ArticlePDF Available

Open Collaboration for Innovation: Principles and Performance

June 2014
Organization Science 25(5)

DOI:10.1287/orsc.2013.0872

Source
arXiv

Authors:

Sheen S. Levine

Mj Prietula

Emory University

The principles of open collaboration for innovation (and production), once distinctive to open source software, are now found in many other ventures. Some of these ventures are internet-based: Wikipedia, online forums and communities. Others are off-line: in medicine, science, and everyday life. Such ventures have been affecting traditional firms, and may represent a new organizational form. Despite the impact of such ventures, questions remain about their operating principles and performance. Here we define open collaboration (OC), the underlying set of principles, and propose that it is a robust engine for innovation and production. First, we review multiple OC ventures and identify four defining principles. In all instances, participants create goods and services of economic value, they exchange and reuse each other's work, they labor purposefully with just loose coordination, and they permit anyone to contribute and consume. These principles distinguish OC from other organizational forms, such as firms or cooperatives. Next, we turn to performance. To understand the performance of OC, we develop a computational model, combining innovation theory with recent evidence on human cooperation. We identify and investigate three elements that affect performance: the cooperativeness of participants, the diversity of their needs, and the degree to which the goods are rival (subtractable). Through computational experiments, we find that OC performs well even in seemingly harsh environments: when cooperators are a minority, free riders are present, diversity is lacking, or goods are rival. We conclude that OC is viable and likely to expand into new domains. The findings also inform the discussion on new organizational forms, collaborative and communal.

A, 2B, 2C. How Elements Interact to Affect Performance. Main effect of Rivalry and interaction with Need Heterogeneity over a combination of three populations: cooperators, the general population and reciprocators (A). Main effect of Need Heterogeneity and interaction with Rivalry over the same populations (B). Interactions between Rivalry, Need Heterogeneity, and population composition (C). Free-Rider populations (not plotted) showed lower performance (<10% in all conditions, p<0.001).

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Performance of the General Population at Various Combinations of Need Heterogeneity and Rivalry 2

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Figure EC4. Flowchart of Agent Behavioral Algorithm

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Organization Science

Articles in Advance, pp. 1–20

ISSN 1047-7039 (print) ISSN 1526-5455 (online) http://dx.doi.org/10.1287/orsc.2013.0872

Open Collaboration for Innovation:

Principles and Performance

Sheen S. Levine

Columbia University, New York, New York 10027, sslevine@sslevine.com

Michael J. Prietula

Emory University, Atlanta, Georgia 30322, prietula@bus.emory.edu

The principles of open collaboration for innovation (and production), once distinctive to open source software, are

now found in many other ventures. Some of these ventures are Internet based: for example, Wikipedia and online

communities. Others are off-line: they are found in medicine, science, and everyday life. Such ventures have been affecting

traditional ﬁrms and may represent a new organizational form. Despite the impact of such ventures, their operating principles

and performance are not well understood. Here we deﬁne open collaboration (OC), the underlying set of principles, and

propose that it is a robust engine for innovation and production. First, we review multiple OC ventures and identify four

deﬁning principles. In all instances, participants create goods and services of economic value, they exchange and reuse each

other’s work, they labor purposefully with just loose coordination, and they permit anyone to contribute and consume. These

principles distinguish OC from other organizational forms, such as ﬁrms or cooperatives. Next, we turn to performance.

To understand the performance of OC, we develop a computational model, combining innovation theory with recent

evidence on human cooperation. We identify and investigate three elements that affect performance: the cooperativeness of

participants, the diversity of their needs, and the degree to which the goods are rival (subtractable). Through computational

experiments, we ﬁnd that OC performs well even in seemingly harsh environments: when cooperators are a minority, free

riders are present, diversity is lacking, or goods are rival. We conclude that OC is viable and likely to expand into new

domains. The ﬁndings also inform the discussion on new organizational forms, collaborative and communal.

Key words: innovation; entrepreneurship; strategy; performance; simulation; model; software; open source;

crowdsourcing; Wikipedia; community; economics; psychology

History: Published online in Articles in Advance.

Open source software is booming. Once the domain of

hobbyists and hackers, it has gained acceptance with

consumers, corporations, and governments. Some exem-

plars of open source, such as the Linux and Android

operating systems, are now commonplace, operating

millions of devices. Together with other products of

open source software, they have been creating billions of

dollars in economic value (European Commission 2006).

Yet the same patterns of collaboration, innovation, and

production can now be found beyond software (Baldwin

and von Hippel 2011, Benkler 2006, von Hippel 2005b).

For example, people collaborate, sometimes with com-

plete strangers, in user-to-user forums (Lakhani and von

Hippel 2003), mailing lists (Jarvenpaa and Majchrzak

2008), and online communities (Faraj and Johnson

2010). Some share openly (and occasionally illegally)

digital media: music, movies, TV programs, and soft-

ware (Levine 2001). People also share processing power

and Internet bandwidth, enabling free services such as

Skype (Benkler 2006, pp. 83–87). In the physical world,

off the Internet, people give, receive, and share tools and

appliances (Goodman 2010, Nelson et al. 2007, Willer

et al. 2012), even host strangers overnight (Lauterbach

et al. 2009, Perlroth 2011)—all without payments or

barter. Such ventures exemplify what we call open col-

laboration (OC), a shorthand inspired by Baldwin and

von Hippel (2011). Here, we deﬁne its principles and

explore its performance.

Firms have been affected by open collaboration,

some negatively, others positively. The free encyclopedia

Wikipedia, a prime example of such collaboration, has

come to match the quality of Encyclopædia Britannica

(Giles 2005), which, after 244 years in circulation, has

ceased printing. Other ﬁrms have been thriving by facil-

itating open collaborations, hosting forums and commu-

nities. This is how ﬁrms such as Amazon, an Internet

retailer, and TripAdvisor, a review site for hotels and

restaurants, established a ﬂow of “user-generated con-

tent”: reviews, advice, photos, and video clips. Fellow

users may beneﬁt from such information, and the ﬁrms

economize on wage-free, royalty-free content (Chevalier

and Mayzlin 2006, Mudambi and Schuff 2010). The

effect of open collaboration may be nascent, but it has

already required established ﬁrms to tweak their strategy,

operations, and marketing (Chen and Xie 2008, Scott

and Orlikowski 2012). It also has an impact outside the

commercial world.

Levine and Prietula: Open Collaboration for Innovation

Open collaboration ﬁts well with the scientiﬁc ethos

(David 1998), and, not surprisingly, it has been ben-

eﬁting scientiﬁc endeavors. For instance, thousands of

volunteers, each contributing just a fraction of a solu-

tion, have been discovering and solving problems too

immense for traditional organizations (Benkler 2004,

Partha and David 1994). Contributors classify celestial

objects in Galaxy Zoo, decipher planetary images in the

Mars Public Mapping Project (Benkler 2006, p. 69), and

labor over terrestrial maps (Helft 2007). Similar patterns

that are labeled with the adjectival “open” have appeared

in medicine (Ortí et al. 2009, Rai 2005), engineering

(e.g., “open design”), and biotechnology (Henkel and

Maurer 2007, 2009). In scientiﬁc publication, the open

science movement aims to disperse authority and expand

collaboration (Lin 2012).

Scholars have been attracted to these novel patterns of

innovation and production. Open source software, a har-

binger of open collaboration, was the topic of several

edited volumes (e.g., Feller et al. 2005, West and Gallagher

2006) and special issues of journals (von Krogh and

von Hippel 2003, 2006). The use of “open source” as

a scholarly term has been growing dramatically, from

just 32 appearances in 1999 to 687 times a decade later

(see the electronic companion, available as supplemen-

tal material at http://dx.doi.org/10.1287/orsc.2013.0872).

We build on these efforts. Here, we extend and general-

ize what prior research called open collaborative inno-

vation projects (Baldwin and von Hippel 2011), peer

production (Benkler 2002), a community-based innova-

tion system (Franke and Shah 2003), Wikinomics, and

mass collaboration (Tapscott and Williams 2006), as

well as instances of collaborative communities (Adler

et al. 2008), transaction-free zones (Baldwin 2008),

crowdsourcing (Afuah and Tucci 2012), collaborative

consumption (Goodman 2010), electronic networks of

practice or online communities (Faraj et al. 2011,

Kollock 1999, Wasko and Faraj 2005), and open inno-

vation (West and Gallagher 2006).

Such open collaborations have drawn scholarly inter-

est because of their social and economic impact. How-

ever, what affects their performance—even why they are

viable—remains a puzzle. We begin by identifying some

deﬁning principles: a system of innovation or production

that relies on goal-oriented yet loosely coordinated par-

ticipants who interact to create a product (or service) of

economic value, which is made available to contributors

and noncontributors alike.

Next, we examine performance. We investigate several

elements that affect the performance of open collabora-

tion. One element is cooperative behavior of contributors

who willingly share their work (or property) with non-

contributors. Performance can beneﬁt with people bene-

ﬁt others at cost to themselves, even if reciprocity is not

guaranteed. But such behavior, desirable as it may seem,

is inherently risky—contributors can be overwhelmed by

free riders, as in the classic tragedy of the commons

(Hardin 1968, Olson 1965). Thus, we draw on recent

evidence of human cooperation to answer a fundamental

question: Why do people share the fruits of cooperation

with noncontributors?

Cooperativeness may be the life-giving element of

OC, but it is not the only element affecting performance.

We add to cooperation, a characteristic of interaction,

two other elements taken from the economics and inno-

vation literature. One is a characteristic of the partici-

pants: need heterogeneity, which is the extent to which

they have heterogeneous (diverse) needs. Another a char-

acteristic of the goods: rivalry (or subtractability; see

Hess and Ostrom 2006), which is the extent to which

one’s consumption of a good interferes with another’s.

To assess the performance of OC, we combine

the three elements—cooperativeness, need heterogene-

ity, and rivalry—in an agent-based model. Because we

envision OC as a general system for innovation and pro-

duction, we use a fundamental measure of economic

performance: efﬁciency in turning inputs to outputs.

We ﬁnd surprising results: OC can thrive even in

seemingly harsh environments, reaching much more

broadly than observers assumed or observed. It performs

robustly even when cooperators are a fraction of partic-

ipants, free riders are present, goods are rival, or partic-

ipant needs are homogeneous (nondiverse).

The results suggest what affects the performance of

OC and—equally important—what does not. Some con-

ditions are commonly assumed necessary but they are

not. First, OC can thrive even if participants are not an

exclusive bunch of cooperators but just a random sam-

ple from the human population, where cooperators are

a small minority. Second, it is not required that par-

ticipants derive immediate beneﬁts from contribution,

such as monetary gains, enhanced professional reputa-

tion, or pleasure. Third, OC is not derailed when the

resources shared are rival or when participant needs are

highly similar. It can perform well even with rival goods

or homogeneous needs; performance suffers only when

the two are concurrent. The model also explains some

intriguing observations, such as the extreme disparity in

contributions to OC, where a small core contributes the

most and many contribute little.

The ﬁndings imply that OC is likely to grow and

spread into new domains. They also inform the dis-

cussion on new organizational forms, collaborative and

communal (e.g., Adler et al. 2008, Benkler 2011, Faraj

et al. 2011, Heckscher and Adler 2006). Human efforts,

it seems, can be harnessed in previously unthought-of

of ways: by relying on goal-oriented yet loosely coor-

dinated participants who interact to create products of

economic value, which they then offer to anyone—

contributors and free riders alike.

Levine and Prietula: Open Collaboration for Innovation

Open Collaboration: Deﬁnition, Beneﬁts,

and Puzzles

Open Collaboration Deﬁned

We deﬁne open collaboration as any system of innova-

tion or production that relies on goal-oriented yet loosely

coordinated participants who interact to create a prod-

uct (or service) of economic value, which they make

available to contributors and noncontributors alike. This

deﬁnition captures multiple instances, all joined by sim-

ilar principles, which are detailed in Table 1. For exam-

ple, all of the elements are present in an open source

software project, in Wikipedia, or in a user forum or

community. They can also be present in a commercial

website that is based on user-generated content. In all of

these instances of OC, anyone can contribute and any-

one can freely partake in the fruits of sharing, which

are produced by interacting participants who are loosely

coordinated.

Economic value is manifested by the substitution of

for-proﬁt services, such as commercial software, Ency-

clopædia Britannica, or technical consultants. Value is

also manifested by the content that open collabora-

tions create for ﬁrms such as Amazon or TripAdvisor.

This content affects other ﬁrms, such as book publish-

ers and hotel operators, whose fortunes grow or shrink

Table 1 Deﬁnitional Elements of Open Collaboration

Corresponding model

Elements Description manipulation Theoretical and empirical referents

Create goods of

economic value

The main purpose is the

creation of products

and services of

economic value.

The dependent variable is a

fundamental measure of

economic performance:

efﬁciency in turning inputs to

outputs.

Benkler (2002, 2006), Cooley (1909),

Shah (2005), von Hippel and

von Krogh (2003), von Krogh and

von Hippel (2003)

Open access to

contribute—and

consume

Participants can freely

contribute but also

consume, regardless of

their contribution.

Any agent can contribute or

seek others’ contributions

without exclusion.

Faraj and Johnson (2010), Kollock

(1999), Lakhani and von Hippel

(2003), Raymond (1999), von Krogh

and von Hippel (2003), Zeitlyn (2003)

Interaction and

exchange is centrala

Participants interact,

exchange, and reuse

each other’s work, all

while engaging in own

work.

Agents search and engage

others to transfer resources.

Anthony et al. (2009, p. 283), Benkler

(2004, p. 1110), Faraj and Johnson

(2010), Faraj et al. (2011), Häﬂiger

et al. (2008, p. 180), Jeppesen and

Lakhani (2010), von Krogh et al.

(2003)

Participants labor

purposefully yet

loosely coordinated

Coordination, structure,

and hierarchy are

emergent and less

speciﬁed than in other

organizational forms

(e.g., ﬁrms, cooperatives).

Agents have individualistic goals

for resources and coordinate

only when engaging in

exchange events. There is no

predeﬁned structure or

hierarchy.

Dahlander and O’Mahony (2011), Kuk

(2006), Lee and Cole (2003),

MacCormack et al. (2006), Mockus

et al. (2005), O’Mahony and Ferraro

(2007), Shah (2006), von Krogh et al.

(2003)

aSome open collaboration systems involve interaction and exchange toward a coordinated creation of an artifact (software code, ency-

clopedia article, etc.), but in others purposeful interaction and exchange are themselves the end goal. This is the case, for example, in

many user-to-user interactions described in prior work (Franke and von Hippel 2003; Lakhani and von Hippel 2003; von Hippel 2005a,

pp. 33–43; Wasko and Faraj 2005). Because interaction is a prerequisite to the creation of any open collaboration artifact, we see it as a

necessary element in the deﬁnition. The model can accommodate instances of open collaboration with or without a coordinated artifact.

It merely affects the interpretation of the performance measure: without an artifact, it is an aggregation of individual performance; with an

artifact, it is a measure of collective performance.

with online reviews (Chen and Xie 2008, Chevalier and

Mayzlin 2006, Mudambi and Schuff 2010, Scott and

Orlikowski 2012).

The deﬁnition also delineates what OC is not. It

excludes traditional ﬁrms (because of the lack of open

access or loose coordination) and markets where individ-

ual agents work independently (no open access and/or

no interaction). It also excludes primary groups (Cooley

1909) such as social clubs and some online communi-

ties, where the raison d’être is social interaction, not

innovation or production.

The Beneﬁts of Open Collaboration

OC provides unique beneﬁts to participants, ﬁrms, and

society. One beneﬁt is the ability to build on others’

work in a direct way, because contributors can directly

view the architecture of the product (Kumar et al. 2011,

MacCormack et al. 2006). In software, it means that

they can reuse code, economizing on skills, time, and

cost (Häﬂiger et al. 2008). Contributors can also interact

directly with others, many of them strangers, to share

and integrate knowledge and other resources. Such vast

exchange characterizes OC, whether in Wikipedia, an

Internet user forum, or a mailing list. However, unlike

in a traditional organization, here contributions come

Levine and Prietula: Open Collaboration for Innovation

from many casual participants, who give as much as

they wish, with no up-front commitment (Benkler 2002,

Jeppesen and Lakhani 2010). Such casual contributions

can lead to better products: in Wikipedia, the most reli-

able contributions are made not by the few prominent

writers but by the many who contributed only once

(Anthony et al. 2009, p. 283). Open source software has

been shown to be safer than pricier commercial alterna-

tives (Bambauer and Day 2011).

When ﬁrms engage with OC, they can reap Schum-

peterian (innovation) rents (Nelson and Winter 1982)

that stem not from their employees, a traditional source

of innovation, but from their users (Bonaccorsi et al.

2006, Chatterji and Fabrizio 2012, von Hippel 2005a,

West 2003). For instance, many Internet security prod-

ucts were improved by probing users, not the (some-

times dismayed) engineers who designed the products

(Bambauer and Day 2011).

The beneﬁts of engaging users in innovation are multi-

ple. Firms economize on research and development costs

by pooling or externalizing them (West and Gallagher

2006), enjoy higher customer satisfaction (Franke and

von Hippel 2003), and beneﬁt from more favorable

beliefs and greater trust from users (Dahlander and

Wallin 2006, Porter and Donthu 2008).

For society, OC can not only improve economic and

social welfare (Bambauer and Day 2011, Benkler 2004,

Maurer and Scotchmer 2006, Strandburg 2009) but also

heighten morality: “Foster virtue by creating a context

or a setting that is conducive to virtuous engagement and

practice” (Benkler and Nissenbaum 2006, p. 403).

Puzzles

OC offers many beneﬁts, impacts economically and

socially, but it is not well understood. Extant theories

of ﬁrm-based and market-based innovation are unﬁt-

ting. Although OC may complement ﬁrm-based and

market-based innovation, it differs greatly from them

(Baldwin and von Hippel 2011, Lee and Cole 2003,

von Hippel and von Krogh 2003). Differences can

be found in the motivation to participate, organiza-

tion, and governance (Dahlander and O’Mahony 2011,

Faraj et al. 2011, O’Mahony and Ferraro 2007, Shah

2006); product design and production (MacCormack

et al. 2006, Mockus et al. 2005); and market behavior

(Casadesus-Masanell and Ghemawat 2006, Economides

and Katsamakas 2006).

Because OC appears so different from other sources

of innovation, some pundits dismissed it as an oddity.

For instance, a prominent practitioner opined that open

source software “goes against the grain of everything

I know about the software ﬁeld”; therefore, “any change

[it fosters] will be limited to one or a few cults emerging

from a niche culture” (Glass 2000, pp. 104–105). Such a

view is not preposterous; it is not clear how OC survives,

let alone thrives. OC is not only voluntary and infor-

mal but also open. Fisheries, cooperatives, kibbutzim,

and research consortia can be voluntary and informal,

yet they are closed and their membership is bound and

stable (Ouchi 1980, p. 129). In all of them, participants

band to produce jointly, but those who share the beneﬁts

must share the costs (Cornes and Sandler 1986, p. 159).

In such arrangements, only contributors may consume

the fruits of cooperation, and they endeavor to deter free

riders. Free riding must be controlled, the thinking goes,

or it will unleash the tragedy of the commons, the the-

oretical expectation that shared property, such as pas-

tureland, will eventually vanish as self-interested users

abuse it (Hardin 1968, Olson 1965).

In contrast, OC operates with vague membership and

porous boundaries, where anyone can consume, contrib-

utor or not. As emphatically open as it is, OC is even

more puzzling than Hardin’s pastoral illustration. Unlike

in a pastureland, here a secure fence can be built and a

sign can be hung above the bolted gate: “Members only.”

Such exclusion of noncontributors is especially easy on

the Internet; it can be done simply by screening users

to allow contributors and block free riders. But in many

instances of OC, numerous users free ride. Even con-

tributors vary widely in their efforts. Empirical accounts

repeatedly show that few participants provide much of

the work, others contribute occasionally, and many oth-

ers contribute little or nothing (Anthony et al. 2009, Kuk

2006, Lancashire 2001, Lerner and Tirole 2005, Madey

et al. 2004, Mockus et al. 2005). But despite free rid-

ing and vastly unequal contributions, collaboration does

not collapse. The major contributors do not revolt. “Who

would ever have imagined that innovation could ﬂourish

under conditions like those?” wondered von Krogh and

von Hippel (2006, p. 975).

The performance of OC has been a puzzle for partici-

pants and scholars alike, and a variety of conjectures and

explanations have been proposed. An early participant

and observer, Raymond (1999) offered a long list of intu-

itive explanations to why participants contribute freely:

perhaps they develop for personal use, derive plea-

sure (“scratching a developer’s personal itch”; p. 23),

enhance their professional reputation, or engage in reci-

procity, referred to as “gift exchange.” Ghosh (1998),

another participant-cum-observer, seconded that OC may

be based on reciprocity, which he called “cooking pot

markets,” where participants simultaneously contribute

and consume others’ contribution. Ghosh ruminated

about other possible explanations, including a diversity

of needs and contributions, reputation, and the nonrival

nature of the goods.

Scholars have been more parsimonious. Some in-

stances of OC ﬁt with self-interest, it was suggested,

because an innovator can sometimes beneﬁt from

freely revealing an innovation. Revealing may be lucra-

tive thanks to complementarities and diffusion of the

Levine and Prietula: Open Collaboration for Innovation

innovation (e.g., Harhoff et al. 2003, Henkel 2006),

which can concur with private beneﬁts such as enhanced

professional prestige (Lerner and Tirole 2002), learning,

and pleasure (von Hippel and von Krogh 2003).

The theoretical model we present here, which focuses

on behavior, ﬁts with prior explanations. It incorpo-

rates them in a general way by referring to charac-

teristics of the interaction (e.g., reciprocal cooperation,

altruism), characteristics of the participants (e.g., diverse

needs), and characteristics of the goods (e.g., nonrival).

By focusing on behavior, it complements prior explana-

tions that turn on intentions and motivations, which are

more difﬁcult to ascertain than behavior. For instance,

cooperative behavior can stem from immediate private

gain, but it can also come from altruism or social move-

ment ideology (O’Mahony and Bechky 2008). More-

over, cooperation often emerges even without immediate

private gains, such as when contributions are unglam-

orous or even anonymous, such as when participants

respond to others’ questions in a user forum (Lakhani

and von Hippel 2003) or engage in mundane soft-

ware maintenance (Glass 2000), Wikipedia administra-

tion (Zittrain 2008, pp. 127–148), or illegal ﬁle sharing

(Levine 2001). Because the model focuses on behavior,

it can also account for contributions motivated by plea-

sure or “fun,” but it does not necessitate this explanation

(which can be tautological).

Next, we review some recent evidence on a central

element in the performance of OC: cooperation. The

performance of OC is also affected by two other ele-

ments: the diversity (heterogeneity) of participants and

their needs, and the rivalry of goods and resources. We

discuss these two elements in turn, followed by the

Table 2 Performance-Related Elements of Open Collaboration

Corresponding Theoretical and

Level of analysis Element Description model elements empirical referents

Individual Cooperativeness

(Study I)

Individuals can be typiﬁed by

their tendency to cooperate.

When individuals are

aggregated, the composition

of cooperative types

distinguishes one population

from another.

Agents are deﬁned as

cooperative types in terms

of likelihood to contribute.

Agent populations are

deﬁned by the distribution

of cooperative types in

them.

Kurzban and Houser (2005),

Lerner and Tirole (2005),

Mockus et al. (2005), Shah

(2006, p. 1005)

Group Diversity in needs

(Studies II and

III)

Participants can have similar or

diverse needs, which implies

that they differ on the

resources they seek.

A resource can be desired by

many or few.

Need heterogeneity, the

extent to which agents

have dissimilar needs and

therefore seek a different

resource, is varied from

homogeneity to

heterogeneity.

Anthony et al. (2009), Baldwin

et al. (2006), Jeppesen and

Lakhani (2010), von Hippel

(2005a, p. 33)

Goods Rivalry

(subtractability)

(Studies II and

III)

Goods differ in the extent to

which one’s consumption

affects another’s; e.g., a

perfectly rival good diminishes

completely when used or

contributed.

The extent to which a

resource is a rival good

varied from nonrival to

completely rival.

Baldwin and Clark (2006),

Cornes and Sandler

(1986), Hess and Ostrom

(2006), von Hippel and

von Krogh (2003)

model, which incorporates all three elements (detailed

in Table 2).

What Affects the Performance of Open Collaboration:

The Human Tendency to Cooperate

Cooperation is central for open collaboration, and it

often takes the form of reciprocity (i.e., “I contribute

because I beneﬁted from others’ contributions”). In an

early study, users who helped others with technical

advice were asked to complete the following sentence:

“I was motivated to answer because0 0 0 0” A variety of

motivations were reported, but the top three reasons were

similar. They all stressed reciprocity: “I help now so

I will be helped in the future,” “I have been helped

before [here]—so I reciprocate,” and “I have been helped

[elsewhere] before—so I reciprocate” (Lakhani and von

Hippel 2003, p. 937). Indeed, recent evidence suggests

that people generally cooperate and reciprocate even

without direct beneﬁts. Beneﬁting from others’ contri-

butions can trigger one’s contribution. We turn to review

the evidence accumulated in evolutionary biology, eco-

nomics, and psychology.

Early theoreticians presumed that, without safeguards,

cooperation would be displaced by free riding. The

prevalent presumption was that “every agent is actu-

ated only by self-interest” (Edgeworth 1881, p. 16).

When OC emerged, scholars sought to explain it as self-

interest. Participants must have some direct and imme-

diate beneﬁt from doing so, the thinking went, or else

they never would have contributed.

However, self-interest is common but not omnipresent.

Scholars, including economists, have long questioned

Levine and Prietula: Open Collaboration for Innovation

whether humans are truly deﬁned by narrow self-interest

(e.g., Dawes and Thaler 1988, Sen 1977). In recent

years, a more nuanced picture has emerged. Experiments

in the laboratory and the ﬁeld have demonstrated that

humans are willing to collaborate, bear costs, and defer

self-interest for the greater good. Reviews concluded that

humans are “super cooperators” (Nowak and Highﬁeld

2011) and “human altruism is a powerful force” (Fehr

and Fischbacher 2003, p. 785). Altruism and coopera-

tion are central to human existence and have been fun-

damental in our evolution, distinguishing humans from

other species (Alexander 1987). Cooperation can per-

sist without contracts or quid pro quo. As the early

accounts of open source hinted, cooperation can emerge

even without direct reciprocity, i.e., a future gain from

the beneﬁciary (Baker and Levine 2013, Fehr and

Fischbacher 2003).

Aiming to quantify the frequency and distribution of

cooperation and reciprocity, Kurzban and Houser (2005)

used an elaborate experimental design to study cooper-

ation between and within individuals. They found that

people are consistent in the extent of their cooperation

in different situations. People’s behavioral types are so

stable as to allow an accurate prediction: “A group’s

cooperative outcomes can be remarkably well predicted

if one knows its type composition” (Kurzban and Houser

2005, p. 1803). The general human population has been

estimated to consist of three cooperative types:

1. Cooperators (13% of the general population) con-

tribute to others at a cost to themselves, uninﬂuenced by

others’ contribution. This behavior resembles pure altru-

ism, one suggested cause of OC.

2. Reciprocators (63%) may contribute to others at a

cost to themselves, but only insomuch that others are

also contributing. Such behavior suggests reciprocity,

also suggested as a cause of OC.

3. Free riders (20%) contribute at a low rate, regard-

less of whether others contribute. Empirically, free rid-

ers (perhaps better called “easy riders”; see Cornes and

Sandler 1984) contribute signiﬁcantly less than others

(but usually more than nothing). This behavior ﬁts the

image of a narrowly self-interested individual.

The remaining 4% are too inconsistent to be categorized.

The ﬁndings have been replicated, for example, in

non-Western and ﬁeld settings (Ishii and Kurzban 2008,

Rustagi et al. 2010), leading a recent review to deter-

mine that “we now have a fairly clear picture about the

preference heterogeneity among participants and the pre-

ponderance of conditional cooperators [reciprocators]”

(Chaudhuri 2010, p. 77).

Reciprocators are of special importance, not only

because they are the largest group in the human

population (see also Fischbacher and Gächter 2010,

Fischbacher et al. 2001) but also because they match

the behavior of those around them. Whereas cooperators

and free riders behave predictably, reciprocators mimic

those around them. This alternating behavior introduces

a dynamic element in which past experiences affect cur-

rent behavior, leading to a virtuous or a vicious cycle:

If you beneﬁted from others’ contributions, you adjust

your behavior so that you beneﬁt others alike; if you

were exploited, you reduce contributions. Such virtuous

cycles are behind the popular concept of “pay it for-

ward” and the scientiﬁc notions of generalized exchange

(Baker and Levine 2013, Molm et al. 2007, Willer et al.

2012) and indirect reciprocity (Alexander 1987, Nowak

and Roch 2007, Nowak and Sigmund 1998). The spread

of cooperation has been documented empirically (Bolton

et al. 2005, Fowler and Christakis 2010, Weber and

Murnighan 2008).

What Affects the Performance of Open

Collaboration: Diversity and Rivalry

Cooperation is central to open collaboration. But we pro-

pose that two other elements also affect performance.

Diversity of Participants and Their Needs. OC par-

ticipants are diverse, empirical accounts show, and

differ in the resources they seek and goods they pro-

duce (e.g., Anthony et al. 2009, p. 283; Benkler 2004,

p. 1110; Jeppesen and Lakhani 2010; Madey et al.

2004). Researchers have documented the pattern across

a variety of products and services: people’s needs are

often homogeneous (for a review, see Franke et al. 2009;

von Hippel 2005a, pp. 33–43).

How diversity affects OC performance was of con-

siderable discussion. Some academics (Bonaccorsi and

Rossi 2003, p. 1244) and practitioners (Ghosh 1998)

argued that diversity supports OC. Higher heterogene-

ity of needs, they proposed, leads to better performance

(von Hippel 2005a, pp. 33–43). It appears plausible;

as Platt (1973) pointed out, the tragedy of the com-

mons occurs because too many individuals seek the same

good; the tragic outcome is caused by low need hetero-

geneity. When people seek a diversity of goods, the com-

mons can thrive. Not incidentally, need heterogeneity

is necessary for realizing gains from trade: exchange is

lucrative if people have nonoverlapping demands (Kemp

1987). Otherwise, why trade?

Although it seems plausible that need heterogeneity

increases performance, at least one study suggested the

opposite (Baldwin et al. 2006). It described users who

shared knowledge, modeled as a nonrival good, and

found that homogeneous user needs led to better perfor-

mance. Similar needs, it was argued, allow users to solve

a problem only once and share the solution, avoiding

duplicate efforts. In our experiment, we consider main

and interaction effects separately, so we can show how

these seemingly differing propositions about diversity

and performance are actually compatible.

Rivalry of Goods and Resources. A good is deﬁned

as nonrival if more consumption of it requires no addi-

tional cost (Cornes and Sandler 1986). People can simul-

taneously enjoy air and sunlight, watch television, and

Levine and Prietula: Open Collaboration for Innovation

listen to radio. Adding consumers does not add cost;

one’s enjoyment does not interfere with another’s. Few

goods are perfectly nonrival. Many goods that are non-

rival initially, such as road use, become less nonrival

(and more rival) as congestion creeps in (Leach 2004,

pp. 155–156).

To early observers, software was a pure nonrival good.

Once software was produced, the cost of sharing it

appeared minuscule, because a contributor could keep

the software while providing a perfect copy to some-

one else. Because one’s beneﬁt does not interfere with

another’s, “you never lose from letting your product

free,” exclaimed Ghosh (1998). Thus, nonrivalry became

central in the discussion of open source software, an

early instance of OC. Nonrivalry was frequently cited in

discussing and modeling of the phenomenon (Baldwin

et al. 2006; Harhoff et al. 2003, pp. 1759–1767). Some

scholars have argued that OC performs well because it

produces “antirival goods” (Weber 2004), which beneﬁt

those who share them.

But others have recognized that OC can involve goods

that are somewhat rival, even if just because contribu-

tions can require attention, time, and effort (Shah 2006,

p. 1005). If we consider that sharing may require an

effort, then even software may not be the pure nonrival

good it seems (Baldwin and Clark 2006, Marengo and

Pasquali 2010).

To accommodate a variety of goods and resources,

we refrain from modeling them as binary: entirely rival

or nonrival. Instead, we employ a continuous range

of rivalry. The results suggest that rivalry matters less

than expected. We ﬁnd that OC can perform even with

rival goods, let alone with goods that are nonrival or

“antirival.”

Modeling the Performance of

Open Collaboration

Computational models are a useful method to study

complex social and organizational phenomena (Burton

and Obel 2011, Davis et al. 2007, Harrison et al.

2007, Levine and Prietula 2012, Macy and Willer 2002,

Prietula et al. 1998) and were employed in some pivotal

studies in organizational theory (e.g., Cyert and March

1963, Levinthal and March 1981, Nelson and Winter

1982). By building an agent-based model, a form of

computational model, we heed Benkler’s (2002, p. 424)

call to study OC through “artiﬁcial life-type modeling,”

and we extend earlier models (Bonaccorsi and Rossi

2003, Madey et al. 2004). Agent-based models are par-

ticularly useful here because they excel in determin-

ing boundary conditions and explicating mechanisms

(Baldwin et al. 2006, Prietula 2011). Aspects such as

contagious behavior are difﬁcult to represent using tradi-

tional analytic models but are easily captured by agent-

based models. We use the agent-based model to conduct

computational experiments: varying elements and rules

while observing interactions and outcomes, unraveling

processes that are unobservable (or nonmanipulable) in

the ﬁeld or the laboratory.

To identify salient elements of OC, we reviewed

empirical accounts and studied theories in organizational

theory, economics, sociology, and psychology, many of

which we review above. We used these sources to decide

which elements should be modeled. We then constructed

the model: abstracting from human behavior, we phrased

rules to describe, parsimoniously and unambiguously,

how agents behave. We then conducted computational

experiments, varying conditions and observing agent

behavior and its outcomes.

The model involves a setting common in many OC

instances: a crowd of agents is working on somewhat

similar tasks. To accommodate a broad variety of phe-

nomena, we focus on behavior and assume little about

the source of the tasks or the agents’ motivation. The

tasks can be equally thought of as assigned by an admin-

istrator, emerging from intrinsic motivation, advancing

self-interested goals, or stemming from any other source.

We do not assume that the agents are particularly moti-

vated to share or help the collective. Rather, we cau-

tiously assume they work primarily on their personal

tasks. While pursuing its own tasks, an agent may be

willing to assist others by providing resources, but only

if asked and in extent commensurate with its cooper-

ative type (cooperator, reciprocator, or free rider). To

remain cautious, we do not assume organizational fea-

tures such as coordination, division of labor, or manage-

rial function.

The model is abstract and general. It applies in many

settings where agents can complete their tasks indepen-

dently but beneﬁt from cooperation, which allows them

to complete the tasks with fewer resources (i.e., quicker,

cheaper, with less individual expertise, etc.). The bene-

ﬁts of cooperation are captured in the measure of per-

formance, which can be thought of as the equivalent

of achieving an organizational goal or increasing col-

lective welfare. The model can represent a highly coor-

dinated effort to create a single artifact, such as in a

software project (e.g., O’Mahony and Ferraro 2007), but

it can also describe a crowd, where each pursues his

own needs, as in online communities or forums (Baldwin

et al. 2006, Faraj and Johnson 2010, Lakhani and von

Hippel 2003). The following overview of the model is

complemented by the electronic companion, which con-

tains a full description of the algorithm, assumptions,

parameters and values, and alternative performance mea-

sures. It also offers examples, a ﬂow chart, pseudocode,

sensitivity analyses, and a glossary.

The Model

Structure. The model consists of a population of 100

agents, each of which has a set of 100 personal tasks.

Levine and Prietula: Open Collaboration for Innovation

Each task requires different resources. One of the ele-

ments manipulated, Diversity, determines the extent to

which a given task requires speciﬁc (as opposed to fun-

gible) resources. The other, Rivalry, affects the cost that

an agent bears when cooperating. The tasks are inde-

pendent, so the agents work asynchronously. A task is

completed when an agent attains a sufﬁcient level of

a resource needed for a task. For instance, a resource

could be knowledge of a computer language and a task

could be the writing of a speciﬁc computer code. An

agent can access a resource in three ways: producing

the resource through work (the costliest option), receiv-

ing it from another, or already possessing the resource.

For instance, one can obtain knowledge about computer

programming (a resource) by learning-by-doing (self-

production), receiving help from a peer (cooperation), or

using knowledge gained previously (prior possession).

Dynamics. Each agent starts with a set of randomly

endowed resources and a set of randomly assigned tasks.

Each agent also has a cooperative type:

1. The model iterates over periods, where each can

represent any ﬁxed time length (e.g., hour, day, week).

In each period, each agent can work on its assigned tasks

and interact with other agents.

2. An agent ﬁrst attempts to complete its tasks by

using the resources it already possesses. But if it does not

have a needed resource, the agent (hereafter, “seeker”)

seeks it by looking for another that has the resource

(hereafter, a “source”). Because cooperation is cheaper

than self-production, a seeker economizes by obtaining

a resource from another. In searching for a source, the

seeker relies on a simple index that shows “who knows

what” (Levine and Prietula 2012), a representation of

transactive memory (Hollingshead 2001, Jarvenpaa and

Majchrzak 2008, Lewis et al. 2005, Wegner 1986).

3. If a potential source is found, the seeker requests

the resource it needs.

3.1. Whether and how much of the resource is pro-

vided is determined by the source’s cooperative type and

availability (see items 3.4 and 4 below), neither of which

the seeker knows beforehand.

3.2. An agent may provide to another any resource

it holds, regardless of whether the resource was obtained

through self-production, transfer, or prior possession.

Thus, although agents produce only for their own use,

never by request of another, they may transfer resources

created for own use.

3.3. If the source obliges, it bears a cost that is

proportional to the Rivalry of the resource it contributes.

The seeker can immediately use the contributed resource

for its tasks and provide it to others.

3.4. If the source does not oblige, the seeker con-

tinues searching until it either obtains the resource

or inquires all of the agents, whatever comes ﬁrst. If

unsuccessful, the seeker begins self-production of the

resource. During production, the agent is unavailable for

other tasks or requests.

4. When an agent completes all of its tasks, it be-

comes dormant but responds to requests. When all

agents complete their tasks, the run is complete.

Cooperation. Axiomatically, it is always cheaper to

achieve a resource through cooperation than through

self-production. Cooperation is desirable because the

beneﬁt to the beneﬁciary is greater than the cost to the

benefactor. Cooperation increases welfare because it is

a positive-sum, not a zero-sum, game. People cooperate

when it leads to an advantage; people do not cooperate

if they can achieve the same outcome by working alone

(Axelrod 1984, von Neumann and Morgenstern 1944).

For instance, Mark saves times by asking Rosemarie, a

colleague, for help with graphics software. If Mark could

have obtained the same knowledge quicker by reading

a manual, he would not have asked for help. Because

cooperation can economize on cost, people’s ability to

cooperate improves their collective performance. This

effect is captured in the deﬁnition of performance.

Performance. If OC is to serve as a general system of

innovation and production, the performance of the entire

population matters. Therefore, we do not measure the

performance of an individual agent but the cumulative

performance in using resources to complete tasks. Even-

tually, all tasks are completed, some through cooperation

(Tc) and some through self-production (Ts). We simply

deﬁne performance (P) in terms of the proportion con-

tributed through cooperation:

P=Tc/4Tc+Ts50

The divisor is determined by the number of agents and

the number of tasks allocated to each. In each run, the

agents complete 10,000 tasks, a quantity that constitutes

a ﬁxed goal. The dividend is a measure of input, and it

is sensitive to cooperation. Cooperation economizes on

inputs, because when an agent completes a task through

cooperation, assisted by another’s resources, it spends

less. Thus, when the dividend increases, it means that

a given outcome was achieved using fewer resources or

that the same resources have accomplished a greater out-

come. Because the divisor is ﬁxed, a greater dividend

means higher performance.

Performance here can be thought of as a measure

of productivity: how much in resources is required to

accomplish a goal. The higher the ratio is, the more efﬁ-

ciently (or cheaply, quickly, with less knowledge, etc.)

the tasks were completed. When interpreting the results,

higher performance always means higher productivity.

It matches common measures of economic productivity

and procedural rationality (Simon 1976). This measure

accounts for both outputs and inputs, so it allows com-

parison across conditions.

Levine and Prietula: Open Collaboration for Innovation

This measure of performance also accounts for the

potential drawbacks of cooperating (Levine and Prietula

2012). For example, when a seeker obtains a resource

from a source, the seeker saves time and effort, but the

source may suffer. When providing a resource that is rival

(to any extent), the source loses at least some of it. If the

source needs this resource in a future period, the source

must obtain it anew by seeking or producing it. This can

be a drag on collective performance. Another potential

drag is wasted effort: an agent can spend time searching

for a resource but ultimately fail to obtain it because it is

held by free riders who would not provide it.

Modeling the Elements that Shape Performance

Cooperative Types. A population can be composed of

cooperative types in varying ratios. Kurzban and Houser

(2005) estimated the prevalence of the three cooperative

types in the general population, but one can imagine sub-

populations with differing ratios, such as a handpicked

group of cooperators. To examine the effect on perfor-

mance, we vary the ratios of the three types.

When modeling cooperative types, we follow care-

fully the empirical ﬁndings. As in the studies on which

we rely, all agents may contribute but in varying quan-

tities. As these studies found, the amount of each con-

tribution is a combination of a base rate, determined

by the agent’s type, and some variation (Kurzban and

Houser 2005, pp. 1804–1805). When asked to provide a

resource, a Cooperator agent contributes with a base rate

that is at least half its own endowment. The exact pro-

portion is determined for each transfer by a draw from

a Gaussian distribution (=0075, =00125). When

faced with a similar request, a Free rider agent con-

tributes strictly below half of its own endowment. The

exact proportion is similarly determined by a draw from

a Gaussian distribution (=0010, =0005). Reciproca-

tor agents adjust their behavior to match the population

trend. The trend is determined by comparing the pop-

ulation contributions () in the prior two periods (p−1

and p−2). If the population contribution is decreasing

(p−1/p−2<1), then Reciprocators act as if they were

Free riders; if it is nondecreasing (p−1/p−2≥1), these

agents act as Cooperators. Reciprocator behavior is ran-

dom in the ﬁrst two periods, after which a trend is

established.

Resource-Need Heterogeneity 4Diversity5.We vary

the Need Heterogeneity of the population by varying

the tasks assigned to the agents thereby varying their

resource needs. An agent’s needs are determined by

the tasks assigned to it. Need Heterogeneity rises when

the agents in the population aim to complete different

tasks; it is maximal when all agents are assigned com-

pletely different tasks. Need Heterogeneity drops when

some agents seek to complete the same tasks; it is

minimal when all agents are assigned the same task. Ini-

tial resource levels are drawn from a random uniform

distribution (see Table EC1 in the electronic companion).

Rivalry. Recall that the model allows for a gamut of

rivalry, not just a binary state. Whenever an agent uses

a resource or contributes to another, the quantity of that

resource decreases according to its degree of rivalry. For

example, if a source contributes a nonrival resource, it

suffers no loss; but if it contributes a resource that is

50% rival, then the source’s stock of that resource is

halved.

Cautious Bias in Model. The model is based on cau-

tious assumptions. We likely underestimate performance

because we omit some mechanisms that enhance coop-

eration: knowledge of others’ cooperative tendencies

(Chaudhuri and Paichayontvijit 2006), participants sort-

ing themselves into collectives (“communities”) accord-

ing to types (Gächter and Thöni 2005, Page et al. 2005,

Shen and Monge 2011), communication between par-

ticipants (Dawes et al. 1977), punishment (Fehr and

Gächter 2000, Gächter et al. 2008, Robins and Beer

2001), shunning (Dreber et al. 2008), and ostracism

(Cinyabuguma et al. 2005). When it comes to rivalry,

we include resources that range from nonrival to com-

pletely rival. For caution, we do not include goods that

are “antirival” (Weber 2004). Also, performance is likely

underestimated because the model does not presume

performance-enhancing institutions such as administra-

tion, coordination, or division of labor. Each agent pro-

duces resources based on its tasks only.

Computational Studies and Results

We begin by investigating how performance is affected

by the composition of cooperative types in the popula-

tion (Study I). Next, we examine the performance con-

sequences of rivalry and need heterogeneity in several

populations (Study II). Finally, we study how perfor-

mance is affected by rivalry and need heterogeneity in

the most relevant environment: the general population

(Study III).

Study I: How Cooperation Affects the Performance

of Open Collaboration

Kurzban and Houser (2005) identiﬁed the distribution

of cooperative types in the general population. But,

as noted, the composition can be different in some

groups—or can be made different. For instance, leaders

can interview prospective participants to sieve cooper-

ators from the others (Gächter and Thöni 2005, Page

et al. 2005). They can expose free riders by facilitat-

ing communication (Dawes et al. 1977), tracking reputa-

tion, and enabling punishment (Fehr and Gächter 2000,

Levine and Prietula: Open Collaboration for Innovation

Gächter et al. 2008, Robins and Beer 2001) and shun-

ning (Dreber et al. 2008). All these can increase coop-

eration, but they come at a cost. If a leader screens

potential participants to admit cooperators, she must bear

costs: for example, conduct interviews, administer tests,

follow on referrals, review work (Baldwin 2008). Simi-

larly, if one tracks reputation or facilitates punishment to

expose free riders, one has to build suitable mechanisms.

Here, we explore questions about the optimal investment

in promoting cooperation: Are more cooperators always

better or is there a point of decreasing returns? How does

one decide how much to invest in bettering cooperation?

Because this experiment focuses on the effects of

cooperative types, other elements were held constant.

Rivalry was set to “none" by deﬁning all resources

as nonrival. Need Heterogeneity was set to "high" by

deﬁning all tasks as completely unique, thereby ensur-

ing that agents do not compete for resources. We

investigated 144 population compositions: the propor-

tion of Cooperators was varied between 12 points

(1%15%110%120%10001100%). The Cooperator pro-

portion was ﬁxed at each point, and the remainder of

the population was varied from all Reciprocators to all

Free riders in 12 steps (99%195%190%180%100010%).

In all of the studies, the number of replications was such

that we could detect absolute effect sizes at =0005 for

all main and interaction effects with power of at least

0.80 (Lenth 2001). In this study, we repeated the exper-

iment with 100 replications in each step for a total of

14,400 runs.

The results are plotted as performance means for each

level of Cooperators in the population (the solid line in

Figure 1 Mean Performance by Proportion of Cooperators in the Population (Solid Line) with 95% Conﬁdence Intervals

100

1 5 10 20 30 40 50 60 70 80 90 100

Cooperators in population (%)

Performance (%)

Cooperators: 5%

Reciprocators: 95%

Free riders: 0%

Cooperators: 5%

Reciprocators: 40%

Free riders: 40%

Cooperators: 5%

Reciprocators: 0%

Notes. Bars show the marginal improvement in performance. The callout shows the effect of Reciprocator and Free rider composition when

Cooperator proportion is ﬁxed at 5%. The star signiﬁes the ratio of cooperators in the general population (13%). Held constant were Rivalry

(none) and Need Heterogeneity (high).

Figure 1). An increase in Cooperators increases perfor-

mance. This (expected) main effect conﬁrms intuition

and supports the validity of the model.

Proposition 1A: Cooperators Improve Perfor-

mance. More Cooperators bring better performance

over a range of population compositions.

Although the performance plot is generally increas-

ing, there is a distinct concavity in the graph. The results

show that higher Cooperator proportion improves perfor-

mance but at a decreasing rate. Large gains occur at the

lowest levels of Cooperators, e.g., when the proportion

increases from 1% to 5% (see the bar graph in Figure 1).

Proposition 1B: The Beneﬁts of Cooperators

Are Diminishing. Increasing the proportion of Cooper-

ators has a diminishing marginal effect on performance.

Therefore, costly efforts to increase cooperation, such

as by screening participants or setting incentive schemes,

may be counterproductive. Efforts to increase cooper-

ation can backﬁre, reducing overall performance. The

optimum depends on the population composition and the

cost of increasing cooperation. For instance, the general

population, with its average of 13% Cooperators, can

reach a performance level of above 50%, whereas popu-

lations with vastly more cooperators show just an uptick

in performance; e.g., increasing cooperators from 60%

to 90% or even to 100% hardly affects performance.

Even if adding cooperators leads to diminishing bene-

ﬁts in performance, we ﬁnd that adding cooperators low-

ers variance in performance, as visible in the narrowing

conﬁdence intervals (see Figure 1).

Levine and Prietula: Open Collaboration for Innovation

Proposition 1C: Cooperators Reduce Variation.

More Cooperators reduce the effect of other types on

performance.

Cooperators beneﬁt performance by decreasing vari-

ation, thereby increasing predictability. To understand

the mechanism behind the stabilizing effect of coop-

erators, we tracked the change in performance as we

ﬁxed the proportion of Cooperators and varied the ratio

between Reciprocators and Free riders. This follow-up

experiment also serves as a sensitivity analysis: it tells

how the results are affected by shifts in the proportions

of the two other types. The detailed performance plot

(the callout in Figure 1) shows the effect as the popu-

lation composition changes from a majority of Recipro-

cators (decreasing from left to right) to a majority of

Free riders (increasing from left to right). Not surpris-

ingly, performance decreases with fewer Reciprocators

and more Free riders. However, the effect of Free riders

is nonlinear—when few, they hardly affect performance.

For instance, when the ratio of Free riders jumps from

0% to 40%, performance drops just by 3%. Only when

Free riders increase substantially does performance suf-

fer noticeably.

Proposition 1D: Free Rider Tipping Point. Perfor-

mance is hardly affected by Free riders until a threshold

is crossed, beyond which performance collapses.

The effect is driven by the change in the ratio of

free riders to reciprocators. Recall that reciprocators

are inﬂuenced by those around them. When cooper-

ators are numerous (toward the right side of the x

axis in Figure 1), reciprocators are shielded from the

inﬂuence of free riders. As a result, variation in per-

formance decreases. When cooperators are fewer (left

side of the xaxis) and reciprocators are more numer-

ous, a bigger chunk of the population is ready to

switch between cooperation and free riding. The ulti-

mate behavior of reciprocators is determined by the

group that they mimic: cooperators or free riders. As

the proportion of free riders grows, they are more likely

to serve as role models, thereby pushing reciprocators

toward lower contributions. This is a path-dependent,

self-reinforcing process (Sydow et al. 2009): as more

reciprocators behave similar to free riders, the popu-

lation’s overall level of contribution decreases, which

reinforces free riding. This process is inherent in social

traps (Platt 1973, Schelling 1978), and similar behavioral

contagion was shown in laboratory experiments (Bolton

et al. 2005, p. 1464; Fowler and Christakis 2010; Weber

and Murnighan 2008).

The accelerated process leads to the rapid decrease—

indeed, a collapse—in performance. How likely are such

collapses? We conducted analysis of tipping-point behav-

ior for the most susceptible populations: where coopera-

tors are a minority. We found that even with populations

that contain as little as 5% or even 1% Cooperators, far

less than in the general population, the tipping point is

extreme—it occurs only when Free riders exceed 70%

(details are in the electronic companion). When Coop-

erators are more numerous, the effect is much reduced.

Tipping-point behavior is altogether eliminated when

Cooperators are more than 20% of the population. In

sum, we ﬁnd that free riders matter little in many practi-

cal situations.

Reciprocators Substitute for Cooperators. The ﬁnd-

ings imply that reciprocators, the most widespread type,

can take the place of cooperators, the rarest type. Because

reciprocators are very common, leaders of open col-

laboration ventures will likely ﬁnd it easier to recruit

reciprocators rather than seek cooperators. For example,

reaching a performance level of 50% is easy at the 10%

Cooperator level but difﬁcult with just 5% Cooperators

(see Figure 1). However, even if an OC venture begins

with such a low level of cooperators, less than half of

the average level in the general population, it can still

reach 50% performance with a simple step—increasing

the ratio of Reciprocators (see the callout in Figure 1).

A group consisting of 5% Cooperators and 40% Recipro-

cators can achieve that level of performance. Because of

this substitution effect, equivalent levels of performance

can be achieved with a range of population compositions.

Some of these compositions are easier to obtain.

Study II: How Cooperation, Rivalry, and

Need Diversity Interact to Affect Performance

In Study I, we ﬁxed rivalry and need diversity (hetero-

geneity). Here, we complement it by examining how

cooperation interacts with these two elements to affect

performance. We study three populations:

1. Cooperator population, which is composed of 98%

Cooperators, 1% Reciprocators, and 1% Free riders.

2. Reciprocator population, composed of 1% Cooper-

ators, 98% Reciprocators, and 1% Free riders.

3. The general population, composed of 13% Coop-

erators, 63% Reciprocators, 20% Free riders, and 4%

inconsistent.

We examined performance by crossing each population

with low (0%) and high (100%) levels of Rivalry and

Need Heterogeneity. We conducted 100 simulation runs

for each combination for a total of 1,200 runs.

The most important ﬁnding is that the performance

impact of Rivalry and Need Heterogeneity is not simple.

Rather, the impact depends on population composition

(Proposition 2C). We also ﬁnd two main effects (Propo-

sitions 2A and 2B) that conﬁrm intuition and match prior

predictions, thereby validating the model.1

Proposition 2A: Rival Goods Hurt Performance.

The lower the rivalry (subtractability) of resources, the

better the performance.

Levine and Prietula: Open Collaboration for Innovation

Intuitively, rivalry adds a cost to transferring

resources. When contributing a rival resource, the source

suffers a reduction in the quantity it holds. If in a sub-

sequent period the source requires the resource it con-

tributed, it has to obtain it anew by production, which

is costly, or by seeking it from another, which may be

futile because of free riding. When resources are rival,

cooperators suffer and so does performance, but when

resources are nonrival, even massive free riding does not

affect availability or performance.

Proposition 2B: Diverse Needs Increase Perfor-

mance. The higher the heterogeneity in needs, the better

the performance.

Intuitively, when participant needs are diverse, com-

petition for resources is lower. Because participants

seek different resources, it is more likely that a needed

resource is held (unused) by another agent. Sharing

of resources is more frequent, gains from trade ensue,

and performance is higher. In contrast, when participant

needs are similar, sharing is still possible, but when a

source contributes a resource, it may need this resource

Figure 2 How Elements Interact to Affect Performance

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[

Notes. Panel (A) shows the main effect of Rivalry and its interaction with Need Heterogeneity over a combination of three populations:

cooperators, the general population, and reciprocators. Panel (B) shows the main effect of Need Heterogeneity and its interaction with

Rivalry over the same populations. Panel (C) shows the interactions between Rivalry,Need Heterogeneity, and population. Free rider

populations (not plotted) showed lower performance (<10% in all conditions; p < 00001).

∗∗A change in Rivalry leads to a statistically signiﬁcant difference in performance for this combination of population and heterogeneity

(p < 00001).

in a future round. So those who cooperate may endure

a constant search for resources, harming performance.

It may appear intuitive that diverse needs promote per-

formance, but, as we noted above, at least one study sug-

gested the opposite: performance beneﬁts from similar

needs as duplicate efforts are eliminated. As we probed

to understand the differing views, we found their source:

the performance consequences of Rivalry and Need Het-

erogeneity are dependent on the levels of each element—

and on the composition of the population.2

Proposition 2C: Rivalry, Need Heterogeneity,

and Cooperation Interact. The performance impact

of each of the three elements is partly dependent on the

other two.

Rivalry can hamper performance (Proposition 2A), but

not always. Performance is affected not only by rivalry

but also by the interaction of rivalry and need hetero-

geneity (Figure 2, panel (A)). For instance, when rivalry

increases from low to high, it can cause major harm or

just a dent in performance, depending on the level of need

heterogeneity. Similarly, need heterogeneity generally

improves performance (Proposition 2B), but its effect

Levine and Prietula: Open Collaboration for Innovation

depends on the level of rivalry. When rivalry is high, a

change in need heterogeneity has a vast effect on per-

formance, but when rivalry is low, a change in need

heterogeneity matters little (Figure 2, panel (B)).

These ﬁndings suggest that OC can perform well even

with rival goods. They also explain the differing pre-

dictions on the effect of high need heterogeneity: high

rivalry generally undermines performance, but the effect

is mitigated when high rivalry is combined with high

need diversity (see the +line in Figure 2, panel (A)).

On the other hand, because the performance impact of

need heterogeneity is similarly affected by rivalry (see

the ×line in Figure 2, panel (B)), then the combina-

tion of low rivalry and high heterogeneity (similar needs)

begets high performance.

The performance impact of either rivalry or hetero-

geneity also depends on the cooperative composition of

the population (Figure 2, panel (C)). With a Cooper-

ator population, which can be thought of as a group

of altruistic individuals, rivalry hardly affects perfor-

mance (see the “open circle” line in Figure 2, panel

(C)). Even in the general population, which lacks such

a concentration of cooperators, rivalry has just a mod-

erate impact (the “open triangle” line). Performance

drops sharply only when high rivalry coincides with

homogeneous needs (“solid circle,” “solid triangle,” and

“solid square” lines). Intuitively, performance suffers

because rivalry affects the cost of contribution. Need

heterogeneity affects the availability of sources. When

resources are rival and needs are similar, cooperating

agents bear a cost and may struggle to ﬁnd an unused

resource from another. In such an environment, even if

most participants are cooperators, the aggregate gains

from cooperation are small. However, even in such a

harsh environment, all three populations reach perfor-

mance levels of 20%–40%. In some situations, this may

sufﬁce.

Study III: Open Collaboration Performs Robustly in

the General Population

We now turn to a detailed investigation in a particularly

important environment—the general human population,

composed of 13% Cooperators, 63% Reciprocators, 20%

Free riders, and 4% inconsistent. In the prior study, we

examined just the extreme values of rivalry and need

heterogeneity. Here, we provide a more elaborate inves-

tigation, varying Rivalry and Need Heterogeneity from

0.0 to 1.0 in increments of 0.1 while observing the effect

on performance. Each combination ran 100 times, yield-

ing 12,100 runs.

By examining the interior values, not just the

extremes, we replicate the ﬁnding in Proposition 2C:

in the general population, neither element has a simple

effect on performance. Rather, the effect of each is partly

dependent on the value of the other elements.

Proposition 3A: In the General Population, Need

Heterogeneity and Rivalry Interact Nonlin-

early. The performance impact of need heterogeneity is

partly dependent on rivalry, and the performance impact

of rivalry is partly dependent on need heterogeneity.

This nonlinear relationship is evident, for example,

at the highest level of Need Heterogeneity. There, a

decrease in Rivalry does not lead to improvement in

performance (in Figure 3, trace edge from point 1

to 2). In contrast, at the lowest level of Need Hetero-

geneity, a similar decrease in Rivalry leads to a marked

improvement in performance, a rise that begins slowly

but then accelerates (trace edge from point 4 to 3).

And between these two extreme points, the performance

effect of change in Rivalry at a given level of Need Het-

erogeneity is nonlinear (compare some of the lines that

connect points on edge to edge ).

This nonlinear relationship is evident also in the

performance effects of Rivalry over levels of Need

Heterogeneity.3For instance, at the highest level of

Rivalry, an increase in Need Heterogeneity leads to an

increase in performance that is linear (edge in Fig-

ure 3). But at the lowest level of rivalry, a similar

increase in Need Heterogeneity brings no improvement

in performance (edge ). In between, the effect is some-

times linear, sometimes not. To see that, trace the lines

that connect any point in edge to edge : some are

linearly increasing, others are ﬂat.

In the general population, a change in the level of

either element brings a nonobvious impact on perfor-

mance. The combination of low Rivalry, assumed to

beneﬁt performance, and low Need Heterogeneity, often

assumed to harm it, generates high performance (point 3)

Figure 3 Performance of the General Population at Various

Combinations of Need Heterogeneity and Rivalry









Levine and Prietula: Open Collaboration for Innovation

at a level remarkably close to the supposedly ideal com-

bination of high Need Heterogeneity and low Rivalry

(point 2). As we saw earlier, when rivalry is low, changes

in need heterogeneity have little effect on performance.

Another counterintuitive result: the combination of

high Rivalry, assumed to harm performance, and high

Need Heterogeneity, generally assumed to beneﬁt it, gen-

erates performance that is on par with the other combi-

nations (point 1). Once again, only when high Rivalry

is combined with low Need Heterogeneity is perfor-

mance low (point 4). Hence, this leads to the following

proposition.

Proposition 3B: In the General Population, Ri-

valry and Need Heterogeneity Compensate for

Each Other. When one element undermines perfor-

mance, the other can compensate.

To grasp the underlying mechanisms, consider the fol-

lowing scenarios. As we noted above, when Rivalry is

high and Need Heterogeneity is low (point 4), cooper-

ation is costly and search is often futile. Those who

cooperate can be depleted of resources and fail to obtain

them from others, and so they must turn to costly self-

production. In such an environment, cooperation brings

puny gains. For OC, such an environment may be the

harshest.

From that low point, an increase in the diversity of

needs (in Figure 3, follow edge from point 4 toward 1)

leads to a performance boost. As Need Heterogeneity

increases, contributions are more likely to boost per-

formance because agents are not seeking identical

resources. Sources are less likely to discover (belatedly)

that a resource they have contributed is needed for their

own tasks. Even as high Rivalry makes each contribu-

tion costlier, gains from collaboration increase perfor-

mance. Thus, performance is so high that decreasing

Rivalry does not improve it much (follow edge toward

point 2). Performance level at the extreme (point 1),

where maximum Rivalry meets high Need Heterogene-

ity, represents some instances of OC in the physi-

cal world, such as Freecycle, where participants share

rival goods, including furniture, clothes, computers, and

ofﬁce supplies (Willer et al. 2012). Sharing rival goods

may appear improbable, but when participant needs are

diverse, performance is so high that decreasing Rivalry

improves it little (follow edge toward point 2).

Another way to increase performance is by reducing

rivalry. As Rivalry decreases, the cost of contribution

decreases too, even with need homogeneity (in Figure 3,

follow edge from point 4). When Rivalry approaches

zero (point 3) and needs are homogeneous, few

contributors sufﬁce to provide the needs of a large

population. At this point, even if Need Heterogeneity

increases, it has little consequence because performance

is already very high (follow edge ). Performance at the

extreme (point 3), where needs are homogeneous and

rivalry is low, is similar to the sharing of design ideas

by user-innovators. There, performance beneﬁts because

a single good design can be shared cheaply and beneﬁt

a multitude (Baldwin et al. 2006).

There are a few practical implications here. When a

leader faces a combination of high rivalry and low need

heterogeneity (similar participant needs), she should

remember that rivalry decreases performance dramat-

ically once it passes an inﬂection point (see along

edge ). If the leader attempts to reduce high rivalry,

she will see modest performance gains. A bigger boost

in performance will come from increasing need hetero-

geneity, because its relationship to performance is linear.

On the other hand, if rivalry is low, an increase will lead

to a substantial drop in performance.

Discussion and Next Steps

Open collaboration is a growing source of innovation

and production, perhaps a new organizational form. It

embodies uncommon combinations: goal-oriented yet

loosely coordinated participants who cooperate volun-

tarily to create freely distributed products and services,

creating an economic impact. Innovators, scientists, and

jurists have described the beneﬁts of openness and urged

support for it (Benkler 2011, Henkel and Maurer 2009,

Lessig 2005, Madison et al. 2010, von Hippel 2005a,

Zittrain 2008). Yet, despite the economic and social

impact of OC, its principles are vague and its perfor-

mance remains a puzzle.

As much as scholars have done for ﬁrms, we aim

to identify some principles of operation and determi-

nants of performance for open collaboration, whether a

software venture, ﬁle sharing collective, or an advice

forum. The model, structured as a typical scientiﬁc the-

ory, is akin to other theories of performance (Merton

1967, Sutton and Staw 1995). We begin with micropro-

cesses of individual behavior and proceed to identify

underlying principles, elements that affect performance,

and connections among them. We then focus on the per-

formance of the entire system of innovation or produc-

tion. The theory is phrased as a formal model of human

behavior (DiMaggio 1995), which speciﬁes processes

and uses an agent-based model to generate distributions

of outcomes. A robust theory should also possess pre-

dictive power (Popper 1959, 1963), being able to fore-

tell, for instance, what kinds of goods can be produced

efﬁciently in open collaboration or where it is likely to

complete with ﬁrms. This is what we aim to achieve. The

theory, expressed in the model, marries prior accounts

of OC with recent evidence on human cooperation. We

investigate the performance impact of variations in coop-

eration, rivalry, and need heterogeneity. We show that

OC is a robust engine for innovation and production, one

that performs well even in unfavorable environments.

Levine and Prietula: Open Collaboration for Innovation

The model shows some main effects that serve to val-

idate it and supports assertions made by others: coopera-

tors improve performance (Proposition 1A), rival goods

hurt it (Proposition 2A), and need diversity helps (Propo-

sition 2B). But the model uncovers some novel effects.

First, as cooperators increase, the beneﬁts they bring

taper off (Proposition 1B). Thus, OC can thrive even if

cooperators are just a sliver of the population. Because

a majority of altruists is not essential, OC can prosper

beyond the realm of those who are naturally inclined to

cooperate, such as hobbyists and hackers. The need core

of cooperators can be found even in a random sample of

the general population.

A majority of cooperators is not essential for high

performance, but they aid by reducing variance (Propo-

sition 1C). When reliable performance is needed, as in

industrial production, many cooperators are beneﬁcial.

The two propositions can assist in leaders in designing

and organizing OC ventures. Based on the speciﬁc of

the initiatives, a leader can contemplate the beneﬁts and

costs of recruiting cooperators.

As much as assumptions about cooperators can be

relaxed, so are assumptions about free riders. We expand

prior arguments (Baldwin 2008, Baldwin and Clark

2006) by showing that free riders matter little, even

when goods are rival. Because they do little harm, efforts

to sieve free riders seem inefﬁcient. Now we can under-

stand why many OC ventures appear so unconcerned

with free riders.

When we model the role of rivalry and need het-

erogeneity in performance, we ﬁnd that these elements

interact with each other and with the population. The

performance impact of rivalry and need heterogeneity

varies with the composition of cooperative types in a

population (Proposition 2C). The interaction suggests

again that OC can thrive even when goods are rival.

The impact of rivalry on performance is not simple but

depends on the cooperative composition and need het-

erogeneity in the population. The needs of users are

often diverse, prior research has found. Thus, OC may

perform well in the general population. In this environ-

ment, performance is stable even if rivalry increases (see

general population in Figure 1 and follow edge in Fig-

ure 2). Currently, OC may appear restricted to nonrival

goods, but we propose that it can expand into rival ones.

Further guidance to leaders of OC comes from the

third experiment, simulating the general population.

Need heterogeneity and rivalry interact to create a com-

plex effect on performance (Proposition 3A), so changes

to either one will have a varying impact on performance.

Leaders should tread carefully because changes can be

costly: if a leader attempts to increase performance

by reducing rivalry, for instance, he has to ﬁnd ways

to abate congestion or reduce contribution cost. But

because the effect of rivalry reduction is not obvious,

he should be aware of the trade-off before acting. Fur-

thermore, performance can be improved without reduc-

ing rivalry or altering need heterogeneity, because either

one can compensate for the other (Proposition 3B). High

performance is possible with high rivalry if the needs

are heterogeneous. And OC can perform well with low

need heterogeneity, depending on the level of rivalry. In

sum, open collaboration can emerge in more places than

currently observed.

The ﬁndings serve to explain bafﬂing prior ﬁnd-

ings, such as the skewed contributions to OC. It is

not a defect, as some observers suspected. The general

population features a handful of people who contribute

unconditionally (cooperators) and two larger groups that

contribute conditionally (reciprocators) or little (free rid-

ers). Disparities in contributions can be expected. The

core of cooperators serves as a “critical mass” (Wasko

and Faraj 2005, p. 52): it sparks contributions from

reciprocators, the largest group. It may be why, when

surveyed or observed, contributors explain their contri-

butions not as paying back to a speciﬁc individual, but

rather speak of a generalized reciprocity (Ekeh 1974,

Yamagishi and Kiyonari 2000). As we noted, in their

survey of helpful users, Lakhani and von Hippel (2003,

p. 937) found that many of them generalized reciprocity

as a motivation: “I have been helped before [in these

user forums] 000so I reciprocate” (also see Bagozzi and

Dholakia 2006; Wasko and Faraj 2005, p. 51).

Limitations and Extensions

To build the model, we made assumptions about coop-

eration, search, modularity, diversity, and performance.

Some of the assumptions are consciously cautious, lead-

ing to a likely underestimation of performance (as

detailed in the Cautious Bias in Model section). Others

are merely realistic, based on accounts of open collab-

oration in the literature. Some assumptions are oppor-

tunities for extensions. The ﬁndings on cooperation, on

which the model relies, assume that a participant has

information about the contribution trend in the popula-

tion. This is true in many cases, such as when a par-

ticipant observes the growth of a Wikipedia entry, the

multiplying lines of codes in a software project, or the

growing pool of shared ﬁles. If a user has only partial

information on others’ contributions, performance may

suffer (Levati et al. 2009). The model requires a simple

index of “who knows what,” akin to transactive mem-

ory, to facilitate search. Such an index often emerges

naturally in the minds of participants (Wegner 1986).

It can also be set up easily in the form of a computer

system (Jarvenpaa and Majchrzak 2008), but without

it, performance will suffer (Levine and Prietula 2012).

When it comes to diversity, resource-need heterogene-

ity is one form of diversity that has been hypothesized

to affect performance (Baldwin et al. 2006; von Hippel

2005a, pp. 33–43). Inclusion of other forms of diversity,

Levine and Prietula: Open Collaboration for Innovation

such as skill (Hong and Page 2004) or network struc-

ture (Santos et al. 2008), may be a useful extension. In

the model, performance is deﬁned as substantive ratio-

nality (Simon 1976, pp. 130–131; Weber 1947, pp. 184–

186): efﬁciency in turning inputs to outputs through

collaboration. Procedural performance measures, such

as how correct or neutral Wikipedia is (Giles 2005,

Greenstein and Zhu 2012), are complementary. Finally,

the model excludes, by design, some elements of open

source that received empirical description elsewhere,

such as recruiting, administration, and governance (e.g.,

Dahlander and O’Mahony 2011, O’Mahony and Bechky

2008, O’Mahony and Ferraro 2007).

Open collaboration is an exemplar of human coop-

eration: people, often strangers, working in concert to

achieve speciﬁc goals, even without direct beneﬁts. The-

oreticians regard such ventures as the toughest test

of human cooperation: “The problem of transient and

anonymous exchange is not only a matter of consider-

able practical interest; it is also one of the most theo-

retically compelling social traps” (Macy and Skvoretz

1998, p. 639). Our investigation suggests that com-

mon assumptions about barriers to cooperation are too

gloomy. Some were surprised that OC could thrive on

the Internet, which is devoid of “the social signaling,

cues, and relationships that tend toward moderation in

the absence of law” (Zittrain 2008, p. 130; also see

von Krogh and von Hippel 2003). Here, we show that

open collaboration can thrive without close personal

relationships. Furthermore, it can scale up, countering

predictions that cooperation would break down in larger

groups (e.g., Olson 1965, Raub 1988).

Writing in Science, Vollan and Ostrom (2010, p. 924)

called for more research to explain variation in human

cooperation. We can advance “a behavioral theory of

human action,” they wrote, by “[u]sing multiple methods

to identify the relevant ‘microsituational’ and broader

contextual variables” and linking them to “differences in

behavior and real-world outcomes.” For such investiga-

tions, we suggest, open collaborations can be natural lab-

oratories for ﬁeld studies and experiments. For instance,

researchers utilized Wikipedia to show how group size

is directly related to voluntary contributions (Zhang and

Zhu 2011).

Where can open collaboration thrive? For the perfor-

mance of open collaboration, hard-to-ﬁnd cooperators

are not all important, and free riders will not necessar-

ily doom performance. Open collaboration can withstand

both rivalry and a lack of diversity in needs. It will per-

form surprisingly well even with a bunch of ordinary

people. It can thrive far and wide, we suggest.

Supplemental Material

Supplemental material to this paper is available at http://dx.doi

.org/10.1287/orsc.2013.0872.

Acknowledgments

The authors are thankful to Carliss Baldwin, Gregory

Berns, Ramon Casadesus-Masanell, Eric von Hippel, Lars Bo

Jeppesen, Chengwei Liu, and Sarah M. G. Otner for their

comments. The authors also thank Ian Lim for his research

support. The authors acknowledge the comments received at

the following conferences: American Sociological Associa-

tion 2006 in Montréal; Academy of Management 2008 in

Anaheim, California; User and Open Innovation workshop

2009 in Hamburg; Mid-Atlantic Strategy Colloquium 2010 at

the University of Maryland; Open Source Software 2010 in

Notre Dame, Indiana; Israel Strategy Conference 2010 at the

Technion; Society for the Advancement of Socio-Economics

2012 in Cambridge; and Academy of Management 2012 in

Boston. The ﬁrst author thanks the Sloan School of Manage-

ment of the Massachusetts Institute of Technology, where the

manuscript was written. The second author acknowledges a

Summer Research grant from the Goizueta Business School,

Emory University; discussions at the Human Social, Culture

and Behavior Modeling Program meetings of the Ofﬁce of

Naval Research; and a grant from the Air Force Ofﬁce of Sci-

entiﬁc Research through the Ofﬁce of Naval Research [Grant

N000140910912].

Endnotes

1The overall main effects for Rivalry and Need Heterogene-

ity were F 411115845=211561 (p < 00001) and F 411115845=

4171102 (p < 00001), respectively. The interaction was

F 411115845=91289 (p < 00001), and a post hoc Tukey analy-

sis indicated that all means differed signiﬁcantly (p < 00001).

2Rivalry by Need Heterogeneity by Cooperative Types interac-

tion: (F 431115845=1149104, p < 00001).

3A linear model is not a perfect ﬁt for either effect, although

it ﬁts Need Heterogeneity over Rivalry values better (r2=

00618) than it ﬁts Rivalry over Need Heterogeneity values

(r2=00149). Nonlinear regression ﬁtting Rivalry over Need

Heterogeneity also had a poor ﬁt (second-order polynomial,

r2=0005; third-order polynomial, r2=0001).

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Open Collaboration for Innovation: Principles and Performance

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