Networks of Tinkerers:a model of open-source technology innovation

Peter B. MeyerU.S. Bureau of Labor Statistics

meyer.peter@bls.gov∗

Preliminary draft, May 2006for session 19 at the

2006 International Economic History Association conference, Helsinki

Abstract

Technologies such as airplanes, personal computers, and open-source soft-ware programs have been developed by networks of hobbyists, not firms orother formal organizations. This paper models individuals who develop atechnology. In the model, agents called “tinkerers” have an exogenous inter-est in improving a technology according to their own criteria, and do not seea way to profit from it. Under these conditions, tinkerers prefer to make anopen-source technology agreement than to work alone. The members of theagreement form an information network with economies of scale. pecialistsin the group may devote their energies to expanding or managing it ratherthan working on the technology itself. Endogenously there are incentives tostandardize on designs and descriptions of the technology, and to specializein a particular aspect. A tinkerer in the network who sees how to produce asufficiently profitable product may create a startup firm and choose to exitthe network. Thus, industries can arise from avocations, as has happened inthe aircraft, personal computer, and open-source software cases.

∗With thanks to Harley Frazis, Tomonori Ishikawa, Anastasiya Osborne, Leo Sveikauskas, CindyZoghi, and participants at seminars at BLS. Opinions expressed in this paper may be those of theauthor but do not represent official views or policies of the U.S. Bureau of Labor Statistics.

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1 Introduction

Some important technologies have been advanced by processes of open sharingamong innovators who did not seem to be motivated by prospective profits. Forexample, many hobbyists around the world tried to make aircraft in the late 1800s,before there were what we now call airplanes. Personal computers were advancedgreatly by hobbyists who met in groups, notably at the Homebrew Computer Club,as discussed in [9] and Freiberger and Swaine (1984). Now there are many open-source software projects in which the source code of recent versions is made publiclyavailable, usually on the Web. The airplane, personal computer, and open-sourcesoftware cases are treated here as three instances of “open source” technology de-velopment processes.

There is a related academic literature on collective invention. Allen (1983) usedthis term to describe the sharing of information among iron blast furnaces in north-ern Britain in the late 1800s. Schrader (1991), Nuvolari (2002), and von Hippel(2005) offer other examples. Harhoff, Henkel, and von Hippel (2003) have modeledthis phenomenon. The technologies in these cases are known to deliver useful out-puts, and most of the enterprises exchanging information are fundamentally profit-minded. This is assumed in the models. The discussion about collective inventiondoes not describe a case where a substantially novel technology appears because ofcollective research by people who are not organized into profit-minded organizations.

The purpose of this paper is to show an abstract, deductive model of that moreextreme phenomenon, open source technology development. deductive, abstractmodel. Three key assumptions seem to be necessary. First, it is assumed that thatthe technology developers, or tinkerers, are exogenously interested in advancingthe technology for one of a variety of reasons. Second, it is assumed that theyhave some way to do it that is effective, from their own subjective point of view.Third, it is assumed that there is great technological uncertainty, so that the playerscannot identify a specific deliverable product for which there are likely customers.When these conditions hold, tinkerers sharing their findings would form a tinkerer’snetwork, which supports open-source technology development.

In the model it is possible to experiment with the effect of various environmentsand policies on the rate at which this process generates innovations. In the model,a new industry can appear when tinkerers see a way through the technologicaluncertainty and identify a new product and customers for it. Such industries wouldnot arise in contexts where networks of tinkerers were discouraged.

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2 Examples

The model is meant to fit these three cases, which have affected output andproductivity on a large scale.

2.1 Before the airplane

An international network of discussion about wings and aircraft existed fordecades before there were commercial airplanes. By the 1870s there were jour-nals in France and Britain on the topic, and by the 1890s there were also journalsin Germany and the U.S.

Octave Chanute corresponded with many of them and can be thought of asan important node of the information network. His 1894 book Progress in FlyingMachines summarized and evaluated much previous experimentation and expressedoptimism about the future of flying machines. This important book laid plain thestate of research in this proto-aircraft field of research. Chanute referred to over 180experimenters in a dozen countries (Meyer, 2006).

The book itself expanded the network of interested participants by making iteasier to catch up on the existing research for new experimenters like the brothersWilbur and Orville Wright. Chanute personally corresponded with many of theresearchers, including the Wright brothers.

Chanute regularly put aircraft builders in touch with one another. He was in-spired by the idea that by communicating and cooperating, experimenters aroundthe world would make success possible. Describing Chanute’s speeches and writ-ings, Stoff (1997, p. iv) wrote that they were “noteworthy for fostering a spirit ofcooperation and encouraging a free exchange of ideas among the world’s leadingaeronautical experimenters.”

Wilbur and Orville learned from the other experimenters and contributed backto them. They corresponded with Chanute many times, and he visited them andsent colleagues to help and participate in their effort.

2.2 The beginning of personal computers

There were many hobbyist clubs in the 1970s working on personal computers. Akey one was the Homebrew Computer Club which met in Menlo Park and Palo Alto,California, starting in March, 1975. Apple Computer and twenty other companiesspun off from members of this club. But most of the members did not join becausethey intended to start companies. Most were interested in making computers forhome. At the first meeting, “it turned out that six of the thirty-two had built their

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own computer system of some sort, while several others had ordered Altairs.” (Levy,2001, p. 202) Altairs were the best available kit for making a hobbyist computer.

“The group had no official membership, no dues, and was open to everyone.The newsletter, offered free . . . became a pointer to information sources and a linkbetween hobbyists.” (Freiberger and Swaine, 1984, p. 106) “They discussed whatthey wanted in a club, and the words people used most were ‘cooperation’ and‘sharing’.” (Levy, p. 202). Homebrew meetings included a presentation, often ofa demonstration of a club member’s latest home creation. Then there was “theRandom Access session, in which everyone scrambled around the auditorium tomeet those they felt had interest in common with them. It worked brilliantly,and numerous companies were formed. A remarkable amount of information wasexchanged at those meetings, and much information had to be exchanged; theywere all in unfamiliar territory.” (Freiberger and Swaine, 1984, p. 106) Memberswere drawn to the hands-on experience of making computers and understanding thecomponent parts. Few focused on the theory of computing, or the social effects ofcomputing.

Steve Wozniak demonstracted a new computer on a board at a Homebrew meet-ing. He did not intend to start a company or sell anything, but his more en-trepreneurial friend Steve Jobs convinced him to go into business together. Theycalled their computer the Apple I, and quickly their computer was in great demand,although only a computer hobbyist could even make use of it.

The Homebrew club was a network of tinkerers, in the language of the model.Its members had informational links to one another by being in the same room,using similar parts, attempting similar projects, and reading the same newslettersand magazines. I have interviewed two of its attendees and asked them why theywent. It was because of their interest in computers, not industry.

The Homebrew club is an useful illustration of many kinds of networks thatexisted starting in 1975 and which helped personal computers along. There wereother similar clubs around the U.S. There was a series of West Coast ComputerFaires. There were bulletin board personal computer systems to which people coulddial in and send email, and discussions on Usenet, which ran on the Internet.

2.3 Open source software projects

Open source software projects have been started by individuals with many dif-ferent interests. The operating system Linux, for example, was started, sponsored,and organized by a student, Linus Torvalds. Now it is a core product of an in-dustry. Many other projects also have this form. The Web itself was invented byTim Berners-Lee who intended to make collaboration easier, not mainly to start anindustry. Many open source software projects have an explicit copyright agreement

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to keep the core technology in the public domain.

In such a project the human-readable source code files are published on a com-puter network. Source code files, usually written in a standard computer language,are given to specialized development tool programs, such as compilers, assemblers,interpreters, and linkers, which generate the machine-readable executable program.

Sharing the source code is useful insofar as it makes possible ongoing improve-ments by many programmers. Users may alter the program for their specific pur-poses. Sponsors of open source projects usually copyright the software in such away that other developers cannot copyright programs using the open source code.This is a powerful mechanism to support collective invention because it is commonknowledge that some later improvements will become part of the shared code.

The moderators of changes in a chunk of source code, also called its owners,determine the final choices in released versions of the software. Users may makea version different from a released one. One criterion of a moderator’s success iswhether the moderator can avoid the project’s source code “forking” into perma-nently divergent, partly-incompatible versions. If that happens, the mutual benefitsof having one standard which improves over time are partly lost.

Several roles and institutions support technology sharing in open source projects:

• Web servers store the source code.

• Intellectual property issues are confronted explicitly by special copyrights.

• The relevant programmers have similar development tools and skills.

• Source control programs keep records of who changed the software and how.

• Moderators control which of those changes stay in the source code.

• Culturally, experimentation is welcome.

• Developers are not scheduled or otherwise restricted from experimenting.

2.4 Conclusions from the examples

One conclusion from these examples is that it is difficult to define in output orengineering terms what the tinkerers, hobbyists, or hackers are accomplishing in theshort run. In the model to come, progress is therefore defined by the individual’sown satisfaction with it, that is, in utility terms. Now we move on to an abstractmodel.

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3 The tinkerer

There is an object, activity, or technology A which the tinkerer owns exclusively.He enjoys A and may also envision a future stream of honors and profits derivingfrom it. It brings in no honors or profits today and any future honors or profits areunlikely and uncertain. A does not depreciate, and it has little market value, farless than what it is worth to the tinkerer.

The notation A is inspired by the examples of hobbyists who developed novelaircraft before what we now call airplanes were invented. To match the other ex-amples, A could represent a project of building a computer, or a computer programthe tinkerer can change.

The tinkerer receives a flow of positive utility from the existence or discussion ofA. The tinkerer is risk-neutral, and values alternative choices according to the netpresent value of expected utility at time t = 0 in this equation:

U =∞∑

t=0

βtat (1)

where at is a positive scalar utility expected from A in each discrete time periodt. β is a discount factor between zero and one applied to utility anticipated in futureperiods. Future at are equal to a0 unless A changes or circumstances change.

The tinkerer can choose to invest in (“tinker with”) A in order to raise futurebenefits at. The choice is binary at each t. The investment costs one utility unitin the present period for the effort, expenses, and the opportunity costs of thetime. The agent believes that tinkering will raise his future utility by p units eachtime period in the future. The notation p stands for a rate of progress, which issubjectively experienced by the agent. We assume p is greater than zero, fixed, andknown to the agent.

A tinkerer chooses whether to tinker based on estimated costs and benefits. Thegross utility benefits from one effort to tinker have a value of p in each subsequentperiod. The total gross benefits of tinkering in the present period are, by a standardseries summation formula:

pβ + pβ2 + pβ3 + pβ4 + . . . =pβ

1− β

The investment to achieve this was one utility unit at time zero. So, the netpayoff to tinkering in period zero is pβ

1−β− 1. The benefits exceed this cost if that is

greater than zero, which it is if:

p >1− β

β(2)

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For example, for a tinkerer who perceives β = 0.95 and p = 0.07, tinkeringincreases expected utility.

The optimal choice about whether to tinker is not a function of the level of at

at the time of the choice, as long as it was positive. So if a0 > 0 and p > 1−ββ

, thisagent will tinker in every period, and each at+1 = at + p. Call this character theclassic tinkerer.

For a tinkerer who tinkers in every period, the value of a future at will beat = a0 + pt, producing a payoff stream of:

Ut=0 =∞∑

t=0

βt(at − 1)

=∞∑

t=0

βt(a0 + pt− 1)

= (a0 − 1)∞∑

t=0

βt + p∞∑

t=0

βtt

=a0 − 1

1− β+ p

∞∑t=0

βtt

In the last term,

∞∑t=0

βtt = β + 2β2 + 3β3 + · · ·

=(β + β2 + β3 + · · ·

)+

(β2 + β3 + β4 + · · ·

)+

(β3 + β4 + β5 + · · ·

)+ · · ·

=β

1− β+ β

β

1− β+ β2 β

1− β+ β3 β

1− β+ · · ·

=β

1− β

(1 + β + β2 + β3 + · · ·

)=

β

1− β

(1

1− β

)=

β

(1− β)2

So, expected utility at time 0 is:

EUt=0 =a0 − 1

1− β+

pβ

(1− β)2

=a0

1− β− 1

1− β+

pβ

(1− β)2(3)

The first term of equation 3 is the present value of the expected utility frompossessing A in its original state. The second term has the present value of the

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costs of endless tinkering. The third term has the present value of the benefits ofendless tinkering.

The earlier condition that p > 1−ββ

has the same meaning in every period—atinkerer who finds it worthwhile to tinker once will find it worthwhile to tinker inevery period if the external conditions remain unchanged. Whereas if p = 1−β

β, the

costs equal the benefits, and if p < 1−ββ

, the costs exceed the benefits. For β = 0.95and p = 0.07, the second term is:

pβ − (1− β)

(1− β)2=

0.07(0.95)− 0.05

(0.05)2=

0.0665− 0.05

0.0025=

0.0165

0.0025= 6.6

So, for these parameters, endless tinkering raises the tinkerer’s present value utilityby 6.6 times the cost of a one-time investment.

4 The network of tinkerers

In order to get quickly to the main proposition, we make extreme, simple, andunrealistic assumptions here, and show the key proposition in equation (4). Mostof them can be weakened. Later sections discuss some more complicated and morerealistic assumptions.

Let there be two tinkerers with identical utility functions working on similarprojects A1 and A2 whose innovative tinkerings could be useful to one another. Leteach one believe that the other has no way to profit from the project using theexisting technology or any likely foreseeable technology. Let the subjective rate ofprogress of the first player be p1, and the subjective rate of progress of player twobe p2. Let some fraction f ∈ (0, 1) of player two’s innovations be useful to playerone’s project, and the same fraction of player one’s innovations are useful to playertwo.

Suppose the two tinkerers have the option of making a costless, verifiable, en-forceable agreement to share a well-defined set of the functional design changes in A1

and A2 and their experimentally discovered effects. Call this agreement a networkof information. At any time, either partner can depart from the network, and thendoes not learn about the subsequent innovations of the other and ceases to sharehis own.

Imagine player one choosing between working alone (“autarky”), whose payoff isin equation (3), and joining in this agreement (“network”) with player two. If playerone thinks player two will tinker and produce any positive flow of innovations, he isbetter off to join the sharing institution. It pays off immediately when he receives anyinformation from player two. Player two’s subjectively determined rate of progressmust meet the criterion p2 > 1−β

βto make him a tinkerer. The rate of innovations

useful to player one might be small.

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If player one expects both players to join, tinker, and share forever, his expectedutility is:

U0 =a0

1− β− 1

1− β+

(p1 + fp2)β

(1− β)2(4)

This expression is greater than the expression in equation (3), supporting the keyclaim of this paper, which is that under the assumptions made, tinkerers prefer tojoin the network than to work alone. This can thus be a model of groups conductingopen-source technology development, if we can relate the assumptions (or weakerones) both to this proposition, and to historical episodes of technology advance.

The model would lose its meaning if the rate of innovations were so high that aplayer’s utility were infinite, but for any finite p1 and p2, the expression on the rightside of equation 4 is finite.

In the examples that motivate this model, rates of progress were barely highenough to meet the criterion in equation (2). The tinkerers do not know verymuch about how to make a good A. They have to experiment. This is because thetechnology is new in historical terms, and not yet useful. The number of tinkererswho can make any progress on a particular class of projects is also severely limitedby those with the wealth, knowledge, and tools to attempt it. So there could be alarge population of people each of whom finds some value in experimenting with newaircraft, but few like it enough, and are good enough at it, and have the resources,to bother. Those few have rates of progress (p) that were even barely big enough.In modeling terms we might imagine that a0, the value of having and working on A,were drawn from a distribution, and a few whose had a positive value for a0, at thepositive tail of the sample, would be tinkerers, or they would have the inclination tobe tinkerers but on some other kind of project. In the aircraft case, even successfulexperimenters considered quitting, and many did.

That is no longer true once the technology is established and competitivelyproduced. Now, there is a known technology of aircraft and thousands or millionsof people are engaged somehow in working on them, but it is a capital-intensiveindustrial activity and the model is not relevant to this.

The agreement does not require sharing everything the experimenters know orlearn. They do not meld minds, memories, or objectives. For example, a tinkerermay discover or learn descriptive, propositional, or scientific knowledge which is notembodied in A, and the agreement does not require sharing that.

5 The occasional tinkerer

Consider an individual with the same utility function but who only occasionallyfinds opportunities to reach the classic tinkerer’s rate of progress. Only once every

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k turns does this person have a chance to make an innovation meeting the criterionp > 1−β

β. Alone, this occasional tinkerer would optimally take these opportunities,

pay investment costs averaging 1k

each period, and produce a net rate of progress pk.

By a derivation like that of equation (3), the net present utility of such a person attime zero is approximately:

Ut=0 =a0

1− β− 1/k

1− β+

(p/k)β

(1− β)2(5)

Suppose n of these tinkerers are joined in a sharing network. Assume that theyall have the same β and p and that fraction f of every tinkerer’s innovations areuseful to each other tinkerer. Assume they have their innovative opportunities inalternating turns. Following a derivation like the one for equation (3), each oneachieves a present value of utility of approximately:

Ut=0 =a0

1− β− 1

k(1− β)+

( pk

+ fp(n−1)k

)β

(1− β)2

=a0

1− β− 1

k(1− β)+

pβ

k(1− β)2+

fp(n− 1)β

k(1− β)2(6)

The fourth term has the benefits each occasional tinkerer receives from experi-ments conducted by the other (n−1) tinkerers in his sharing network. Each one hasfp(n−1)β(1−β)2

higher present utility by joining the sharing network than from staying out.He might be imagined to leave the group just before his own innovations, keep themsecret, and rejoin when the group had made further innovations, but this is not ahigher-utility proposition than just staying in the group, and this path of behaviorwould disappear from the model if there were even tiny costs of leaving or rejoiningthe network, such as a frictional costs or punishment by the others. For simplicity,assume no one exits with the incentive to reenter immediately.

Collectively a group of k occasional tinkerers produces one innovation per timeperiod. So if a number of slow-progress tinkerers can find one another, the group canproduce as much as a classic tinkerer. They also have the same incentive as a classictinkerer would to join in larger-yet sharing networks with other groups of tinkerers.The earlier assumption that each tinkerer is highly productive, that is to have ahigh rate of progress through experimentation, is therefore not critical to generatinga tinkerer’s network. That is important in interpreting the history in which so littlenet progress seems to have been made by so many experimenters. But if we think of”all Boston-area aeronautical experimenters” and ”all readers of French aeronauticaljournals” as each representing one classical tinkerer, it becomes plausible that theyare making rates of progress meeting the threshhold. The essential assumption isthat tinkerers are interested in a common problem and have some way to makemutually helpful progress on it according to their own subjective opinions.

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There is a kind of economy of scale here. This is a positive sum game in whichall the participants make a contribution. If there are enough occasional tinkerers,their low rates of private progress combine to form high rates of social progress. Ahigh rate of social progress then makes attachment to the group more desirable tooutside tinkerers. With many tinkerers, it becomes more important realistically tomodel costly internal frictions in the network, or a complicated internal structure ofadministration and information sharing. Specialized software such as open-sourceweb www.sourceforge.net, and groupware like source code control systems, supportcollaboration, coordination and information sharing at low cost.

A larger network will tend to make faster progress than a small one. So membershave an incentive to reduce barriers to communication within the network, or withpeople who might join the network. And it implies that networks in places whichhave fewer such barriers will solve problems before networks in places which havesuch barriers. So for example, the use of English is functional to an opensourceproject because there are more potential tinkerers who can interact in English.Historically, big technological problems have tended to be solved first in placeswhere free association of persons is allowed, and a free press. Possibly this can bedemonstrated statistically holding other factors constant in a way that would defendthe proposition that networks of innovators affect economic growth.

6 Notes on the assumptions and notation

Apart from aircraft, the model is meant to describe tinkerers (or experimenters)such as Steve Wozniak, developer of what became the Apple I personal computer,Richard Stallman of the free-software movement, Tim Berners-Lee, the creator of theWorld Wide Web, and Linus Torvalds, the founding author of the Linux operatingsystem. These individuals created important technologies and appear not to havebeen driven originally by the prospects of selling their creations.

In the real world, several overlapping forces can cause a utility stream like at.Tinkerers may find a project inherently interesting and absorbing. The tinkerer mayenjoy the project or obtains benefits from some service it provides. The tinkerer mayanticipate receiving honors and prestige or career benefits. Tinkerers may also enjoythe anticipated possibility that the project A will change the state of human affairs,as the airplane and personal computer have done.

The activity could also support some profit-making or career effort of the tin-kerer, as long as this goal is not competing with the efforts of the others. So forexample a government laboratory’s programmers may join an open source develop-ment effort not because they love it, but because it’s useful to the project, and thelaboratory’s managers have no objection to sharing their new software with the restof the world.

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It has been assumed that the agent cannot sell the technology at a profit, andcannot foresee doing it either. This is an extreme assumption of technological uncer-tainty as described in Tushman and Anderson (1986), Dosi (1988), and Rosenberg(1996) and whose effects are documented in Meyer (2005). Realistically the valueof p is not knowable to the agent, who hazards a guess and acts on it. Regardlessof the true value of p, a long stream of attempts without success might convincethe agent that it had a low value, and that he should cease trying. The populationof tinkerers with projects like p could be severely selected in favor of those whobelieved for historically accidental reasons that they had a high p.

Since tinkerering is experimental, it might be better to model progress p asstochastic. There are two reasons to make it fixed in the beliefs of the agent. Oneis that the model would be more complicated and harder to compute analyticallyif p were probabilistic, but that the core implications about incentives would notbe changed. Another reason to avoid probabilistic modeling is that investment andpayback are subjective here, and an agent may believe he has a better understandingof A after trying an experiment which does not actually improve A in functionalterms. This may, to him, reflect progress, and it may be worth sharing with theother tinkerers that he tried a device of a certain kind and it did not produce thedesired effect.

The idea of an enforceable sharing network is not well matched by the historicalreality in which cooperation among tinkerers did not seem to have any enforcement.Ideally in the model, agreements should be individually rational for each player, andnot require enforcement. One rationale could be that tinkerers gain more from oneanother’s work if each is familiar with the previous work of the other. In the model,f would rise if the network were long lasting, or if the two members in particularhad a long history together.

Many other circumstances affect f . If the tinkerer is an American working onfixed-wing aircraft in 1900, he may choose not to read a French journal about balloondevelopments, even if the balloon work is productive in its own terms (measured byp2), but because he does not read French, or because he thinks balloon innovationsare not likely to apply to fixed wing aircraft.

The calculations above incorporate the extreme assumption that there are nodiseconomies of sharing. E.g. no time shortage for a person trying to keep up withthe literature. A fixed cost to members of each member or each interaction wouldmake this go away. Then we would appropriately have decreasing returns to scale forlarge enough networks, and it would induce pressures such as perhaps to exclude thelowest-productivity members. But the algebra would be complicated and it doesn’thelp highlight the core incentives so it’s not here for now.

The economies of scale observation tells us why sub-groups do not usually breakoff historically. Subgroups are not better off doing the same activity in smallergroups with the same membership in this model. What could make them break off

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is if f were lower than some unmodeled friction, perhaps because subgroups wereworking on substantively different technologies, likes kites and balloons, or if thenetwork generated many unhelpful distractions.

6.1 Relation of the histories to the model assumptions

From these examples both of the key assumptions can be defended as plausiblyrelevant axioms. Tinkerers by the dozen express an explicit interest in the tech-nological activity itself, or in idealism related to the technology, or in honors andprestige related to the technology, or in a vague hope that the technology will givethem some entrepreneurial possibility in the future. They do not appear to investtheir time, money, and energy into the technology as earnings-maximizers or profit-maximizers. This supports the assumption that we can model this activity as beingin their utility functions not mediated by future revenues. The technological uncer-tainty assumption can be defended by a Chicago school argument: if a big industryarose from aircraft, from personal computers, and from Linux (or some other area ofopen source software), then why weren’t the powerful technological firms of the timealready doing these activities? In the model, it happens because the uncertaintywas too great to identify a clear stream of future profits.

The sharing institutions in the historical cases do not usually look like enforceablecontracts. However, the model shows these tinkerers would be willing to enter suchan agreement rather than work alone. I hope extensions can show that a less-enforceable agreement which produces the same effects is in their interest too. Anumber feel that they have an obligation to share with the group, or that it isvirtuous to do it, as discussed in Meyer (2003).

Tinkerers in a new technology operate at some kind of frontier, and so almost bydefinition are rare. Anyone might be interested in building an airplane, but the oneswho make history are among the few who try it before it is common knowledge howto do it. In this model the tinkerers have an strong interest in a particular subjectand had the capability to advance it and attempted it at a time in history whenit had not already been done. If instead we imagine that there is no technologicaluncertainty, and that the way ahead to a marketable design is clear, then by Chicago-school arguments it would not make sense that a profit-seeking institution was notalready doing that. Technological uncertainty is therefore a necessary assumption.

Tinkering is not usually capital-intensive. So another explanation for why tin-kering is not observed constantly everywhere is that once the expensive equipmentis useful for activity A it is no longer in the range of tinkering activities (exceptperhaps within organizations). Also, tinkering tends to arise in environments whennot very much specialized training is required. In the model, it has been assumedthat there are no capital requirements or training requirements.

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7 Standardizing and specializing

Only the fraction f ∈ (0, 1) of the discoveries made by player two are usable toplayer one. Suppose for a cost cs player one can adjust some arbitrary elements of hisproject A1 to look more like A2, and that this would raise the fraction of player two’sinnovations which applied to his own project from f to f2. This models the choiceto standardize the engineering. Player one’s expected utility from standardizing is:

U0 =a0

1− β− 1

1− β− cs +

(p1 + f2p2)β

(1− β)2

Comparing this to equation 4, a player would pay the standardization cost if:

βp2(f2 − f)

(1− β)2> cs

In words, player one benefits more from standardizing if, ceteris paribus: (a) theother tinkerers are producing a large flow of innovations p2; (b) the cost of standard-izing cs is small; (c) the gain in the fraction of useful innovations from the others(f2 − f) is large.

The same formal argument can explain why experimenters develop and try tostandardize on their technical language for describing their new technologies. Thiscan reduce communication costs and also clarify thinking. In one relevant example,Wilbur Wright published a journal article (Wright, 1902) asking other experimentersto cease using “angle of incidence” to mean the angle between a wing (or otherairfoil) and the ground. The better definition, he argued, was the angle between theairfoil and the flow of air coming at it; the angle with respect to the ground was notrelevant. This request was an effort both to improve the thinking processes of otherexperimenters and lower frictional losses in communication.

In a more important example, Lawrence Hargrave’s experiments showed thata box-shaped kite was more stable than a single flat kit was in a gust of wind.This specialist contribution helped glider flyers standardize on a biplane (two wing)design for gliders.

Standardization explains partly why players publish their findings. We have as-sumed that the agreement among the players to share all findings was enforceable,but this is not the case historically. But when they anticipate standardizing, it isuseful to each one for the other one to know his own technology. Player two cancommunicate more easily with player one if player one’s work is common knowledge.Then the language and concepts of player one are available to both for purpose ofcommunication. It also means they would be able to compare options for standard-ization and choose the best one, in the sense of moving the project forward or raisingf the most. This incentive can be formalized by making f() a decreasing function of

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a player’s own history of making new findings public. More publications by a playershould make it easier for other players to communicate with him or to standardizeon his own design choices without his paying any cost. If f is a declining function ofthe number of findings a player has shared, it partly substitutes for the enforcementof the rule that players should share all their findings. Each one has an incentive toshare in order to get the others to learn from his own findings, and to standardize onhis own choices (rather than having to pay the costs to standardize on the choicesof others).

This is important in the software context where a project can “fork”–split overtime into incompatible versions–if the contributors do not agree to standardize. Thehistory of projects that actually did fork is quite painful (cite) and so hackers areregularly willing to pay some price in effort to re-unify a project on which peoplework independently. In this model, they are willing to pay some price to maintainthe economies of scale of the project.

For f2 = 0.55, f = 0.5, p1 = 0.07, and β = 0.95, p2β(f2−f)(1−β)2

= 1.33. In thisillustration, the cost of standardization exceeds the cost of a normal investment,but is worth undertaking because it raises the useful inflow of innovations by 10%.

A tinkerer may also take steps to make the device easier to learn or easier touse, which is another different pathway to delivering progress p or raising usableprogress ratio f .

Thus standardization and specialization among tinkerers can be rationally ex-plained as intrisic to technological development, without reference to market pro-cesses. It is a natural result of exchanging information, and in this setting it can beexplained without reference to competition or market exchanges. The network is asearch technology for the tinkerer for those kinds of valuable information he doesnot specialize in obtaining by experiment.

8 Joining and searching costs

Let cj be a cost to a tinkerer to join an existing sharing institution or to start anew one. Then the present expected payoff to one tinkerer who joins with anotherone in a network is, from equation 4:

U0,network =a0

1− β− 1

1− β+

(p1 + fp2)β

(1− β)2− cj (7)

His outside option is to work autarkically, from equation (3).

U0,autarkic =a0

1− β− 1

1− β+

pβ

(1− β)2

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He prefers to pay the cost to join if:

U0,network > U0,autarkic

a0

1− β− 1

1− β+

(p1 + fp2)β

(1− β)2− cj >

a0

1− β− 1

1− β+

p1β

(1− β)2

(p1 + fp2)β

(1− β)2− cj >

p1β

(1− β)2

fp2β

(1− β)2> cj (8)

A tinkerer is then predicted to joins, ceteris paribus, if (1) costs of joining, cj, aresmall enough, (2) the flow of innovations from the others in the group, p2, is largeenough, (3) the innovations are relevant enough to his own project, as measured byf , and (4) he values future events highly enough, that is, β is high enough.

Given the standard parameters f = 0.5, p = 0.07, β = 0.95, the value of theexpression in equation 40 is 13.3. So cj can be much greater than the cost of anexperiment, and it is still worth joining.

If there are multiple networks of tinkerers, and some have costs to join, he mayjoin some and not others, according to the comparison of net present benefits ofjoining each network, which are characterized by each network’s p2, f , and cj. Thenet benefits to a tinkerer of joining a network are fp2β

(1−β)2− cj

Suppose now that there is a cost to the members of an existing network tosearch for candidates to join it. Call this cost csearch. This parameter can helpdiscuss how the interest of a tinkerers’ network in expanding is mediated by thereal-world problem that usually few people know it exists and how to communicateto it. The problem is addressed in the real world by members who write books, editjournals, make speeches, talk about their hobby to people who may be interested ormay not be, or broadcast emails.

That creates a new first stage. In that stage, a tinkerer chooses between autarkywith payoff a0

1−β− 1

1−β+ pβ

(1−β)2and the costs of searching for a new member for their

network:

U0,network =a0

1− β− 1

1− β+

(p1 + fp2)β

(1− β)2− csearch

Net benefits of searching for a tinkerer to create a network are fp2β(1−β)2

− csearch.

But suppose the anticipated p2, given the state of the technology, is too smallfor the search to be worth it:

fp2β

(1− β)2< csearch =⇒ p2 <

csearch(1− β)2

fβ

This might be true for each of many tinkerers operating in autarky. If they are

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occasional tinkerer types and that k is large, it could be that many, working inisolation, make almost no progress.

Suppose cj is small, but csearch is large and that progress is slow in the sense thatk is large. Then one might imagine a situation in which the tinkerers would join anetwork and make progress, but the search costs are such that they will not find oneanother. Here we have a situation in which an information failure alone prevents aPareto-improving institution from appearing.

An individual might specialize in expanding the network, e.g. through speech-making, book-writing or other publicity. Steps by tinkerers to making A easier tolearn or easier to use can also lower the search costs by making it easier to see thevirtues of A.

9 Entrepreneurial exits from the network

The model assumed that tinkerers operate under technological uncertainty andso could not see how to make a version of A for which there would be enough demandto make a profit.1

Suppose, now, that a tinkerer has an insight, and can imagine a version of theactivity A or the stream of utility at for which manufacturing is possible, and forwhich there might be customers. This change in belief may be caused by advances inthe technology, or changes externally, or by a long process of reflection. A growingpopulation of tinkerers inside the network may be the natural market for the newproduct, in which case the tinkerer already knows the customers and what theywant.

Suppose a tinkerer or some entrepreneur or firm envisions a way to profit fromproject A. The tinkerer considers going private. Suppose the tinkerer has the optionto pay an expected present utility cost of R to conduct directed research and capitalinvestment, and then believes it will be possible to manufacture a product versionof A, and earn an expected present value of utility of M in monopoly profits. Risksare incorporated into M . If the tinkerer were to continue to share experimentalfindings or equipment, this would reduce M . If it were to reduce M by more thanthe value of the utility of staying in the equilbrium, he drops out of the tinkerer’snetwork. So a tinkerer is predicted to exit the network to start a firm if (M −R) isgreater than the expression in equation 4.

1In casual conversation one might say that he does not see a version of A that is “good enough”to sell, but with radically new products, both supply and demand may be hard to foresee. Early air-craft developers tended to dramatically underestimate the military consequences of aircraft. Earlypersonal computer makers dramatically mis-estimated demand. Errors in forecasts by industryanalysts was the metric of technological uncertainty used in Tushman and Anderson (1986).

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To be consistent with the story told up to here, this is a zero probability event,but the model is not brittle on this point. Such an exit could be expected with asmall probability event. For simplicity of exposition assume it was a zero probabilityevent.

Starting in late 1902 the Wrights were decreasingly willing to share informationthrough Chanute to his network. After their successful flights of 1903-5, the Wrightsobstained a patent in 1906, and started an aircraft business. Chanute had criticizedothers who kepts secrets before[1 Ader, Langley], and his conflicts with the Wrightsgrew more severe; at some point they were not on speaking terms any more. Similarconflicts are seen between RMS and other open source programmers.

This kind of conflict also occurred in the Homebrew club. Steve Wozniak, oneof the most effective hobbyists, did not want to start a company, but his friendSteve Jobs talked him into it. They created the Apple I. Others started companiestoo. The club then changed qualitatively. Members who had started companiesstopped coming, partly because keeping company secrets would be uncomfortableat Homebrew. Keeping secrets for private advantage violated what Levy (2001)called the Hacker Ethic – that information should be freely available. From Levy(2001), p. 269:

No longer was it a struggle, a learning process, to make comput-ers. So the pioneers of Homebrew, many of whom had switched frombuilding computers to manufacturing computers, had not a commonbond, but competition to maintain market share. It retarded Home-brew’s time-honored practice of sharing all techniques, of refusing torecognize secrets, and of keeping information going in an unencumberedflow. . . . Now, as major shareholders of companies supporting hundredsof employees, they had secrets to keep.

“It was amazing to watch the anarchists put on a different shirt,”[former Homebrewer] Dan Sokol later recalled. “People stopped com-ing. Homebrew . . . was still anarchistic: people would ask you about thecompany, and you’d have to say, ‘I can’t tell you that.’ I solved thatthe way other people did—I didn’t go. I didn’t want to go and not tellpeople things. There would be no easy way out where you would feelgood about that. . . . ”

It no longer was essential to go to meetings. Many of the people incompanies like Apple, Processor Tech, and Cromemco were too damnedbusy. And the companies themselves provided the communities aroundwhich to share information. Apple was a good example. Steve Wozniakand his two young friends [and employees], Espinosa and Wigginton,were too busy with the young firm to keep going to Homebrew.

Most entrepreneurial breakouts do not make a big impact, but once there are

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a few startups, an industry exists. Major industries have started this way. Onlyafter there are firms then does activity A appear in economic statistics of output,employment, investment, and wages.

The model make explicit how a kind of progress predates the industrial en-trepreneurs. Tinkerers make progress before the industry starts, according to sub-jective criteria, not market criteria. If the tinkerers were blocked or delayed, thiswould tend to delay the appearance of the industry.

The same issue arises with respect to open source software, although there aremore differentiated ways of handling the problem. The source code to the operatingsystem Linux is freely available on the Internet, but there are also public companiesdistributing and developing it and complementary products. Such companies includeRed Hat and SuSE/Novell, which are publicly owned, and many smaller companies.There are a variety of licenses for open source software which in various ways keepsome of the code in the public domain. These intermediate solutions but reducesthe conflict inherent in the binary choice described in the model.

10 Intellectual property

For simplicity we consider here only a two-tinkerer case. Assume all the utilityfunctions are linear in money and have been normalized to the money metric.

Suppose now that a tinkerer has property rights to his designs and can charge aprice to use the design information he transmits to the network. He may impose acost cip for each information transmission on each network member who makes useof it.

U0 = a0

1−β− 1

1−β+ (p1+fp2)β

(1−β)2

imagine he receives c1 times fp1 in copyright payments, and pays out c2 timesfp2.

U0 = a0

1−β− 1

1−β+ (p1+fp2)β

(1−β)2+ (c1fp1−c2fp2)β

(1−β)2

We have assumed there are no frictions in the copyright payments mechanism,such as lawyers, contracts, checks, or disputes. The result is that the tinkerer isbetter off with a copyright system if

(c1fp1−c2fp2)β(1−β)2

> 0

This would be the case only if either he charges more than other people for hiscopyrights than they charge him, or if he produces a greater flow of progress thanall the others in the network do. These are extreme cases. Generally speaking,each tinkerer would be better off if there were no intellectual property protection.Without intellectual property rules, the technology A will tend to advance more

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quickly.

A tinkerer’s preferences on this subject change once he is an entrepreneur. TheWrights obtained a patent in 1906 and enforced it fiercely, possibly to their detrimentwhen they would have benefited more from making a deal with engine experts oran experienced manufacturing company.

Classic tinkerers tend not to be fans of copyrights, patents, or other intellectualproperty rules that get in the way of grasping the best available technology and justusing it. ”Fair use exception” rules which allow the use of patented technology whennot producing for sale help them. The incentives of tinkerers change if they startfirms and conduct R&D directed toward making sellable products. It is not modeledhere but presumably at that point they want barriers to entry. The Wrights wentthrough this transformation. After about 1905 they did not produce new innovationsin aircraft, and were not very successful at manufacture, but instead made moneyfrom their patents and licenses, and pursued possible patent infringements.

11 Categories of evidence

A tinkerers’ network model is relevant when certain kinds of evidence are present:

(1) There are diverse predictions of a technology’s future; that is, it is uncertainin a social sense.

(2) Individuals are observed to communicate novel technical findings and designsabout the technology to one another without explicit rewards.

(3) They do not have an obvious profit motivation; e.g. the Wrights say theydid not get into this field to get rich. (quote them before and after) ditto SteveWozniak; quote him. Ditto Berners-Lee. Ditto Torvalds. Also, their statementsaside, there is no obvious product which could be sold at the time they enter thefield, and it would not make rational sense to assume there was one, in advance ofunderstanding the situation.

(4) They specialize and standardize their tools. This can help qualitatively dis-tinguish them from people who are entertaining themselves with a hobby like playinga game or building a collection. In a tinkerer’s hobby there is an idea of progress.For example, when Hargrave reported results from his box kite experiments, otheraeronautical experimenters learned from them and adapted to the findings with-out imitating them. Thus they behaved as if they were motivated by some idea ofprogress.

By contrast a collector of stamps does not treat steps taken by others as progress.When one collector gets a new stamp, the others still want one like it. Similarlywhen one skateboarder invents a new move, others want to do it themselves; they

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are unlikely to just learn from it in order to do something new.

(5) They participants refer to the idea that they are making progress, not onlyhaving fun. In practice this may be measured by the frequency of particular wordsin the text of the communications. The activity should also evolve over time, inresponse to events that some participants interpret as progress.

(6) Some players specialize in managing or expanding the network of personsengaged in the activity, at a cost.

Evidence on some of these could help make inferences about others. That’s aservice of a deductive model.

The size of innovation flows will be positively related to the number of peoplewith values of of a0 high enough to stimulate them to some kind of action. State-ments of the innovators, and their behavior toward networks, constitute indirectkinds of evidence. Innovation flows will tend to be greater if individuals have greaterp’s and their interchanges have higher value of f . Innovation will be discouraged byhigh investment costs, search costs, and joining costs.

Supply and demand for innovations are not separately modeled here, becausethere is no price variable in the tinkerers’ network.

12 Other applications and implications

The flow of innovations could be reduced by changes in the environment. Con-sider policies or environmental factors which affect the ease of publishing a journalor forming an association. This reduction in the flow of information reduces theexpected utility of a tinkerer. If for a cost the tinkerer could emigrate to a placewhere the restriction did not apply, we can imagine information restrictions alonereducing the flow of innovations both directly by reducing communication flows, andby driving tinkerers away.

Through reductions on informational interaction, the growth benefits of tin-kerer’s networks could have been constrained in a number of historical cases. Con-straints on informational interaction with the outside might have restrained tech-nological improvement in Tokugawa Japan. French laws restricting what could beprinted meant some were printed in Belgium. Printers were allowed general free-dom to print after 1689 in England (Carlos, Neal, Wandschneider, 2006, p. 4).Paper costs used to be high enough to restrain tinkerer’s networks, and there wasgeographical variation in this.

This class of arguments has been made before, less formally. Mokyr, 1993, p.34, writes: “By the middle of the nineteenth century, there were 1,020 associationsfor technical and scientific knowledge in Britain with a membership that Inkster

21

estimated conservatively at 200,000 (Inkster, 1991, pp. 73, pp 78-79).” Elsewherein the same text Mokyr writes: “The key to British technological success was thatit had a comparative advantage in microinventions.”

13 Conclusion

This model provides axioms and a language to describe independent technologydevelopers. High-productivity tinkerers are called ”classic tinkerers” here. Low-productivity tinkerers could also form tinkerer’s networks. Idealists might sponsornetworks by somehow whether or not they were tinkerers themselves, perhaps bypaying costs, publishing journals, writing books, or making speeches.

Tinkerers in the model choose to share information to maximize their combinedflow of useful innovations. This purposeful choice in the model generates flows ofinnovations that other economic models of technological change often take as given.

Tinkerers can start an industry when there is technological uncertainty. Theywill have a tendency to migrate where costs of forming tinkerer’s equilbria are lower,e.g. toward places where free assembly and a free press is tolerated. An industrymay form, if some of tinkerers foresee specific customer demands for specific productsarising from the activity. Such new technology industries would arise more quicklyin circumstances where tinkerers networks were allowed and encouraged than inplaces where they were not.

In this model, innovation is an output of individuals, rather than organizations.This differentiates this model from many in the economics literature. The collectiveinvention phenomenon in the economics literature is an intermediate form of activity,like this one but with more similiarities to industrial organization models.

One benefit of modeling innovation as a function of individuals is that the predic-tions are more easily portable to cases where organizations are not relevant, or don’thave the forms of businesses, governments, and other hierarchies. The model maydescribe technological developments occurring before capitalism, in non-capitalistsocieties, in nonprofit organizations, as well as among hobbyists.

The model also gives us a way to model technical visionaries less like employees,and more in the way they think of themselves. It can help describe the behaviorof engineers operating autonomously inside corporations and other organizations.There is a descriptive literature about “skunkworks” which characterizes such en-gineers as driven by internal interest, and constrained by the corporate hierarchy,rather than following the orders of a corporate hierarchy. It may also be a model forthe behavior of scientists, artists, and persons with a political or religious ideologywho appear to be driven by internal forces, but who then also work together innetworks to achieve common goals.

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[12] Mokyr, Joel. 1990. The Lever of Riches: technological creativity and economic progress. OxfordUniversity Press.

[13] Mokyr, Joel. 1993. Editor’s introduction. The British Industrial Revolution: an economicperspective. Westview Press.

[14] Nuvolari, Alessandro. 2002. Open Source Software Development: Some Historical Perspec-tives. ECIS working paper.

[15] Pavlicek, Russell C., 2000. Embracing Insanity: Open Source Software Development. SamsPublishing.

[16] Raymond, Eric S., 2001. The Cathedral & the Bazaar: Musings on linux and open source byan accidental revolutionary. O’Reilly.

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