Discussion Paper No. 703

FIRST-TO-INVENT VERSUS FIRST-TO-FILE:
INTERNATIONAL PATENT LAW
HARMONIZATION ANDINNOVATION

Kaz Miyagiwa

November 2007

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

First-to-invent versus first-to-file:
International patent law harmonization and innovation

Kaz Miyagiwa*
October 29, 2007

Abstract:
The U.S. has been under pressure to abandon the unique first-to-invent feature of its patent law
for awarding patents. The opposition to reform however argues that switch to a first-to-file rule,the international norm, will undermine innovation. We evaluate this argument in a dynamic
stochastic model of a patent race. The result generally supports the opposition’s argument.
JEL Classification numbers: L3, O31,O34
Keywords: 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 Economic
Research, 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, Emory
University. I thank Yuka Ohno and seminar participants at Hitotsubashi and Kobe Universities for comments. A
research grant from Microsoft’s academic research program is gratefully acknowledged. Any opinion expressed arethose of the author’s.

First-to-invent versus first-to-file:
International patent law harmonization and innovation
Abstract: The U.S. has been under pressure to abandon the unique first-to-invent feature of its
patent law for awarding patents. The opposition to reform however argues that switch to a firstto-file rule, the international norm, will undermine innovation. We evaluate this argument in a
dynamic stochastic model of a patent race. The result generally supports the opposition’sargument.
1. Introduction
Despite recent successes in harmonizing patent law internationally, the U.S. patent law
still retains some unique features. One such feature is the first-to-invent rule.1 When two people
apply for a patent on the same invention, virtually all other governments in the world issue apatent to the person who filed his application first. In the U.S., however, determination is madeas to priority of invention and a patent is awarded to the person who can demonstrate to havediscovered the invention first.2 Although the U.S. has repeatedly demonstrated its willingness
to conform to the international norm, the opposition remains strong.3
The opposition to patent law reform in the U.S. embraces two arguments. One is thatthe first-to-invent feature of the U.S. patent law protects small inventors who may take longer
to prepare patent applications and who therefore would lose to major corporate inventors in a1

Another prominent feature of the U.S. patent law was its confidential filing system. Until the Intellectual Property
and Communications Omnibus Reform Act of 1999, all patent applications were kept secret until patents were
granted. 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 bill
however, has not been approved, as of this writing. Also at the 2007 G8 Summit meeting in Germany, President
George W. Bush formally stated his support for a first-to-file rule.

2
first-to-file system.4 However, Lerner (2003) calls this argument spurious, noting that 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, establishingdates for prototypes, and so on at a hearing before the USPTO (U.S. Patent and 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. Cohen and Ishii (2005) find in an empirical study that interference does nothelp 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 patentbar that specializes in international law.”
A second argument employed by the opposition group is that a first-to-file rule will
undermine innovation, because a patent issues not to the inventor but to the individual who isfastest in filing a patent application. To bolster this argument the opposition adduces theundeniable fact that the U.S. has led the world in inventions for more than a century andattributes that remarkable record to the first-to-invent feature of the patent law that the nation
has had since 1836.6
The objective of the present paper is to evaluate the argument that a first-to-file rule4

See, e.g., Stephenson (2005).
See Cohen and Ishii (2005) for a detailed study of the interference process.
6
For example, one writes “It should be understood that it is because the U.S. has a first to invent structure and therest of the world 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.)5

3
undermines innovation relative to a first-to-invent rule. In doing so, we focus on two types ofrisks faced by an inventor. A first is the risk of losing his invention to someone who discovers it
later. First-to-invent eliminates this risk, giving an inventor time and security to experimentwith and perfect his invention. However, first-to-invent can also expose an inventor to anotherrisk, the risk that he may be wasting resources trying to discover the same invention that has
already been discovered. First-to-invent can increase this risk by allowing inventors to takemore time before filing for a patent. Due to these two risks it is not a priori clear whether firstto-invent is more conducive to invention relative to first-to-file.
To study how these risks affect the incentives to invent, we develop a dynamic modelof a patent race. We assume a stationary environment, in which two firms engage in a patent
race over an infinite time horizon. A firm’s discovery date is stochastic, and depends on thelevel of investment in R&D a firm makes at the beginning, e.g., the size of the lab it builds or
the type of equipment it installs. It is natural to expect that, the greater the level of investment in
R&D, the greater is probability of discovery.
Once having made a discovery, a firm faces two options. One is to file immediately fora patent. The other is to improve the quality of the invention before filing for a patent. A strong
novelty requirement or scope protection is assumed, so if there is a patent on the unimproved
invention the improved version will not be patented separately.
The model thus has two stages. In the first stage, each firm chooses a level ofinvestment in R&D, which determines its probability of discovery in the second-stage game.
This is consistent with the finding of Cohen and Ishii (2005) that most patent races are amongmajor corporate research laboratories chasing well-defined research topics, where initial setups

4
are of utmost importance in conducting research.
The second stage consists of an infinite number of periods. In each period, nature firstchooses “success” or “failure” for each firm according to the firm’s probability of discovery
determined in stage 1. The firm can, by incurring some cost (say, of operating the lab
equipment), learn what nature chose for it, but not what it chose for the rival. Thus there is an
informational asymmetry in the model. Conditional on having made the invention, a firm
decides whether to file for a patent immediately or improve the quality of the invention before
filing. The improvement process is not stochastic but takes time.
Our results can now be summarized. In first-to-invent, the model has the uniqueequilibrium outcome in which both firms choose to improve the invention. First-to-file resultsin the same equilibrium outcome at certain parameter values, but admits This also is anequilibrium in first-to-file, in which case the two rules are equally effective in inducing R&D
efforts. Depending on the parameter values, however, first-to-file can results in firms filing for apatent immediately upon discovery. In the latter equilibrium outcome, we find firms investing
less in R&D efforts in first-to-file. Thus, our analysis lends some support to the claim of the
opposition to patent law reform in the U.S.
The literature has already examined various aspects of patent 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 patentpublication (Aoki and Prusa 1996, Aoki and Spiegel 2003). However, there is, to the best of theauthor’s knowledge, no formal analysis of the first-to-invent feature of the U.S. patent law, with5
the exception of Scotchmer and Green (1990). Their work however differs significantly fromthe work on hand both in focus and in setup.
Scotchmer and Green (1990) consider two firms racing to improve some base-leveltechnology already patented to a third-party. There are two innovations: intermediate and final.
Two features set their work apart from ours. First, probability of innovation is exogenous so therelative effect of the two patent rules on R&D efforts is unexamined. More importantly, in theirmodel there is complete information; a firm knows it when the rival discovered theintermediate innovation, whether it is patented or not. So, unlike in this paper, firms do not face
the risk of wasting resources trying to discover the invention that has already been made.
As regards the focus, Scotchmer and Green (1990) are more concerned with thevarying degrees of novelty requirements of patent law. In their model, patenting theintermediate invention reveals its content to the rival firm, enabling the rival to bypass theintermediate step, thereby accelerating discovery of the final innovation. If the novelty
requirement is so strong that the intermediate innovation infringes the existing patent on thebase-level technology, however, the intermediate innovation is not patented, thereby retarding
discovery of the final innovation. Even with a weaker novelty requirement, the inventor may
forgo patenting the intermediate invention to force the rival out of competition. However, sucha shakeout is less likely to arise in first-to-file because the rival could get a patent on theintermediate 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

6detailed description of the model. Sections 3 and 4 are devoted to the study of first-to-file, andfirst-to-invent, respectively. In Section 5 we compare the incentives to innovate under these tworules. Section 6 concludes.

2. Environment
We consider an R&D race between two firms, which are symmetric and designated by j
= A, B. The model has two stages. In the first stage, firms simultaneously choose levels ofinvestment in R&D at cost kj, knowing that this investment level determines a firm’s
probability of discovery in the second stage. The second stage has an infinite number of
periods, running from 1. In each period, firms simultaneously decide whether or not to conduct
R&D. If they do, each incurs the operating cost c, and discovers the invention with probabilitypi(ki) during that period. Without conducting R&D, firms have no chance of a discovery.
As outlined in section 1, once having discovered the invention, the inventor can file fora patent immediately or choose to improve the quality of the invention. The improvement
process is assumed deterministic but time-consuming. We assume for simplicity that it takes
one period to complete it. Whichever option a firm chooses, a patent is issued at the end of theperiod in which it files an application. The invention has value m > 0 without improvement andvalue M with improvement, both evaluated at the time of discovery. We assume M > m;otherwise no firm would be interested in the improvement. We also assume strong novelty or
scope requirements of patent law so that the improved version cannot be patented separately if
a patent has already been issued on the original invention. Therefore, in the absence of rivalry
the inventor would always choose to improve the invention. However this need not be the case7
when firms compete. More importantly, unlike Scotchmer and Green (1990), we assume
incomplete information; unless the inventor gets a patent, the rival does not know that there has
been a discovery.
The final assumption we make is that the firms incur no cost other than the R&D costs.
This ensures that our results are not influenced by the difference in non-R&D-related costs suchas patent application fees and legal and court fees as may arise in interference proceedings, andallows us to focus on the issue on hand.

3. First-to-file
We begin with a first-to-file rule. We first specify the payoffs. In each period of thesecond-stage game nature’s choice gives rise to potentially four possible states. Consider firstthe state in which nature assigns “success” to both firms. In this case, depending on what thefirms do next, there are three cases to consider. First, if both firms file for a patent immediately,each firm gets a patent with equal probability; therefore, the expected payoff is m/2 per firm.7
Likewise, if both choose to improve their inventions, the expected payoff is M/2 per firm. A
third is a case in which firms take different actions. For example, if A files immediately but B
waits, a patent issues to A, so A gets m and B zero payoffs.
Consider next the second state of nature, in which only A makes a discovery. By filing
immediately for a patent, A gets a patent valued m. On the other hand, if A waits one period toimprove, B may discover the invention the following period and beat A to the patent office,7

When an application for a patent is prepared and filed depends on the lawyers who are handling it. Thus, theinventor may not have full control over when an application is filed. Further, if two applications are filed on thesame invention on the same day in Japan, two applicants are asked to negotiate with each other and file a new
application under one name.

8
reducing A’s payoff to m/2. The third state of nature occurs when B alone makes a discovery,
and is symmetric to the second state. The fourth and final state occurs when neither firm
discovers the invention, in which case no firms take further action until the following period.
We are now ready to solve the game. We focus on a stationary equilibrium. Formally, afirm’s strategy in the second stage game is an infinite sequence of actions (file immediately fora patent or wait one period to do so) for each period t ≥ 1, conditional on having discovered theinvention and the rival not having awarded a patent. A strategy is stationary if it specifies atime-independent action for all t ≥ 1.

3.A. Equilibrium in which the invention is improved
We begin with the equilibrium, in which upon discovery each firm waits one period toimprove the invention before filing for a patent. In this case, the firms do not know for surewhether the rival discovered the invention during the previous period. However, the firm forms
beliefs as to the probability that the rival had made the discovery in the previous period. Thus,
the firms play a game of incomplete information, and we look for a Bayesian-Nashequilibrium, according to which the equilibrium strategies are sequentially rational, given
beliefs, while beliefs are Bayes-consistent with the strategies on the equilibrium path.
Let EA(pB; t) denote A’s period-t beliefs as to the probability that B discovered theinvention in the previous period, conditional on non-issuance of a patent to B to date. For t ≥ 2,
this belief must equal the value of pB B chose in the first stage. For t = 1, EA(pB, 1) = 0 because
there is no previous period in which to make a discovery.

9Suppose that A discovers the invention in period t ≥ 2. A then improves it and files for apatent in period t + 1. The equilibrium value of the invention to A is M if B did not discover theinvention in period t, a probability (1 – pB) event, and M/2 if B did, because each inventor isequally likely to get a patent on his invention. Thus, the equilibrium expected value of theinvention to A is
(1 – pB)M + pBM/2 = (1 – pB/2)M = V.
This value is of course conditional on B not having discovered the invention in period t – 1.
However, A does not know whether B made the discovery in t – 1, so A cannot condition its
decision to conduct on R&D on B’s discovery in the previous period. Thus, the equilibrium
value of conducting R&D in period t is
(1 – pB)pAV – c,that is, getting V is weighted by the probability that A discovers the invention in period t and B
did not in period t – 1.8 A reaches period t without the invention, conditional on not having
discovered it from period 1 through period t – 1, a probability (1 – pA)t-1 event, and conditional
also on B not having made the discovery through period t – 2, a probability (1 – pB)t-2 event.
The difference in probability can be understood by recalling that A can observe whether B has
made the discovery through period t –2 but not the last period because of the one-period
information lag.

8

With probability p B had made a discovery in the previous period and files for a patent in period t. In that caseB
A’s equilibrium payoff is zero since A is not filing for a patent in period t.

10
The above argument does not apply exactly to period 1 because there are no previous
periods. For t = 1 the expected profit is just pAV – c, because in t = 1 A knows that B did not
make the invention in the previous period. Making use of these facts, and letting δ denote thediscount factor, we can write A’s expected profit in the second stage as follows:(pAV – c) + δ(1 – pA)[(1 – pB)pAV – c](1)

+ δ2(1 – pA)2(1 – pB)[(1 – pB)pAV – c]+ δ3(1 – pA)3(1 – pB)2[(1 – pB)pAV – c] + ….
Turning to the first stage, firms simultaneously choose levels of investment in R&D,
which determine the value of the pj above. The notation simplifies however, if we let firms
directly choose probability pj ∈[0, 1) instead of investment levels. We thus let k(pi) denote theinvestment cost, which satisfies the following properties: k(0) = 0, k’ > 0, k” > 0, k’(0) = k(1) =∞, where primes denote differentiation. Now, collecting terms, substituting for V, andsubtracting k(pA), we arrive at the following expression for the expected profit to firm A in thefirst stage:(2)

pA (1 − pB / 2)M − [1 + δ pB (1 − pA )]c− k( pA ) .
1 − δ (1 − pA )(1 − pB )A takes pB as given and chooses pA to maximize (2). The first-order condition isarranged to yield(3)(1 – pB/2)M[1 – δ(1 – pA)(1 – pB) – δpA(1 – pB)]
+ δ{pB[1 – δ(1 – pA)(1 – pB)] + (1 – pB)[1 + δpB(1 – pA)]}c

11– [1 – δ(1 – pA)(1 – pB)]2k’(pA)= (1 – pB/2)M[1 – δ(1 – pB)] + δc – [1 – δ(1 – pA)(1 – pB)]2k’(pA) = 0,9
which defines A’s best-response function r1*(pB), where the subscript 1 implies that firms wait
one period to improve the invention. The rival’s best-response function obtains similarly. The
Nash equilibrium is a pair of probabilities (pA, pB) that are best responses to each other.
Focusing on the symmetric equilibrium, we denote the common equilibrium probability by
p1*.
We next check a firm’s incentive to deviate. Suppose that A, having discovered theinvention in any period t ≥ 2, files for a patent in period t. A’s payoff is m, conditional on B nothaving discovered the invention in period t – 1.10 If B made a discovery previously, B also files
for a patent in period t according to the equilibrium strategy, so A’s payoff is m/2.11 Since B
would have discovered the invention with probability pB, the expected payoff to A from adeviation equals
pBm/2 + (1 – pB)m = (1 – pB/2)m.
In comparison, the equilibrium strategy yields zero payoff to A if B discovered in the previous
period and V = (1 – pB/2)M if B did not. Since B makes a discovery with probability pB, the9We assume the second-order condition holds at the optimum. It is guaranteed if k’(p ) rises sharply enough.
j
Even if B discovers the invention in the current period, it will not file for a patent till the next period in
equilibrium.
11
We assume that an interference process does not favor either firm despite the difference in quality between the
two applications.
10

12equilibrium payoff to A is (1 – pB)(1 – pB/2)M. Therefore, A has no incentive to deviate if andonly if(1 – pB)(1 – pB/2)M ≥ (1 – pB/2)m,or(4)(1 – pB)M ≥ m.
The first period differs in that B could not have discovered the invention earlier.

Therefore, deviating in t = 1, A gets m, which is compared with the equilibrium payoff, (1 –pB)M. Thus, (4) is valid for preventing deviations at t = 1 as well. Using symmetry, we write
the no-deviation condition for both firms as(5)(1 – p1*)M ≥ m.
Further, p1* being the symmetric equilibrium probability, A has no incentive to deviate

from p1* when choosing an R&D investment level in the first stage as long as (5) is satisfied.
Similarly, B has no such incentive, either. We thus conclude that investing p1* in the first stage
and waiting one period to file for a patent after discovering the invention is an equilibrium
strategy if (5) is satisfied.

3.B Equilibrium in which firms file immediately for a patent
We consider next the equilibrium in which both firms file for a patent immediately.
Supposing that A discovers the invention in period t ≥ 1. The equilibrium payoff is m if B does
not make a discovery in period t but m/2 if it did because then each can get a patent with equal
probability. Thus, the expected payoff is13
v = (1 – pB)m + pBm/2 = (1 – pB/2)m.
In this equilibrium, when a patent was not issued to B in the previous period, A believes
with certainty that B did not discover the invention in that period. That is, EA(pB, t) = 0 for all t≥ 1, conditional on a patent not having issued to the rival. Then, A can condition its decision to
conduct R&D in the current period on a patent not having issued to B previously. Thus, A
avoids the risk of duplicating the invention made by the rival. The expected equilibrium value
for A of conducting R&D in period t is therefore pAv – c. Since A conducts R&D in period t
only if neither firm made the discovery between period 1 and period t – 1,
We can now write A’s expected profit as:(pAv – c) + δ(1 – pA)(1 – pB)(pAv – c)+ δ2(1 – pA)2(1 – pB)2(pAv – c) + ….
Summing and subtracting the cost of R&D investment, we obtain the first-stage expected profit
to A:
(6)

pA (1 − pB / 2)m − c− k( pA )1 − δ (1 − pA )(1 − pB )A maximizes this with respect to pA, given pB. The first-order condition:(7)m(1 – pB/2)[1 – δ(1 – pB)] + δ(1 – pB)c
– [1 – δ(1 – pA)(1 – pB)]2k’(pA) = 0

implicitly defines A’s best response function r0(pB), where subscript “0” reminds us that firms
file for a patent without no (zero) improvement on the invention. By symmetry, putting pA = pB

14
in (7), yields the symmetric Nash equilibrium levels of investment (probabilities), which wedenote by p0*.
Now consider a deviation. Suppose that, having discovered the invention in period t, A
chooses to improve the invention. If B also makes a discovery in period t, B files immediately
for a patent and is awarded a patent in first-to-file, so a deviation yields zero profit to A. On theother hand, if B does not discover the invention in period t, A’s payoff depends on whether or
not B will make a discovery in period t + 1. If B does, B files immediately for a patent, so A’s
expected profit will be M/2. If B does not, however, A will earn M instead of m. Thus, thepayoff to A from a deviation would be (1 – pB)[pBM/2 + (1 – pB)M]. If this is less than theequilibrium payoff, that is, if
pBm/2 + (1 – pB)m ≥ (1 – pB)[pBM/2 + (1 – pB)M],
then A has no incentive to deviate. Simplifying and using symmetry, we can rewrite the above
inequality as:m ≥ (1 – p0*)M.
We have obtained:

Proposition 1: In first-to-file,(A) the model possesses the equilibrium in which both firms choose to improve the quality of
the invention. In it, the equilibrium probability p1* satisfiesm ≤ (1 – p1*)M;15(B) the model possesses the equilibrium in which both firms choose to file immediately for apatent on the original invention. In it the equilibrium probability p0* satisfiesm ≥ (1 – p0*)M.

Proposition 1A says that firms choose to improve the invention if m ≤ [1 – p1*]M; i.e., if thevalue of the improved invention is greater than that of the original invention, discounted by theprobability of discovery by the rival. An analogous interpretation is made as to Proposition 1B.
Finally, it is straightforward to check that there is no asymmetric equilibrium in first-tofile as the firm has no incentive to postpone filing if the rival files immediately for a patent.

3.C. A comparison of equilibrium R&D efforts
We now compare the levels of investment in R&D in two types of equilibriumoutcomes. The next proposition gives the result (the proof is in the appendix).

Proposition 2: p1* > p0*; that is, in first-to-file firms invest more when they improve theinvention than when they file immediately for a patent.

This seems intuitive. Since the improved invention is more valuable, firms exert more effort in
R&D in the equilibrium in which they can improve the invention.
In Figure 1 we present a numerical example, where we set δ = 0.9, M =100, m =60, c =10 and k = 10pA/(1 – pA). The best-response functions closer to the origin correspond to the16equilibrium in which firms file immediately and those further out to the equilibrium in whichfirms improve the invention. The equilibrium probability values are p1* = 0.62 and p0* = 0.53,
which is consistent with Proposition 2.
The next question is what determines which equilibrium to occur. Proposition 2 implies
that 1 – p0* > 1 – p1*. Therefore, if(8)m/M ≥ 1 – p0* > 1 – p1*

1 firms file for a patent right away. On the other hand, if(9)

1 – p0* > 1 – p1* > m/M,

firms improve the invention. Finally, if(10)

1 – p0* > m/M > 1 – p1*,

the both conditions in Proposition 1 fail, implying there is no equilibrium in pure strategies.
However, there is an equilibrium in mixed strategies in the second-stage game; i.e., firms
randomize between filing immediately and waiting one period to file for a patent. Denote pm*
is the symmetric equilibrium level of investment in R&D when firms randomize in this fashion,
In each period t ≥ 1, the mixed-strategy payoff from improving the invention is lessthan the corresponding payoff with pure strategies, and the mixed-strategy payoff from filingfor a patent immediately upon discovery is greater than its counterpart from the pure-strategy
game. Therefore, given that firms invest more in R&D when expecting a greater profit in thesecond-stage game, pm*, the equilibrium level of investment in R&D using mixed strategies, isless than p1* and greater than p0*. Therefore, we have (see the appendix for details)

17
Lemma 1: p0* < pm* < p1*.

Thus, whenever firms choose to file immediately for a patent with positive probability, firms
invest less in R&D than when they choose to improve the invention with certainty.

4. First-to-invent
We next turn to first-to-invent. The game structure is the same as in the previous
section. Again, focusing on a stationary equilibrium, begin with the equilibrium, in which,conditional on having discovered the invention, each firm waits one period to improve theinvention. Given the structure of the model the expected payoff is exactly the same as with
first-to-file, given in (1). It is recalled that the symmetric equilibrium probability is denoted byp1*.
We check if a firm has a profitable deviation. Suppose that A deviates and files for apatent immediately upon discovery in period t, say. If B also discovers the invention in period t,with first-to-invent B will be able to challenge A’s priority of invention in period t + 1. Given
that an interference process does not favor either firm, A can defend its priority in aninterference proceeding only with probability 1/2. Hence, the deviation reduces A’s payoff to
m/2 from M/2, the equilibrium payoff. On the other hand, if B does not discover the inventionin period t, a deviation yields m instead of the equilibrium payoff M. In each case, the deviation
reduces A’s profit, and hence A has no incentive to deviate upon discovery.

18
Consider next the equilibrium in which both firms file for a patent immediately. The
expected payoff to A is given in (6) and the first-order condition in (7). The symmetricequilibrium is denoted by p0* as before.
Now suppose that A deviates and improves the invention, upon discovery in period t. If
B also discovers the invention in period t, B files for a patent on the unimproved invention.
However, A can contest B’s claim of priority of invention in an interference hearing thefollowing period, thereby raising A’s expected payoff from m/2 to M/2.12 On the other hand, if
B did not discover the invention in period t, a patent will be issued to A, the first inventor,
regardless of what happens to B later, thereby raising A’s payoff from m to M. In either case, adeviation is profitable for A, and hence filing immediately for a patent is not an equilibrium
strategy in first-to-invent. We have obtained

Proposition 3: In the unique equilibrium with first-to-invent, firms always improve theinvention before filing for a patent.

Finally, the model does not possess asymmetric equilibrium outcomes because filing for apatent before the rival offers no advantage in first-to-invent.

5. A comparison

12

Strictly speaking this is not an entirely correct statement ; B may earn profit during the one period before it ischallenged. However, as this profit will be surrendered to A, the true patent holder, this strengthens our case.

19
We are now ready to examine whether first-to-invent furthers innovation relative tofirst-to-file as claimed by the opposition to reform in the U.S. As we showed above, the tworules yield the identical outcome when first-to-file induces firms to improve the invention; thatis, if the value of the patent on the improved invention is sufficiently large. The two rules differ
when first-to-file induces firms to file for a patent. The following results straightforwardly from
Propositions 1-3 and Lemma 1.

Proposition 4: (A) If in first-to-file firms improve the invention, the two rules are equallyconducive to R&D. (B) If in first-to-file firms file immediately for a patent (with positive
probability), first-to-invent induces more efforts in R&D than first-to-file.

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 acommitment is impossible to make, first-to-invent guarantees such a result by eliminating therisk of losing the invention to a latecomer. In contrast, first-to-file does not provide suchguarantee. As we saw, if the improvement results in insufficient value added, firms choose to
file immediately for a patent in the fear that it will lose patent rights to the rival who invents
later. But the reduced value of invention diminishes the incentive to invest in R&D.

5. Concluding remarks
The U.S. has been under pressure from the international community to abandon theunique first-to-invent feature of its U.S. patent law. The opposition however remains strong in20
the U.S. One argument voiced by the opposition is that the first-to-invent feature of the U.S.
law makes the U.S. the innovation powerhouse that it is and switch to the first-to-file rule, theinternational norm, will undermine innovation. In this paper we examine this claim in astochastic model of R&D competition. Our findings render some support to the opposition’sargument.
Our results are derived under some simplifying assumptions. First, the improvement of
the invention takes one period to complete. If it takes more than one period, that increases therisk of losing the invention to the rival who invents later but files earlier. Thus, first-to-filewould prompt the firm more to file immediately for a patent. We thus believe that relaxing theone-period-wait assumption will not change our result and is more likely to strengthen it.
Another simplifying assumption we make is 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 as much in first-to-invent as infirst-to-file and still get greater profit due to the improvement. On the other hand, should theoperating costs fall with R&D investment, perhaps because the greater investment in R&D themore efficient the lab is to operate daily, then it strengthens our case.
Finally, it is possible to reformulate our model in a continuous-time setting in thesecond stage. This extension has the advantage of avoiding simultaneous discoveries, but
complicates the exposition. It however does not alter our qualitative result, provided that aninventor has to wait a fixed period to improve the invention.

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Appendix
A. Proof of Proposition 2
Write the first-order condition (3) as
G(pA, pB) ≡ (1 – pB/2)M[1 – δ(1 – pB)]
+ δc – [1 – δ(1 – pA)(1 – pB)]2k’(pA) = 0,
Recall that the best-response function is denoted by r1(pB). Similarly, write the first-ordercondition (6) by
H(pA, pB) ≡ m(1 – pB/2)[1 – δ(1 – pB)]
+ δ(1 – pB)c – [1 – δ(1 – pA)(1 – pB)]2k’(pA) = 0,
with the best-response function r0(pB). Set pA = r0(pB) and take the difference:G[r0(pB), pB] – H[r0(pB), pB]= (1 – pB/2)[1 – δ(1 – pB)](M – m) + δpBc > 0
for pB > 0. Since H[r0(pB), pB] = 0 by definition, the inequality implies G[r0(pB), pB] > 0.
Given that G[r1(pB), pB] = 0 and concavity of G with respect to pA (the second-ordercondition), we conclude that r1(pB) > r0(pB), i.e., 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.

22
B: Proof of Lemma 1
Focus on the symmetric mixed-strategy equilibrium. Suppose that, having made a discovery inperiod t, an inventor files immediately with probability λt ∈[0, 1]. In period 1, when A files, A
expects to get(B1)

pB[λ1m/2 + (1 - λ1)m] + (1 – pB)m.

This has the following interpretation. With probability pB B also makes a discovery in t = 1,
and files for a patent in period 1 with probability λ1, which yields m/2 to A. If B does not file
immediately, a probability-(1 - λ1) event, A gets m. In addition, with probability 1 – pB B does
not make the discovery in t = 1, so A gets m. On the other hand, by improving the invention A
gets
(B2)

pB(1 - λ1)M/2 + (1 – pB){pBλ2M/2 + pB(1 - λ2)M + (1 – pB)M}.

In this case, B makes a discovery with probability pB and improves the invention withprobability 1 - λ1, thereby yielding M/2 to A (If B files in t = 1, A gets zero for payoff). This
explains the first term. The second term represents the profit to A if B does not discover theinvention in t = 1. In that case, B still has the chance of making a discovery in period 2. If it
does make a discovery, B files for a patent right away with probability λ2, which yields M/2 toA, or improves the invention with probability (1 - λ2), yielding M to A. Lastly, if B does notmake a discovery in t = 2, A gets M. When A adopts a mixed-strategy in t = 1, these two
payoffs must be equal.
Similarly, for t ≥ 2, the profit from filing immediately

23
(B3)

pB(1 - λt-1)m/2 + (1 – pB){pB[λtm/2 + (1 - λt)m] + (1 – pB)m}(t ≥ 2) equals that from improving the invention:(B4)(1 – pB){pB(1 - λt)M/2 + (1 – pB){pB[λt+1M/2 + (1 - λt+1)M] + (1 – pB)M}}.

Compared with (B1), (B3) has the extra term (first term) because in period t ≥ 2 with positive
possibility B files for a patent on the invention it discovered in period t - 1.
Now consider a class of mixed strategies in which firms mix in the first n periods andchoose to improve the invention for t > n. Let p- m(n) denote the symmetric equilibrium level ofinvestment in R&D. For example, for n = 1, letting λ2 = 0 in (B2) and equating it to (B1) yields
pB(1 - λ1/2)m + (1 – pB)m = pB(1 - λ1)M/2 + (1 – pB)(1 – pB/2)M.
This determines the equilibrium λ1 = λ1*. The total expected profit to A is[pB(1 - λ1)M/2 + (1 – pB)(1 – pB/2)M – c]+ δ(1 – pA)

pA (1 − pB / 2)M − [1 + δ pB (1 − pA )]c− k( pA ) .
1 − δ (1 − pA )(1 − pB )The first-order condition isδ(1 – pA){(1 – pB/2)M[1 – δ(1 – pB)] + δc} – [1 – δ(1 – pA)(1 – pB)]2k’(pA)= 0.
A comparison with (6) indicates that the best-response function implicitly given by the above
condition lies strictly inside r1(pB). Thus, we can then find the symmetric equilibrium
probability p- m(1), which is less than p1*. Continuing this way, we can compute p- m(n) for each24
n and can show that p- m(n) is a decreasing sequence. Since the sequence is bounded it
converges, say, to p- m*. Similarly, let pm(n) be the equilibrium investment in R&D in a game in-which firms commit to randomizing for the first n period switching to filing immediately
without improvement. Then, pm(1) > p0* and pm(n) is an increasing sequence. Since it is--bounded, this sequence converges, say, to pm*. It is also readily shown that pm(n) < p- m(n).

-Thus, pm* = p- m* = pm*. Therefore, p1* > pm* > p0*.

-

-

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27

pA
1
With improvements

Without improvementspB
01