for the maximum of (6) yields

(7) (r + hb )e−rΔ (µ / r − f ) + cN − k '(ha )(r + ha + hb )

2 = 0 ,

where

(8) N ≡ e−(r+hb )Δ + (1− e−(r+hb )Δ )(1+ hbr + ha

)2 > 1.

The symmetric Nash equilibrium obtains by setting ha = hb in (7) and is denoted by h1*.

We next check the inventor’s incentive to deviate. Suppose that A, having discovered

the invention at t, files for a patent immediately instead of improving the technology as in the

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equilibrium. Then, filing first, A gets the patent and the payoff of m/r – f, whether or not B has

already discovered the invention. This profit should be compared with the equilibrium profits,

which are either e−h1 *Δe−rΔ (µ / r − f ) if t ≥ Δ, or e−h1 *te−rΔ (µ / r − f ) if t < Δ. It follows that A

has no incentive to deviate at any t ≥ 0, if

m/r - f ≤e−h1 *Δe−rΔ (µ / r − f ) .

We have obtained the following result.

Proposition 1: In first-to-file:

(A) The model possesses the equilibrium in which both firms choose to file immediately for a

patent on the original invention, if the equilibrium probability h0* satisfies

(9)m / r − f

e−rΔ (µ / r − f )≥ e−h0 *Δ .

(B) The model possesses the equilibrium in which both firms choose to improve the quality of

the invention if the equilibrium probability h1* satisfies

m / r − fe−rΔ (µ / r − f )

≤ e−h1 *Δ .

Finally, it is straightforward to check that there is no asymmetric equilibrium in first-to-

file as the firm has no incentive to postpone filing if the rival files immediately for a patent.

Also, the model does not possess the equilibrium in which the firms never file for a patent, for

in first-to-file filing is necessary for establishment of priority of invention.

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3.C. A comparison of the two equilibrium R&D efforts

We now compare the levels of investment in R&D in the two equilibrium outcomes

above. Since the proof of the next result does not offer useful insight, we relegate it to the

appendix and report only the conclusion.

Proposition 2: h1* > h0*; that is, in first-to-file firms invest more in R&D when they improve

the invention than when they file immediately for a patent.

Since the improved invention is more valuable, this conclusion seems obvious, but not so given

the fact that the inventor takes the risk of duplication and hence incurs higher R&D costs (N >

1 in Equation (8)).

The next question we examine is what determines which equilibrium to occur. Note

that h0* < h1* implies exp(- h0*Δ) > exp(- h1*Δ). Thus, if

m / r − fe−rΔ (µ / r − f )

≥ e−h0 *Δ > e−h1 *Δ

the firms file for a patent right away, while if

e−h0 *Δ > e−h1 *Δ ≥ m / r − f

e−rΔ (µ / r − f ),

the firms improve the invention, as we stated in Proposition 1. However, Propositions 1 and 2

give rise to the case in which

(10) e−h0 * >m / r − f

e−rΔ (µ / r − f )>e−h1 * .

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If (10) holds, the both conditions in Proposition 1 fail, implying there is no equilibrium in pure

strategies. However, as we show in the appendix, there is an equilibrium in mixed strategies;

i.e., the firms randomize between filing immediately and improving the invention. In this

mixed-strategy equilibrium, the equilibrium expected profit equals m/r – f, implying that the

firms invest h0* in R&D. The next proposition then summarizes the findings of this section.

Proposition 3: In first-to-file, the firms invest h1* in R&D if

m / r − fe−rΔ (µ / r − f )

≤ e−h1 *Δ ,

and h0* (< h1*) if the inequality above is reversed.

4. First-to-invent

We turn next to the first-to-invent rule, one of the main features of the American patent

law. In first-to-invent, when both firms apply for a patent, priority is determined through

interferences as explained in the introduction. As noted there, both firms equally share the cost

of an interferences hearing. We let I denote the cost of the interference per firm. For the next

two subsections we assume that the inventor files for a patent after the improvement process.

The assumption is relaxed in Subsequent 4.C.

4.A. Equilibrium in which firms file immediately for a patent

The equilibrium outcome is the same that we obtained and discussed for first-to-file.

Here, we need only to check the incentive to deviate under the first-to-invent rule. Thus,

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suppose that, having discovered the invention in period t, firm A deviates, choosing to improve

the invention instead of filing immediately. Then, with the probability [1 - exp(- hbΔ)], B will

make a discovery and file for a patent before A does. While this reduces the profit to A to zero

in first-to-file, in first-to-invent A can establish its priority before an interference hearing at the

additional cost of I. This suggests that a deviation yields:

e−hbΔe−rΔ (µ / r − f ) + (1− e−hbΔ )e−rΔ (µ / r − f − I )

=e−rΔ[(µ / r − f ) − (1− e−hbΔ )I ] .

That is, in first-to-invent firm A’s priority is secure, now matter what, but the cost of the

interference must be borne when firm B files for a patent before A completes the improvement.

Now the no-deviation condition can be stated as:

(11) m / r − f ≥ e−rΔ[(µ / r − f ) − (1− e−hbΔ )I ] ,

or in this equivalent form:

(12)m / r − f

e−rΔ (µ / r − f )≥ 1− (1− e

h0 *Δ )Iµ / r − f

.

A comparison of this condition with that in (9) under the first-to-file rule indicates that, if µ/r – f

> I, or the cost of the interference hearing is less than the value of the improved innovation,

valued at the time of filing, then the right-hand side of (12) exceeds that of (9), meaning that the

firms file immediately for a patent in first-to-invent for a narrower ranges of parameters than

they do in first-to-file.

4.B. Equilibrium in which the invention is improved

17

The equilibrium outcome is the same that we obtained in Subsection 3.B under the

first-to-file rule. The difference between the two rules again manifests itself in the inventor’s

incentive to deviate. Filing immediately for a patent, A would obtain m/r – f only if B did not

discover the invention during the preceding interval [t - Δ, t) for t ≥ Δ. If B has made the

discovery before A, B will challenge A in an interference and get the patent, requiring A only to

foot the bill of an interference hearing. Thus, a deviation yields

e−h1 *Δ (m / r − f ) − (1− e−h1 *Δ )( f + I ) .8

Subtracting this from the equilibrium profit, we obtain the following no-deviation condition

e−h1 *Δe−rΔ (µ / r − f )– [e−h1 *Δm / r − f − (1− e−h1 *Δ )I ]

= e−h1 *Δ[e−rΔ (µ / r − f ) − (m / r − f )]+ (1− e−h1 *Δ )( f + I )> 0.

Since this always holds, improving the invention is the equilibrium in first-to-invent for all the

relevant parameter values.

To sum the discussion of this section so far, if (11) fails, improving the invention is the

only equilibrium outcome. In contrast, if (11) holds, filing immediately for a patent is also the

equilibrium outcome. In the latter case, however, the latter is risk-dominated by the equilibrium

in which they improve the invention. Thus, we conclude

Proposition 4: In first-to-invent, the equilibrium with firms improving the invention risk-

dominates the one with firms filing immediately.

8 Strictly speaking, B will claim its priority when it finishes the improvement, that is, between t and t + Δ, so the costI should be discounted by the expected date of the interference. Since this does not matter for our result as seenbelow, we ignore this detail to keep the notation simple.

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4. C. Equilibrium in which firms never file for a patent

We have so far assumed that an inventor always patents his/her invention. It is easily

seen that filing for a patent is the equilibrium behavior in first-to-file, for the inventor must file

to claim priority. However, in first-to-invent the first inventor never has to file for a patent

unless he must sue. Given that there is the filing cost, then, it is not all too clear why there is so

much filing activity in the U.S. In the remainder of this section we examine this puzzle.

For this purpose we need the following additional assumption. If the two firms have the

inventions, the flow profits to each are less than when only one inventor possesses the

invention. A decrease in profit alerts the first inventor of the rival’s discovery, even if neither

has patented the invention. Without this assumption the relationship between the firms ceases to

be rivalrous.

With this additional assumption, consider the equilibrium in which an inventor never

files for a patent unless to sue for a patent infringement. As before, we first describe the

equilibrium and then check the incentive to deviate. In the equilibrium, firm A improves the

invention but does not file for a patent until firm B files for a patent. If B has not discovered the

invention yet, then firm A, on completing the improvement process, receives the revenue µ

until B makes a discovery. When that happens, A, altered by falling profits of the rival’s

discovery, files for a patent and establishes priority at an interference hearing. This suggests the

following profit to A, valued at the time of the completion of the improvement:

µ + hb (µ / r − f − I )r + hb

= µ / r − hb ( f + I )r + hb

.

As the first inventor, A is assured of the revenue µ/r, but must incur the additional costs (f + I)

of filing and the interference whenever B makes a discovery.

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We have so far assumed that firm A discovers the invention before B. Suppose instead

that B discovers the invention first. Then, firm A will be challenged in an interference hearing

and will lose the case, incurring the loss of (f + I). Since B would have discovered the invention

before t with the probability 1 – exp(– hbt), we obtain the following expected profit to A:

e−hbt (µ / r − hb ( f + I )r + hb

) − (1− e−hbt )( f + I )

= e−hbtµ / r − ( f + I )(1− e−hbt + hbe−hbt

r + hb) ≡ U.

This is the value of the invention to A at the time of discovery. The rest of the modeling adds no

insight to our understanding, we relegate it to the appendix. Here we simply denote the

equilibrium level of investment in R&D by h2*.

Now, consider a deviation by A, who files for a patent after the improvement at t + Δ. If

B has the invention before t, B will respond by calling for an interference hearing, and B will

win the case. If B did not have the invention before t, A receives the patent and B immediately

drops out of the race. Thus, the expected profit to A from the deviation is

(1− e−h2 *t )(−I ) + e−h2 *tµ / r − f .

Subtracting this from U, we have the following no-deviation condition for never filing for a

patent

e−h2 *trf − h2

*Ir + h2

* ≥ 0.

or more simply

(13) rf > h2*I.

20

Proposition 5: In the first-to-invent rule, the firms file for a patent after the improvement if and

only if

(14) rf ≤ h2*I.

Intuitively, since the first-to-invent rule guarantees priority of invention for the first

inventor, there seems little need to file for a patent unless the inventor must sue. However, an

interference hearing is a very costly choice. Alternatively, filing for a patent, the inventor can

send a clear signal, prompting the rival to drop out of the race, and obviating interference

hearings forever. Given that interferences are extremely costly in reality, (14) is likely to hold.

This may explain why there is much filing activity in the U.S. without suing, when the

inventors never really have to file to establish priority of invention.

5. A comparison of first-to-file and first-to-invent

We now answer the question whether first-to-invent furthers innovation relative to first-

to-file in the next proposition.

Proposition 6:

(A) If in first-to-file the firms file immediately for a patent (with positive probability), first-to-

invent induces more efforts in R&D than first-to-file does.

(B) Suppose that in first-to-file the firms improve the invention. If (14) holds, first-to-file and

first-to-invent are equally conducive to R&D.

21

(C) If (13) holds, inventors file only when they sue. First-to-invent is more conducive to R&D

than first-to-file.

The first two parts of the proposition are simply the summary of what we have already

established. First, suppose that (14) holds, so the firms file for a patent on competing the

improvement. Suppose further that the value of the patent on the improved invention is

sufficiently large. Then, the firms invest h1* under the first-to-file and first-to-invent rules. On

the other hand, if first-to-file induces the inventor to file immediately for a patent, then, h1* >

h0*; the firms invest more in R&D under the first-to-invent rule than under the first-to-file rule.

Part (C) of Proposition 6 compares the levels of investment in R&D when (13) holds. If

(13) holds, the inventor finds saving the filing fee worthwhile relative to incurring the cost of

interference. However, delaying filing for a patent also exposes the inventor to the increased

uncertainty, because he never finds out whether the rival has discovered the invention until he

discovers his own. Despite this, we can show in appendix that h2* > h1*, which is part (C).

Our main findings are based on the following intuition. In our model firms prefer the

improved version to the original and would exert more effort in R&D if they could agree to

commit to taking time to improve. Although such a commitment is impossible to make, first-

to-invent guarantees such a result by eliminating the risk of losing the invention to a latecomer.

In contrast, first-to-file does not provide such guarantee. As we saw, if the improvement results

in insufficient value added, firms choose to file immediately for a patent in the fear of losing the

patent to the late inventors. But the reduced value of invention diminishes the incentive to

invest in R&D.

22

5. Concluding remarks

Despite considerable pressure from the international community to conform to the

international norm, the first-to-invent feature of its patent law draws much support in the U.S.

One supporting argument is that the first-to-invent feature makes the U.S. the innovation

powerhouse that it is. In this paper we evaluate this claim in a stochastic model of R&D

competition. When there is a discovery, the inventor can file immediately for a patent or take

time to improve the invention for an increased value before filing. We find that when this

incremental value is substantial there is no difference between first-to-file and the first-to-invent

rule. If the incremental value is less substantial, however, the first-to-invent rule induces more

efforts in R&D than the first-to-file rule.

In first-to-invent, inventors never have to file for a patent unless to sue. Yet, there is,

despite the filing fees, much filing activity in the U.S. that does not involve suing. Our model

also addresses this empirical puzzle. We find that such a result arises in equilibrium only if the

filing fee is expensive relative to the interference fee, the condition unlikely to be met in reality.

Thus, our analysis suggests that firms file for a patent to avoid having to sue the rival. If that

condition is satisfied, however, it only reinforces our result: first-to-invent induces strictly

greater efforts in R&D than first-to-file.

Our results are derived under some simplifying assumptions. One is the assumption

that the operating cost is constant at c. Should it increase with investment in R&D, maybe

because a larger lab requires more maintenance cost, then that would make investment in R&D

less attractive. However, it would be unlikely to reverse our finding because one can invest just

23

as much in first-to-invent as in first-to-file and still get greater profit due to the improvement.

On the other hand, should the operating costs fall with R&D investment, perhaps because the

greater investment in R&D the more efficient the lab is to operate daily, then our case is likely

to be strengthened.

In this paper we focus on individual firms’ incentive to invest in R&D for some well-

defined R&D target under the two rules, where strategic interactions are important. In the real

world, innovations can give rise to innovation cycles or subsequent innovations, some of which

may be inconceivable before the original innovations are discovered (see, e.g., Green and

Scotchmer, 1995, and O’Donoghue 1998, on some issues). In this case, the issue is less on the

strategic interaction of the rival firms but on how fast the original invention spawns successive

inventions in society. It is important that the two rules be compared in such a context. It is also a

worthwhile exercise to construct a growth model to examine the effect of the two rules on the

growth rate. Finally, while we compare the two rules as two alternatives in one country, it

would be useful to investigate the effect of patent law harmonization in a model of two

countries, letting one country switch from the first-to-invent rule to the first-to-file rule, which

is already in use in the other countries. We leave these exercises for future research.

24

Appendix

A. Proof of Proposition 2

Let Ga(ha, hb) denote the left-hand expression of (2). This vanishes when ha is evaluated at the

optimal value, r0(hb), i.e., Ga(r0(hb), hb) = 0. Similarly, let Ha(hA, hB) denote the left-hand side

of (7). Now, we compute

Ha(r0(hb), hB) - Ga(r0(hb), hb)

=[e−rΔ (µ / r − f ) − (m / r − f )](r + hb ) + (N −1)c > 0 .

since N > 0 as shown in the text. Given that Ga[r0(hb), hb] = 0, the inequality implies Ha[r0(hb),

pb] > 0. Then, since Ha is concave with respect to ha (satisfying the second-order condition)

and Ha[r1(hb), hb] = 0, we conclude that r1(hb) > r0(hb), i.e., firm A’s best-response function

lies further out when both inventors improve the inventions than when both file for a patent on

discovery. The same holds true for B. Proposition 2 follows.

B: The mixed-strategy equilibrium in first-to-file

Focusing on the symmetric mixed-strategy equilibrium, suppose that, having made a discovery

at t, an inventor improves the invention with constant probability λ ∈[0, 1]. If he discovers the

invention at t, by filing immediately he guarantees the profit m/r – f. By improving the

invention he expects to earn {exp(-hbΔ) + λ[1 – exp(-hbΔ)]}exp(-rΔ)µ/r – f. In the mixed-

strategy equilibrium these two profits are equal. Thus A’s expected profit equals m/r – f. As this

is the same as that in the equilibrium in which the firms file for a patent immediately, the

equilibrium investment in R&D for the present case is also given by h0*. Then

25

m ={exp(-h0*Δ) + λ[1 – exp(-h0*Δ)]}exp(-rΔ)µ

determines the value of λ:

λ = m − e−(h0 *+r )Δµ(1− e−h0 *Δ )e−rΔµ

which lies strictly between zero and unity as required.

C: Risk dominance in first-to-invest

Consider the following bimatrix, where two firms simultaneously choose between F = file

immediately and W = wait to improve the invention.

F W

F a, a b1, b2

W b2,b1 d, d

The payoffs, taken from the text, are as follows:

a = m/r – f ≥ b2 = (µ / r − f )e−rΔ − (1− e−h0 *Δ )I

d = e−h0 *Δe−rΔ (µ / r − f )> b1 =e−h0 *Δ (m / r − f ) − (1− e−h0 *Δ )( f + I ) .

When the firms have chosen h0*, the game has two equilibria (F, F) and (W,W). (W,W) risk-

dominates (F, F) if the product of the deviation losses is higher for (W, W), i.e., if the following

inequality holds (Harsanyi and Selten, 1988):

(b1 – d)2 - (b2 – a)2 > 0 .

This condition holds because, rewriting the let-hand side as

26

(b1 – d + b2 – a)(b1 – b2 – d + a),

we find the first term negative, and also the second term, since

b1 – b2 – d + a = (1+ e−h0 *Δ )[(m / r − f ) − (µ / r − f )e−rΔ ]− (1− e−h0 *Δ ) f < 0.

D: The equilibrium R&D investments when the firms delay filing for a patent in first-to-invest

The first-stage profit to A is written

e−rte−hat (hae−rΔU − c)

0

∞

∫ dt − k(ha ) ,

where U is defined in the text. Substituting for U and evaluating the integral, we write the

above as

hae

−rΔ{µ / r + ( f + I )( rr + hb

)}

r + ha + hb – hae

−rΔ ( f + I ) + cr + ha

- k(ha).

Maximizing this with respect to ha, we obtain the first-order condition:

(A1) (r + hb )e−rΔµ / r − {1− (1+ hb

r + ha)2}re−rΔ ( f + I ) + c(1+ hb

r + ha)2

- (r + ha + hb )2 k '(ha )= 0.

Setting ha = hb and solving the above equation yields the equilibrium R&D investment, h2*. To

compare that with h1* we evaluate the right-hand side of (A1) at h1* and subtract it from the

right-hand side of (7). The result is

(A2) {hb + r(1+hb

r + ha)2} f + {(1+ hb

r + ha)2 −1}(I + ce−(r+hb )Δ ) > 0

27

where hb = h1*. Since the right-hand side of (7) vanishes at h1*, (A2) implies that the marginal

profit (the right-hand side of (A1) is positive at h1*, implying that h2* > h1*.

28

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