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Competitive Search and Preemptive Exclusion
In the context of research and development programs, entry-deterance has manifested
itself in preemptive patenting, whereby a monopolist will patent untested research leads toprevent competitors from challenging its position in the market.
the lure of monopoly power impacts …rm behavior in the search for a new product prior tothe discovery of a success. We model the research and development process as a compet-itive search through research leads, with the incorporation of competition representing acontribution to the existing literature. We …nd that, in the presence of competition, a …rmmay have the incentive to preemptively exclude its competition from searching a portionof the research leads. Such preemptive exclusion increases the probability that a discoveryof a success will result in monopoly pro…ts.
We discuss the implications of the results for
the issue of bioprospecting as a motivation for pharmaceutical …rms to contribute to theconservation of biodiversity.
Our …ndings suggest that pharmaceutical …rms are willing
to enter bioprospecting agreements with host nations, with the caveat that there may beconcern about the ability of host nations to adequately protect the intellectual propertyrights of the pharmaceutical …rms.
Bren School of Environmental Science and Management, 3424 Bren Hall, University of California Santa
Barbara, CA 93106-3060. email@example.com
In his seminal work Capitalism, Socialism and Democracy (1942), Schumpeter argues that theprospect of monopoly power drives investment in research and development, and hence, inno-vation in a capitalist society. While monopolists price their products to maximize pro…tability,leading to a loss of consumer surplus, Schumpeter argues that market power can increase so-cietal welfare by extending the suite of products available for consumption.
monopoly power are known to impact behavior once a …rm achieves that position in a market,begging the question: to what extent does the lure of monopoly power impact a …rm’s behavioras it is competing for that much- coveted position within a given market?
The research and development process is often a competition between multiple …rms seeking
an innovation that will secure monopoly rents. We develop a theoretical model in which …rmsengage in a competitive search through research leads, hoping to achieve a monopoly position inthe market. Our goal is to identify the impact of competition for monopoly pro…ts associatedwith research and development innovation on …rm behavior prior to the discovery of a usefullead.
Acknowledging competition between innovating …rms allows the possibility of preemptive
exclusion –one …rm may purchase exclusive access to research leads before making a discoveryto ensure its monopoly position, should a success exist within the pool of research leads. Westudy the situation in which the discovery of a new product yields pro…t that does not impactpro…ts from existing products. We …nd that the premium associated with monopoly power canmake the strategy of preemptive exclusion optimal behavior. In our model, monopoly poweris not guaranteed upon discovery of a useful technology, because it is possible that a competing…rm could make a discovery from among the pool of remaining leads. This possibility providesvalue to successful leads that exist within the pool, but which occur later in the sequence ofleads than the initial successful lead (such leads have been deemed redundant in the literature).
Our …ndings have important implications for research and development and patent pro-
tection in industries characterized by some degree of competitive search for successes.
relevant example is the pharmaceutical industry, which is characterized by costly research anddevelopment e¤orts that are rewarded with patents for useful discoveries, providing …rms withmonopoly power in recognition of their successes. Within the pharmaceutical industry, bio-logical prospecting (bioprospecting), the act of combing through natural organisms in searchof compounds that might be of use in addressing human diseases, is an example of the re-search and development process as a competitive search through a pool of research leads. Our…nding regarding the incentive for preemptive exclusion, under certain conditions, allows us tocomment on the utility of bioprospecting as a conservation tool.
Simpson, Sedjo, and Reid (1996) (SSR) consider the viability of bioprospecting as a con-
Appropriately, SSR describe the search for biochemically-active compounds
within the pool of organisms that exist in biologically diverse eco-regions as a search througha pool of research leads. The model that we propose utilizes the framework of a competitivesearch through a pool of research leads in order to identify the attributes of such pools thatwill motivate preemptive exclusion.
In addition to providing a framework suitable for answering the question of interest, SSR
also o¤er an assertion worthy of further consideration.
SSR focus on a …rm that enjoys monopoly position in a certain market. In this context, theauthors argue that redundant cures are of no value and can therefore be ignored in the pro…tfunction of the search-conducting …rm. Considering the competitive environment in whichsuch research and development searches occur, it seems possible that the existence of multiplesuccessful leads within a research pool might pose a threat to the ability of any competing …rm
to enjoy monopoly power in a given market.
As such, although the redundant cures might not be directly valuable to the pioneer dis-
coverer in the form of potential additional pro…ts, possessing rights to these leads might be ofvalue in increasing the probability that the discoverer will be rewarded with monopoly powerfollowing a discovery.
The results presented below con…rm that, under certain conditions,
the pro…t implications of redundant leads are su¢ cient for a …rm engaged in a patent race topreemptively exclude (i.e., before the …rm has achieved the monopoly position) its competitorfrom searching portions of the research pool. It seems that our …ndings might provide reasonto reevaluate the conservation potential of pro…t-maximizing pharmaceutical …rms.
Prior to introducing our model, we present a brief example to highlight the impact of
competition on the value of exclusive access to research leads. The in‡uence on …rm behavioris partially driven by the negative impact that so-called redundant leads can have on therevenues associated with research and development success. Following this intuitive example,we present a review of the impact of monopoly position on …rm behavior. The theoretical modelis then introduced and used to identify the impact of a potential monopoly position in a marketon …rm behavior.
The conclusion of the paper provides commentary on the implications of
these results regarding the conservation potential of pharmaceutical …rms.
The following example presents the key determinants of …rm behavior during a competitivesearch through a pool of research leads.
Consider two …rms, A and B, searching for a new
product from within a pool of research leads (i.e., the discovery does not impact pro…ts as-sociated with existing outputs).
Assume that the research pool consists of two leads.
…rm is equally likely to test a given lead …rst, meaning that a coin toss determines the searchorder of each lead. Let R represent the revenues that accrue to a monopolist following successin the research and development process (i.e., the discovery of a success in the search throughthe research pool).
Let Rd represent the revenues that accrue to each …rm when both …rms
make a discovery, where Rd < R . Each …rm faces the same choice before the search of the
pool begins: purchase exclusive access to some portion of the existing leads, where the cost ofexclusive access is denoted by k, or engage in the search for a useful product by testing the leadfor its potential as a marketable product. Let c represent the cost of testing the lead. Let prepresent the probability that either lead will be a success.
In the case of two leads, each …rm must choose between purchasing exclusive access to both
leads, purchasing exclusive access to one lead, or engaging in a competitive search through bothresearch leads. Figure 1 presents an overview of the possible outcomes of such a search processfor each of the two …rms engaged in the search.
The expected pro…ts of the three potential
actions facing the …rms engaged in this competitive search are presented below.
The expected pro…ts of buying exclusive access to both leads are given by
Equation 1 indicates that if a …rm excludes its competition from all available research leads,
it will reap monopoly pro…ts if a discovery exists in the pool. This result will be achieved so longas both leads in the pool do not fail to yield a marketable product. Another possible strategyfor a …rm engaged in a competitive search through research leads is to purchase exclusive accessto one of the two existing leads.
The expected pro…ts of buying exclusive access to one lead
Figure 1: Choice set and associated outcomes for a …rm engaged in a competitive search throughtwo research leads.
The …rst four terms in equation 2 represent the expected revenues associated with all possible
combinations of success and failure for two research leads (e.g., success/fail; success/success withone …rm discovering both successes; success/success with each frm discovering a success; andfail/success), with the …rst probability component associated with the lead to which the …rmhas purchased exclusive access. The …nal strategy available for a …rm engaged in a competitivesearch through two research leads is to engage in search without purchasing exclusive access toeither lead. The expected pro…ts of searching without exclusion are given by
In this strategy, the …rm does not face the cost of purchasing exclusive access.
there is a decreased probability of enjoying monopoly power for a given number of successfulleads if the …rm faces competition when searching each lead.
Without delving into the algebra associated with identifying the optimal behavior for a …rm,
we are able to identify two components of such a decision that are of importance in determiningthe viability of purchasing exclusive access to research leads. It is clear that threshold values fork under which preemptive exclusion will obtain are determined by the probability with whichany lead will be a hit and the revenue premium associated with a monopoly position in themarket relative to a market in which an oligopoly (in this case duopoly) exists. The presence ofcompetition during the search process, as well as the possibility that multiple successes mightexist within the research pool, interact to result in di¤erent revenues based on how many of theexisting successes a single …rm possesses. When the discrepancy between monopoly returns andoligopoly revenues is su¢ ciently great, a pro…t-maximizing …rm will bene…t from preemptivelyexcluding its competition from a portion of the research leads.
For example, consider …rm A in the illustrative example choosing between excluding its
competitor from searching one of the two leads or simply engaging in the competitive searchthrough both leads.
In this case, the …rm compares the two values presented in equations 2
and 3, leading the …rm to choose preemptive exclusion of its competitor from one research leadwhen
The terms on the right-hand side of the inequality represent the expected revenue premium
a¤orded the …rm when it is able to conduct its search process in the absence of competition.
Noting that the right-hand side is a positive number, we can state that preemptive exclusionwill be optimal behavior, for certain values of k, when a …rm is engaged in a competitive searchthrough two research leads.
We see that the presence of competition makes the decision not to search a lead costly for a
…rm because ignoring it, or treating it as redundant, allows for the possibility that it might bea success that is discovered by its competitor. The discovery by …rm B diminishes the rewardsassociated with …rm A’s research and development process, providing an incentive for …rm Ato decrease the probability of such an outcome occurring. The preemptive exclusion of …rm Bfrom one or both of the research leads is one strategy that …rm A can employ to achieve thisobjective.
The remainder of the paper is spent illustrating the generality of this result and
discussing its implications for …rms engaged in competitive search through research leads.
Following Schumpeter’s analysis of the impact of monopoly power regarding innovation andinvention in capitalist economies, a signi…cant portion of the industrial organization literaturehas attempted to identify the impact of monopoly power on investment in research and de-velopment.
Many e¤orts have focused on the research and development investments made
by …rms that already enjoy monopoly power.
While this focus di¤ers from the crux of our
e¤ort, understanding the theories that drive post-discovery behavior will make our discussionof pre-discovery behavior more intuitive.
Previous work has demonstrated that monopolists will protect their position in a given
In the research and development literature, Gilbert and Newbery (1982) show that
monopolists will patent leads that have yet to be tested to ensure the persistence of theirmarket power. To be clear, their result is not that the existing monopolist will utilize furtherdiscoveries to dominate the market; Gilbert and Newbery …nd that the later patents may gounused and unlicensed simply to preserve the spoils of monopoly power.
There are a number of factors that can lead to the existence of monopolies, and the one
most germane to research and development is patent protection.
…rms racing to develop a patentable product has been thoroughly analyzed in the economicsliterature and has been modeled in various ways to focus on speci…c aspects of the research anddevelopment process. Scherer (1967) studies this problem through the framework of Cournotcompetition.
Loury (1979) uses a static model (i.e., the level of research and development
investment at a given …rm is identical across time periods) to identify the impacts of uncertaintyon the relationship between research and development expenditures and innovative progress.
Gilbert and Newbery achieve their result by approaching the patent race as a bidding game,in which the bids represent allocations to research and development.
incorporating game theory into the analysis of the research and development process includeDasgupta and Stiglitz (1980), which identi…es the impact of industry structure on research and
development expenditure, and Fudenberg et al. (1983), which studies impact of a head-start inthe research and development process on the level of competition, and therefore the ine¢ ciency,associated with the research and development process.
A monopolist is able to set market price above the marginal cost of production, enjoying
greater pro…tability than a competitive …rm, which provides meaningful incentive for a mo-nopolist to protect its position in the market.
Threats to monopoly power can result from
regulatory action or the behavior of other …rms in the market.
attempting to enter the market on the behavior of the monopolist is relevant to the current dis-cussion regarding the impact of competition on pre-discovery behavior during a search througha pool of research leads.
It is well documented that monopolists will take steps to deter the entrance of potential
The form of entry-deterrence most relevant to our e¤ort has
to do with the research and development e¤orts of a …rm that already enjoys market powerfollowing a previous research and development success. Gilbert and Newbery use a model of…rm behavior to determine how the presence of the patent system impacts the market structureof an industry.
In the Gilbert and Newbery model, a preexisting monopoly is threatened by the potential
that a substitute might be discovered during the research and development e¤orts of a competi-tor. The monopolist faces the choice of allowing entry to occur or of patenting the substitutetechnology.
In the simple model, Gilbert and Newbery represent the time of innovation as
a deterministic function of the expenditures on research and development.
of research and development leads to innovation being attributed to the …rm that spends themost money on research and development.
In this context, the authors …nd that the threat
to monopoly power posed by a potential entrant is su¢ cient to incite the monopolist to putforth more money into research and development e¤orts than the potential entrant so long asentry results in a reduction of total pro…ts below the joint-maximizing level. The authors …ndthat the monopolist can sustain its market power so long as potential entrants rationally expectrivalry to diminish industry pro…ts.
The …nding that optimal behavior for an incumbent …rm, be it a monopolist or not, might
include the patenting of innovative technologies to protect its market position is not merelya theoretical result.
Gilbert and Newbery use the term “patent thicket” to describe the
patenting of many inventions by a …rm, some of which are neither used nor licensed to others,in reference to a 1978 antitrust case between SCM Corporation and Xerox Corporation. Andin the context of their model, such behavior is referred to as preemptive patenting, where a…rm takes out patents on certain innovations simply to prevent them from being patented byits competitors. In this context, patent thickets are empirical manifestations of the theoreticalbehavior described by Gilbert and Newbery and Reinganum (1983), lending credibility to theidea that …rms will engage in costly activity to protect their market position from potentialentrants.
However, since the publication of their work, patent thickets have been applied to highly
technical industries in a far less condemnatory manner. The term patent thicket is also usedto refer to the group of patented technologies that are related to a single, technologically-complex product.
Generally, no single …rms holds the patents to the various processes that
are relevant to a single product and …rms tend to license technologies to competitors with theunderstanding that such behavior will be reciprocated if necessary. In this case, the term patentthicket merely denotes the fact that technologically intricate products require the aggregationof multiple patented processes for production. Because such processes often have multiple uses,their rights are frequently held by multiple …rms and there is a tendency for open licensing,without any of the protective, exclusionary behavior associated with the concept of monopoly
Generally, the term patent thicket is used to describe the behavior studied by
Gilbert and Newbery, while the use of the term to describe the existence of multiple patentedprocesses associated with a single marketable product tends to be speci…c to the high-technologysector.
Thus far, research and development has been modeled as a process of investment that re-
sults in success after a threshold level of investment has been reached. While this perspectiveis useful in order to identify the game-theoretic implications of monopoly power on the innov-ative process, it seems to lack descriptive power in certain aspects of the actual research anddevelopment process.
For certain industries, the development of new products is related to
the identi…cation of a useful technology, such as a compound useful in cancer treatment forthe pharmaceutical industry, an idea that can be described in words or on …lm for authorsor screenwriters, or a new pocket of natural gas or petroleum for the oil industry. In theseindustries, there is no guarantee that investment in research and development will produce anyreturns, as embodied by the identi…cation of a useful product. As such, modeling the researchand development process as a search through potential research leads seems useful.
model, we analyze the impact of competition on …rm behavior during the research and develop-ment process, where successes result in the development of products which lack a pre-existingmarket so that the discovery does not impact the existing products and pro…ts of the …rm.
We begin our discussion of …rm behavior during the research and development process byconsidering the post-discovery behavior of a …rm. We take this approach to defend our decisionto model the process as a competitive search through research leads and to con…rm that itachieves the same predictions of post-discovery behavior as those reached in models of totalresearch and development expenditures, such as the model presented by Gilbert and Newbery.
After identifying the predicted post-discovery behavior, we move on to develop models of pre-discovery behavior for a single …rm searching through research leads and for a …rm engaged in acompetitive search through research leads hoping to achieve monopoly position within a givenmarket. This comparison allows us to comment on the impact of competition on the demandfor exclusive access to research leads.
Consider a …rm engaged in a competitive search, with one other …rm, through n research leads,where the probability of a lead being a success, p, is constant across all leads. Let R representthe revenues from discovery of a success that would accrue to a monopolist. We assume that therevenues associated with discovery will be diminished if both …rms engaged in the search makea discovery, and refer to an individual …rm’s share of these revenues as Rd, where Rd < R .
Let the …rm discover a successful lead when testing lead i, meaning that there are n
We assume that the discovery-making …rm will stop searching
through leads following its discovery. Now, we want to determine the optimal action for a …rmto take in order to protect its newly-achieved monopoly status. Let k represent the cost that a…rm must pay to exclude its competition from searching a given research lead and let this costbe constant across leads. Having paid the cost k, we assume that a …rm is able to prevent itscompetition from testing that lead. Preemptive exclusion is the term that we use to describea …rm’s decision to spend k in order to ensure unique access to a research lead before havingsearched the lead. In choosing to purchase unique access to a portion of the remaining leadsfollowing a discovery in lead i, the …rm will attempt to maximize the following function,
which describes the pro…t accruing to a pioneer discoverer following its decision to purchaseunique access to m leads,
This equation allows the discovery-making …rm to determine if it would ever be optimal to
prevent its competition from accessing certain portions of the remaining leads.
1 designates the pro…t-maximizing actions that the discovery-making …rm will take facing thegiven function,
Proposition 1 In competitive search, optimal post-discovery behavior will consist of one of thefollowing actions: protection of the success; protection of all remaining leads; or no protection.
The …rm will never choose to exclude its competitor from a subset of the remaining leads.
Proof. The proposition will hold so long as the maximum of
of the range for m. If the second derivative of the expected pro…t function with respect to thenumber of leads to which a …rm has purchased exclusive access is non-negative over the entirerange of m, then we know that the function will achieve its maximum value at either m = 1 or
m = n i. So, let us look at the second derivative: @2 i;m = (R
The three pieces of the equation are clearly all non-negative. From economic theory, we knowthat the pro…t of a monopolist is greater than the total pro…t in a duopoly market.
monopoly pro…t is necessarily greater than one …rm’s share of the total duopoly pro…t, makingthe …rst term positive for all values of m.
The middle term will be positive for all values of
0, and will be zero for all values of m if p = 0. Finally, the third term will
be positive for all values of m if p 6= 1, otherwise it will be equal to zero for all values of m.
It is clear that the second derivative will be positive for all values of m for most probabilities(i.e., 0 < p < 1).
Furthermore, if the second derivative is ever equal to zero, then it will be
zero over the entire range of m, meaning that the derivative will take a constant value acrossm, which also precludes a maximum of
Proposition 1 provides support for the concept of "preemptive patenting" suggested by
Additionally, the results presented in the proposition provide some
intuition for the existence of patent thickets. In order to protect its position in a new market,a …rm might be willing to patent numerous potential technologies, without expecting to derivedirect pro…ts from associated products. Having displayed the ability of the search-based modelto predict post-discovery behavior, we are now able to address the focal question of this paperhaving to do with the pre-discovery behavior of a …rm engaged in a competitive search throughresearch leads.
We begin our exploration of the impact of competition on …rm behavior during the research anddevelopment process prior to the discovery of a success by considering a single …rm searchingthrough a pool of leads.
Let the pool of research leads contain n separate leads, and let the
probability with which any lead contains a useful compound, p, be constant across leads. Weassume that the result of a test on any given lead reveals no information about the probabilityof success for any leads other than the one being tested (i.e., we assume that the probabilityof success is independently and identically distributed across research leads). Let the cost ofsearching each lead be constant, c, and let R represent the revenue associated with a discovery.
Because there is uncertainty about whether or not a success will occur when testing eachresearch lead, we let
represent the expected number of leads that will be searched before a
discovery is made, which is important in the determination of the overall cost of search. Havingidenti…ed the individual components, we are able to de…ne the pro…t function of a single …rmsearching through a pool of research leads as:
We can see clearly that the expected pro…t of a search increases as the number of leads
being searched increases, but that this increase occurs at a decreasing rate (i.e., @E[ ] > 0,
@2E[ ] < 0). The above expected pro…t function introduces two terms that require explanation.
represents the expected number of searches that will occur given a pool of n leads, each with
equal probability of success. We can develop a formula to express the probability of searchingall leads given n leads: P (search n leads) = (1
p)n 1, which follows from the fact that the
probability of searching the …rst lead is one, and each subsequent lead will be searched only ifthe previous leads are unsuccessful.
We see that the expression for the expected number of
searches given n remaining leads is the sum of a geometric series:
p). This result provides us with a well-de…ned expression for the expected number of
Now, let us consider how such a …rm would react to the opportunity to gain exclusive access
to a subset of the research leads. Let x represent the number of research leads (out of the ntotal leads) to which the …rm purchases exclusive access and assume that the cost of exclusiveaccess is constant for each lead and represented by k. Because there are no competing …rms,exclusive access does not alter the revenues associated with discovery in any of the exclusiveleads, so that we can represent the expected pro…t awaiting the …rm in this case as:
For a …rm operating in the absence of competition, there is no incentive to purchase exclusive
access to any of the research leads, because it enjoys de facto exclusive access in the absence ofcompetition.
Preemptive exclusion is a costly behavior, which does not provide any bene…ts
to a sole …rm engaged in a search for research leads. Additionally, there is no incentive for the…rm to search through any research leads following the discovery of a success, because thereare no competitors to threaten its monopoly pro…ts by making a discovery.
Proposition 2 Given discovery of a success on lead i, a …rm searching through leads in theabsence of competition will not search any of the remaining n i leads for additional discoveries.
Proof. Assume that the research pool consists of 2 leads. Let the …rst lead be a success, sothat after searching the …rst lead, the …rm has pro…ts of
…rm searches the second lead. Even if the second lead is a success, under the assumption thatthe discovery of additional successes does not increase the market demand facing the …rm, the…rm’s pro…ts become
2c. It is clear that the …rm’s pro…ts decrease with continued
search following a discovery (i.e., marginal pro…ts are negative for all post-discovery searches).
This logic can be applied to research pools of n leads, for all n. A …rm engaged in a search inthe absence of competition has no incentive to continue searching through the pool of researchleads following discovery of the …rst successful lead.
Note that this result is derived in the framework of the SSR model.
this angle, it becomes quite intuitive, under the assumptions of the model, that a single …rmsearching for new technology does not bene…t from the existence of multiple useful technologies.
This outcome provides the motivation for the term redundant leads.
We are now ready to introduce competition into the search for useful research leads. Our
model incorporates the role of competition in two ways.
of multiple …rms impacts the probability of any given …rm discovering a useful research leadfrom within the pool. Second, we acknowledge that in the presence of multiple useful researchleads, the number of …rms competing for monopoly position within a given market impacts therevenues associated with a successful product.
The probability that a …rm engaged in a competitive search through research leads will be
the …rst to test a lead will be some function of the number of …rms engaged in the search. Wespecify the form of this function under the assumption that each of the …rms searching throughthe pool of research leads is equally likely to be the …rst …rm to test a lead. This assumptionseems readily defensible, although its applicability to the research and development process isdependent on another assumption which might be less realistic: we assume that all …rms searchthrough the pool of research leads in the same order (see Appendix for further discussion ofthis assumption).
Let us now show that the presence of competition decreases the expected value of the pro…ts
associated with the discovery of a useful research lead. This impact is driven by the potentialthat there might be multiple successful leads located within the research pool.
discussion, we have deemed additional useful leads in the pool that occur later in the searchorder than the initial success to be redundant leads. However, our current discussion, whichallows for competition in the search process, emphasizes that such a term is inappropriatebecause the presence of multiple successes can change the pro…ts of research and developmentsuccess.
In addition to a¤ecting the probability that a given …rm will experience a research and
development success, the existence of competing …rms can impact the pro…ts associated withdiscovery based on the split of discoveries between a given …rm and its competition.
a single …rm is engaged in a search through research leads, the bene…ts of discovery are …xedwhether the …rm …nds one useful lead or multiple useful leads related to the same marketableproduct, so long as ownership of multiple products does not allow a …rm to increase the numberof consumers to which it can sell its products (i.e., so long as discoveries are perfect substitutes).
This is not the case when multiple …rms are engaged in the competitive search through a poolof research leads. Proposition 4 identi…es the impact of competition on the revenues associatedwith research and development success.
Proposition 3 The presence of competition during a search for successful research leads de-creases the expected revenues associated with discovery of a success.
Proof. We de…ne the revenues for a monopolist associated with a successful search through apool of research leads as R. For a …rm engaged in a competitive search, the revenues associatedwith discovery depend on the proportion of existing successful leads that a given …rm is ableto discover. Let h represent the total number of hits, or successes, that exist in a pool ofresearch leads. Let f represent the number of existing successes that are discovered by a …rm’scompetitors. We assume that if f = 0, then the revenues associated with discovery for a …rmfacing competition will be equivalent to the revenues for a monopolist.
the function of h and f that is used to adjust the monopoly revenues of discovery as (h f) .
Given this speci…cation, it is clear that the rewards of discovery for a …rm competing againstother …rms to discover research successes are less than the rewards of discovery that await amonopolist.
The pro…t function for a …rm engaged in a competitive search for marketable products will
Clearly, h can take on any integer value between 0 and n.
again elementary to understand that f can take on any integer value between 0 and h.
model of the expected pro…ts from the research and development e¤ort assumes that a …rm’s
pro…ts associated with discovery are related to the proportion of total successes controlled bythat …rm. This proportion is given by (h f) .
Given an expression for the probability of making a discovery, as well as the manner in
which multiple successes can each be of value to a …rm engaged in a competitive search througha pool of research leads, we can de…ne the expected pro…ts of engaging in such a search asfollows:
The formula presented in equation 6 to capture a …rm’s expected pro…ts from search di¤ers
markedly from the formula presented in equation 5, due to the impact of competition on the…rm’s pro…ts.
We discussed above that the presence of multiple …rms searching through a
pool of research leads will impact the probability that any given …rm will be the …rst to testa particular lead. Similarly, we introduced the idea that the discovery of multiple successfulleads would be bene…cial to a …rm engaged in competitive search due to the impact on revenuesassociated with competing …rms making their own discoveries. The value of making multiplediscoveries, which helps a …rm approach the monopoly pro…ts associated with research anddevelopment success, is also behind the two remaining changes in equation 6 relative to equation5.
In the case of a single …rm engaging in a search through research leads, the bene…ts of a
discovery cannot be impacted by the number of discoveries made by its competition, because itis assumed that such competition does not exist. The fact that a single discovery is su¢ cientfor a …rm to enjoy monopoly pro…ts is manifested in the functional form of the probability ofdiscovery.
In equation 5, we describe the probability of discovery as the complement of the
probability that no successful leads exist in the pool of research leads. This approach indicatesthat there is no bene…t to the …rm of discovering more than one success during its research anddevelopment process, as there is a cost of searching through additional leads while there is nobene…t of making multiple discoveries.
Such logic is inappropriate when considering the bene…ts of discovery for a …rm engaged in
a competitive search through research leads.
We have assumed that the revenues associated
with research and development success are dependent on the number of discoveries made by a…rm relative to the total number of discoveries made by all competing …rms. More precisely,we have made the assumption that multiple existing successes in a pool of research leads wouldresult in the development of products that would be perfect substitutes for each other.1
number of discoveries made by a …rm, rather than the probability that at least a single successexists within the pool for research products, is of interest in determining the expected pro…tsassociated with a competitive search through research leads. As such, equation 6 accounts forthe possibility of any possible number of successful research leads existing in the pool as well asthe probability that a single …rm possesses all possible combinations of the existing successesin order to determine the expected revenues of competitive search.
The …nal di¤erence between equations 5 and 6 has to do with the number of leads that
a …rm will search through in the presence or absence of competition.
to search through a pool of research leads without fear of competitors challenging its marketpower through discoveries of their own, we assume that the number of leads tested is a functionof the probability that any given lead will be a success.
1 While this may seem to be an overly restrictive assumption, examples from the pharmaceutical industry
with aspirin and ibuprofen o¤ering nearly identical results as well as the competition between Viagra, Levitra,and Cialis, lend a sense of realism to this assumption.
ensure monopoly pro…ts, we develop the expected number of leads searched by assuming thatsubsequent leads are tested only if a discovery has yet to be made. This logic is not appropriatewhen the …rm is racing against competitors to search through the pool of research leads. In theface of competition, a …rm is not guaranteed to hold a monopoly position following the discoveryof a single successful research lead. However, the …rm is able to approach this monopoly positionby increasing its number of discoveries toward the total number of successful leads that exist inthe pool. This distinction emphasizes the direct and indirect value of multiple successes thathas been previously discounted in the literature through the interpretation of such researchleads as redundant successes. It also leads us to Proposition 4:
Proposition 4 When the cost of search lies below a certain threshold (c < p R ), the presence
of competition induces a …rm to test all research leads, which would not occur if it were operatingin the absence of competition.
Proof. We consider the case in which a …rm has the least incentive to continue testing followingdiscovery of a success in order to prove proposition 4. Let there be a pool of n research leadsand let the search of the …rst n
1 leads, which are all successes, have occurred. Further, let
a single …rm have been the …rst to test each of the n
1 successes so that it possesses all of the
successes with one lead remaining. If the …rm does not engage in the search of the last lead,its expected pro…ts are E[ jsearch n 1 leads] = (1 p)R + p n 1 R (n 1)c. If the …rm does
search the last lead, its expected pro…ts are E[ jsearch n leads] = (1 p)R + p n 1 R + p R nc.
The pro…ts of searching the last lead are greater than not searching it so long as c < p R .
It seems that this case represents the situation in which the …rm has the least to gain fromsearching through all leads, so that as long as the cost of search lies below the above threshold,competition is su¢ cient to induce a …rm to search through all research leads in the pool.
Acknowledging that multiple successes can be of value during competitive search motivates
the possibility that a …rm might be willing to prevent its competition from searching a portionof the research leads. In order to approach the monopoly rewards of research and developmentsuccess that exist in the absence of competition, a …rm might take action to gain exclusive accessto a portion of the research leads. Such a strategy would serve to increase the probability thatit would hold a monopoly position in the market if successful leads were to exist in the pool ofresearch leads.
Before pursuing the impacts of such action analytically, let us …rst de…ne the actions that a
…rm could take, in practice, to a¤ord the unique opportunity to search through a pool of researchleads. We take such an action to be de…ned by the costly exclusion of others from a potentiallyrewarding subset of the research leads. In the oil industry, such an action might include theleasing of access to areas that might include pools of petroleum and natural gas, before anydiscovery regarding the presence of oil or natural gas has occurred.
industry, such an action might involve a …rm paying a host country for exclusive access to asubset of natural organisms before any compounds found within the organisms in the subsethas been con…rmed to be biochemically responsive to a given human disease (e.g., entering intoa bioprospecting agreement).
Such an action in the high-technology industry might include
the patenting of several technological processes before the marketable uses of such processeshas been determined (note, this is a clear pre-discovery parallel to the post-discovery behaviorstudied by Gilbert and Newbery, which those authors termed preemptive patenting).
Let us consider that it is possible for a …rm engaged in a competitive search to pursue a
strategy of preemptive exclusion, where we de…ne preemptive exclusion to mean pre-discoverybehavior of a …rm that limits the pool of research leads to which its competitors have access.
Now, let x represent the number of research leads that the …rm preemptively excludes itscompetitors from searching, at a cost of k per lead.
value between 0 and n, inclusive. The …rm faces no competition during its search of the x leadsto which it has secured unique access; however, the revenues that will follow from discoveriesmade in this pool of leads are dependent on the outcome of the competitive search through theremaining n
We have identi…ed the potential revenues associated with a pre-discovery strategy of preemp-
tive exclusion. Given this understanding, we are able to determine the …rm’s expected pro…tfunction from engaging in a competitive search with preemptive exclusion. The appropriateformula is:
Any successes that exist within the x leads that the …rm chooses to preemptively exclude its
competitors from searching, will be discovered by the …rm. However, the revenues associatedwith discovery will depend on the percentage of total hits controlled by the …rm. Therefore,we incorporate the pool of leads to which a …rm has exclusive access in two ways.
First, because the revenues associated with discovery will depend on the outcome of the
x remaining leads, we need to identify the number of
successes that will exist in the exclusive pool, in order to determine the expected pro…ts ofsuch a strategy. We represent the number of successes as a binomial random variable
the x leads isolated through preemptive exclusion.
This choice is based on the fact that the
probability of any given lead being a success is a Bernoulli random variable with probability ofsuccess p, so that the number of successes in a pool of x leads is a binomial random variable.
Second, we need to determine the probability with which each possible number of discoveries
from the exclusive pool occurs. Lacking competition during the search through these leads, the…rm will discover all successful leads that exist in the pool. As such, we can model the possiblenumber of successes using the unmodi…ed formula for a Bernoulli process.
Having identi…ed the expected pro…ts associated with a strategy of preemptive exclusion, we
must now determine whether or not a pro…t-maximizing …rm engaged in a competitive searchthrough a pool of research leads would ever choose to preemptively exclude its competitionfrom a portion of the research leads in order to increase the pro…ts associated with discovery.
By asking this question, we will be able to identify the impact of competition on the value ofexclusive access to the marginal research lead. This point of interest leads us to the followingproposition:
Proposition 5 Over a certain range of values for the cost of exclusion, the optimal behaviorfor a pro…t-maximizing …rm involved in a competitive search through research leads will involvethe preemptive exclusion of its competition from a portion of the leads in the research pool.
Proof. To prove propsition 5, we compare the expected pro…ts that await a …rm when x = 0and when x = 1. Clearly, when x = 0, the …rm’s expected pro…ts are as described in equation6, which we will describe here as
nc. When x = 1, the …rms expected pro…ts are
and we see that the pro…ts of preemptive exclusion are greater than those under competitive
The intuition behind the result described in Proposition 6 was …rst presented in the simple
example of two …rms searching through a pool of two research leads. The value of preemptiveexclusion comes from the resulting decreased likelihood that a …rm’s competition will make adiscovery from the reduced pool of research leads to which it has access.
likelihood of competitor discovery, a …rm is able to increase the rewards that it will receivefrom success in its own program of research and development, increasing its incentive to investin such a program.
It must be mentioned that the discussion of preemptive exclusion thus far has proceeded
in order to demonstrate that …rms engaged in competitive search have an incentive to engagein such behavior.
This discussion has not aimed to suggest that this strategy will increase
the pro…ts of the search for research leads in practice; the propositions above have identi…edincentives for any …rm engaged in such competitive search, meaning that all …rms searchingthrough the pool would have incentives to behave in this way. Presumably, the outcome wouldbe a bidding war to enjoy preemptive exclusion, meaning that the pro…ts of such behaviorwould be dissipated. Nevertheless, that outcome does not alter the key insight a¤orded by thisanalysis: the incentive to preemptively exclude competitors from a portion of the research poolexists. It is this …nding, which di¤ers from previous studies that is of greatest interest and isof relevance to the issue of bioprospecting as a means of conservation.
The incorporation of competition into the search of research leads, which results in the
viability of preemptive exclusion, increases the value of the marginal research lead to a company.
In the presence of competition, if a …rm does not search a lead, it not only misses out on thepotential discovery of a success, it also decreases the value of any other successes that it may…nd by allowing the lead to be searched by its competition. The impact of competition on themarginal value of a research lead, which has not been addressed in previous studies that modelthe research and development process as a search through research leads, seems relevant to theprocess of bioprospecting.
As such, following an update on the state of the world regarding
bioprospecting practices, we reconsider the conservation potential of pharmaceutical …rms inthe next section.
International recognition of the importance of biodiversity has led environmental groups tosuggest that pharmaceutical …rms might play a role in the conservation of tropical ecosystems,where much of the world’s biodiversity is found, due to the role played by natural compoundsin the research and development of new pharmaceutical products. SSR discounts such a notion,arguing that the value of the marginal species in some of the most biologically-diverse regionsof the world is insu¢ cient to prompt pharmaceutical …rms to spend money preventing habitatdestruction in those regions. Our e¤ort re-evaluates the viability of bioprospecting as a con-servation mechanism by viewing bioprospecting as a race for monopoly power and concludesthat pharmaceutical …rms could contribute to the conservation of biodiversity.
The incorporation of competition into the research and development framework, modeled
as a search through research leads, provides insight into the pre-discovery behavior of …rms.
Such a model provides a realistic version of pharmaceutical research and development e¤ortsand allows for the possibility that …rms could gain through the conservation of biodiversity.
Our theoretical …ndings suggest that the demand for exclusive access to natural compoundsmay exist.
In our theoretical model, …rms are able to preemptively exclude their competitors from
searching segments of the research pool by purchasing exclusive access to research leads. Thisframework is analogous to the existing practice of pharmaceutical …rms signing bioprospecting
agreements with host nations, where a host nation is the country whose territory encompassesan area of great biological diversity.
A bioprospecting agreement is essentially a contract
stipulating that a pharmaceutical …rm will pay a mutually-agreed upon sum to a host nation forthe privilege of gaining exclusive access to a speci…ed subset of native organisms. Then, it seemsreasonable to interpret bioprospecting agreements as a form of preemptive exclusion, wherebya pharmaceutical …rm will pay for unique access to a number of species, ideally preventing itscompetition from searching those leads.
Our model of …rm behavior during a competitive search through research leads is consistent
with the existence of bioprospecting agreements in practice, an outcome that is not supportedwhen the search process is modeled in the absence of competition. While previous studies havementioned the 1991 bioprospecting agreement signed between Merck and INBio, the NationalBiodiversity Institute of Costa Rica, it is often described as a goodwill act and the dearth ofother existing bioprospecting agreements has been used to support the argument that pharma-ceutical …rms have nothing to gain from biodiversity conservation.
In fact, there are numerous examples of existing bioprospecting agreements; however, the
details of the agreements are not readily revealed. The INBio web page notes that the instituteentered into 21 di¤erent bioprospecting agreements with 18 di¤erent international pharmaceuti-cal …rms in a ten-year period from 1991 to 2001. Although this is by no means a comprehensiverecord of existing bioprospecting agreements, this practical evidence of pharmaceutical …rmspurchasing exclusive access to research leads indicates that there is demand for such agreements.
Furthermore, the formation of bioprospecting agreements is behavior that can be predicted byour model of …rm behavior during a competitive search through research leads.
Within our model, a …rm is able to guarantee exclusive access to a research lead by paying
Implicitly, we are assuming that this costly action ensures that the …rm has
a property right (intellectual or otherwise) to that lead.
the formation of bioprospecting agreements will be su¢ cient to ensure complete property-right protection.
Accordingly, it is essential to be familiar with the guiding principles of
bioprospecting agreements in order to determine if and how such agreements di¤er from ourmodel of exclusive access.
In 1992, the Convention on Biological Diversity (CBD) developed guidelines for bioprospect-
ing agreements to ensure that host nations would be able to share in the pro…ts associated withsuccessful product development. The CBD aimed to guarantee that host nations would receivejust compensation for protecting their native biodiversity. The principle objective of the CBDwas the conservation of biological diversity, as well as equitable bene…t-sharing of productsderived from organisms, including a call for contracts to emphasize training of host peoples inthe practice of sample collection and compound testing (Article 1). The CBD simultaneouslyrecognized the importance of intellectual property rights and allowed for their transfer to theprospecting …rm conditional on the host nation’s approval: host nations acknowledged thatpharmaceutical …rms would need their intellectual property rights to be defensible within hostnations in order to enjoy the monopoly pro…ts of drug-discovery that justify their signi…cantresearch and development programs.
The protection of intellectual property rights is essential for pharmaceutical …rms to hold
monopoly positions following research and development success.
Trade Related Aspects of Intellectual Property Rights (TRIPS) further developed the ability of…rms to protect intellectual property internationally. The World Trade Organization (WTO)encouraged all member countries to develop national legislation that supported the goals putforth in the TRIPS agreement as quickly as possible.
concern from the pharmaceutical …rms that their willingness to enter into exclusive use contractswith host-nation organizations might not result in monopoly power upon the discovery of a
This concern is based on fears that the host-nation might be unable to
control access to the species covered by the agreement or that the legal environment in thehost-nation might not be su¢ cient to support patents on compounds identi…ed as useful. Whilethe vast majority of host countries have taken this step, the credibility of such an action is notuniform across countries. As such, pharmaceutical …rms have taken to obtaining samples frombotanical gardens in industrialized countries, where they can be assured that their discoverieswill enjoy meaningful legal protection.
Such actions might be interpreted as a signal that
pharmaceutical …rms are unwilling to participate in more costly bioprospecting agreementswith host countries; however, the anecdotal evidence from Costa Rica, mentioned above showsa signi…cant number of bioprospecting agreements since the CBD. This evidence, and theseemingly unique nature of the legal infrastructure and credibility of the government in CostaRica relative to other host nations, might also suggest that the pharmaceutical …rms dependon the unique access to research leads for success in their industry, which is ensured by credibleproperty right legislation and enforcement in host countries.
Additional support for the argument that there is demand for unique access but concern
about enforceability of intellectual property rights is that more recent research e¤orts havefocused on the structure of existing bioprospecting agreements and the host-nation character-istics that impact this structure. Mulholland and Wilman (2003) present a theoretical modeldepicting the process of contract formation and discuss its predictive ability in the context ofcertain existing agreements. Sampath (2005) identi…es optimal property rights structures andinstitutions for regulating bioprospecting and uses these features as predictors of success orfailure for several existing agreements. The shift in the bioprospecting literature to a focus oncontract formation and an evaluation of existing agreements rea¢ rms the belief that demandfor bioprospecting agreements, and the exclusive access to these natural compounds that theyguarantee, exists.
Mulholland and Wilman explore the formation of bioprospecting agreements in the context
of a dynamic principal-agent model so as to identify components of agreements that are essentialif bioprospecting is to be of any use in the e¤orts to conserve biodiversity. The authors stressthat appropriate institutions must exist for host nations to turn the potential pharmaceuticalvalue of in situ biodiversity into incentives for conservation as well as returns for both thepharmaceutical …rms and the host nation itself. Generally speaking, their results indicate thatproperty rights, of the intellectual and more tangible varieties, will play an important role indetermining the impact of bioprospecting on the e¤ort to conserve biodiversity.
Sampath reviews many of the fundamental elements of bioprospecting in order to identify the
institutions that must exist for equitable sharing of the potential gains from bioprospecting.
She notes that regardless of the e¤orts made at the international level, including the textdeveloped during the CBD and the TRIPS agreement, the most critical determinants of thecontinued existence of bioprospecting agreements will be national laws. And she argues thatthe de…nition of property rights regarding genetic resources and the knowledge that has beenaccrued over the long-run by traditional societies through laws at the national level that alsodelineate the appropriate rules of contracting will be essential for bioprospecting to occur in amanner satisfactory to both prospecting …rms and host nations.
The e¤orts of Mulholland and Wilman and Sampath reinforce the importance of well-de…ned
and credibly-enforced property rights for the potential pro…ts associated with new pharma-ceutical products to promote conservation e¤orts in host countries.
theoretical model of …rm behavior during a competitive search, the protection of intellectualproperty rights is of fundamental importance in order for pharmaceutical …rms to enter intobioprospecting agreements with host countries. However, in order to achieve the conservationof biodiversity, the property rights to the value of the in situ biodiversity is almost of equal im-
portance. Without clear assurance that their e¤orts to conserve will result in …nancial rewardfor themselves, local decision-makers will not feel as though they are residual claimants to thefruits of their e¤orts and the key cog in the conservation machine will be missing.
We have found that monopoly power, which has been previously shown to impact the behaviorof …rms holding such a position, can also in‡uence the behavior of …rms who are competingto hold such a position.
The revenue premium associated with holding a monopoly position
is shown to in‡uence both the pre-discovery and post-discovery behavior of …rms engaged ina competitive search through a pool of research leads.
the threat to monopoly revenues associated with discovery posed by the potential presence ofmultiple successful leads within a single research pool.
In previous e¤orts to model the value of the marginal research lead during a search through
research leads, it has been assumed that the discovery of a successful research lead will unam-biguously result in monopoly pro…ts. In this context, there is no value attached to the presenceof successful leads subsequent to the pioneer success, a result that we implicitly obtained inProposition 2 above. In addition to other necessary conditions, this result is contingent on theassumption that if a …rm does not test a research lead, it vanishes from existence.
assumption allows multiple successes that exist in the pool of leads to be deemed redundant.
However, it seems more natural to assume that if a given …rm does not test a research lead, itwill remain in the pool of research leads, where it might be tested by another …rm.
The introduction of competition into the framework of the search for a successful research
lead assigns value to each of the successes that exist in the pool, transforming these subsequentsuccesses from valueless redundancies into reward-threatening substitutes. Realizing that thebene…ts of discovery will be diminished if a …rm’s competition is able to identify a discovery fromthe remaining pool of research leads provides incentives for the …rm to decrease the probabilityof such a counter-discovery occurring. Under certain conditions, the increased marginal valueof any given research lead is then signi…cant enough to prompt the strategy of preemptiveexclusion.
This …nding, because the assumed conditions su¢ ciently parallel the process whereby phar-
maceutical …rms search for useful compounds from natural sources, seems poised to o¤er ameaningful contribution to the debate about the conservation potential associated with bio-prospecting. It is clear that multiple pharmaceutical …rms are engaged in the search for novelorganic compounds for use in the drug-development process2 ; therefore, it seems unreasonableto assume that any discovery in the process will unambiguously result in a monopoly position inthe resulting drug market. Of further relevance is the fact that bioprospecting agreements areclear examples of preemptive exclusion, whereby the …rms are paying host nations for exclusiveaccess to a portion of the relevant research leads in return for the nation’s assurance that anypotential discoveries will be granted meaningful intellectual property right protection.
fect, these results seem to provide both theoretical and anecdotal evidence that there is demandfrom pharmaceutical …rms for the opportunity to preemptively exclude their competitors fromportions of the research lead pool.
While this paper has o¤ered evidence that there is demand amongst pharmaceutical …rms for
exclusive access to research leads, it has also implicitly suggested that there is not an adequate
2 The empirical support for this statement is provided by the fact that Eli Lilly and Company, Bristol-Myers
Squibb, and Merck & Company, have each entered into bioprospecting agreements with INBio.
no means a comprehensive list of existing bioprospecting agreements, though it seems su¢ cient to support theabove statement.
supply of such access being o¤ered by host nations. Within the model, a …rm is willing to spendmoney to exclude its competition from a segment of research leads because this costly activityensures that its competition will not have access to those leads, increasing its probability ofenjoying monopoly power upon the discovery of a success. In practice, as Sampath indicates,the legal environment in many of the host nations is insu¢ cient to o¤er pharmaceutical …rmsthe level of intellectual property rights that they desire.
may need to take strides to modify their legal environment before they will be able to share inthe bene…ts from bioprospecting and before pharmaceutical …rms will be able to contribute tothe conservation of biodiversity.
The assumption that the pool of research leads is searched in the same order by all …rmscompeting for monopoly power in the market is made for computational simplicity, otherwisethe probability of any research lead yielding a successful product would vary based on whetheror not the item had been searched by competitors.
in a research development program would happen to search potential leads in the exact sameorder.
However, it does seem reasonable that competitive …rms with the same information
might choose to order the leads in the same manner based on the probability of success (i.e.,…rms would test the items with the highest probability of success …rst). Our assumption relieson the logic of symmetric information while maintaining a constant probability of success acrossleads.
Rausser and Small (2000) study the impact of sorting potential research leads on the value
of the marginal lead in a response to the SSR …nding that the potential value of organismswith regard to pharmaceutical products is not su¢ cient for pharmaceutical …rms to subsidizeconservation. Rausser and Small motivate their research e¤ort by commenting on the valueof information in the search process, noting that in practice searches are not conducted byproceeding through objects in a random order.
Rather, search is conducted e¢ ciently, with
the e¢ ciency stemming from an ordering of the objects to be searched by their prospect ofproviding a reward.
Using their model of search through a sorted pool of leads, Rausser and Small determine
that, under certain conditions, the information rents associated with identifying di¤erent prob-abilities of success amongst the pool of leads can be su¢ cient to impact development andconservation decisions.
The authors note that when the number of leads to be searched and
the pro…ts from research and development are both large, the incentives for conservation arisealmost uniquely from the magnitude of the search costs and the quality of information availableto sort the leads. Having identi…ed theoretical support for the use of pharmaceutical …rms asproponents of conservation, Rausser and Small reconsider the attempt made by SSR to esti-mate the value of natural compounds as inputs in the drug-development process. By addingthe information rents that accompany a sorted search process into the valuation of areas ofhigh biodiversity, Rausser and Small develop per hectare values for areas with high numbers ofendemic species that are two orders of magnitude larger than those estimated by SSR.
It should be noted that work by Costello and Ward (2005) re-evaluates the …ndings of
Rausser and Small and attributes the di¤erence in valuation of biodiversity hotspots to anassumption regarding the appropriate metric of biodiversity.
the …ndings of their research e¤ort, the model developed by Rausser and Small provides someintuition for our approach regarding the assumption of an identical search order across …rms.
We acknowledge that this assumption may not be intuitive, but we do not believe that relaxingit would impact our …ndings.
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Overview of clinical studies with sodium selenite1998 – 2011Note: Even if not mentioned specifically, sodium selenite has always been given in addition to standard therapy, not as an alternative to standard therapy!Note: Cancer prevention studies are not included. Some minor pilot studies or preliminary publications have also been omitted, if consecutive high quality studies have been publishe